**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# **Materialization and Construction**

# **Towards Self-shaping Metamaterial Shells: A Computational Design Workflow for Hybrid Additive Manufacturing of Architectural Scale Double-Curved Structures**

E. Özdemir(B) , L. Kiesewetter(B) , K. Antorveza(B) , T. Cheng, S. Leder, D. Wood, and A. Menges

Institute for Computational Design and Construction, Keplerstr. 11, 70174 Stuttgart, Germany {icd.mail,e.ozdemir,laura.kiesewetter,icd.mail<EMAIL_ADDRESS>
**Abstract.** Double curvature enables elegant and material-efficient shell structures, but their construction typically relies on heavy machining, manual labor, and the additional use of material wasted as one-off formwork. Using a material's intrinsic properties for self-shaping is an energy and resource-efficient solution to this problem. This research presents a fabrication approach for self-shaping double-curved shell structures combining the hygroscopic shape-changing and scalability of wood actuators with the tunability of 3D-printed metamaterial patterning. Using hybrid robotic fabrication, components are additively manufactured flat and self-shape to a pre-programmed configuration through drying. A computational design workflow including a lattice and shell-based finite element model was developed for the design of the metamaterial pattern, actuator layout, and shape prediction. The workflow was tested through physical prototypes at centimeter and meter scales. The results show an architectural scale proof of concept for self-shaping double-curved shell structures as a resource-efficient physical form generation method.

**Keywords:** Self-shaping wood · 3D printing · Robotic fabrication · Mechanical metamaterials · Material programming

# **1 Introduction**

Shell structures are advantageous in architecture because the geometric stiffness resulting from the double curvature makes them highly material-efficient [1]. Recent advancement in computational modeling and simulation technology gives architects and engineers sophisticated tools to design elegant and geometrically performative structures with ease [2, 3]. However, constructing double-curved designs with conventional construction techniques is laborious and requires complicated machining or large formwork with excessive waste production. On the construction site, forming or using large formwork depend highly on skilled manual labor and intricate scaffolding [4].

This research proposes an alternative to contemporary shell construction practice: By using a material's intrinsic properties, forming instructions can be embedded into the

© The Author(s) 2022

material system and conventional forming methods can be replaced with self-shaping. The structure is made of a hybrid material system combining self-shaping wood actuators with a tunable 3D-printed metamaterial patterning (MMP). It is designed to be fabricated in a flat configuration, reducing the complications and excess of 3D forming. It then autonomously self-shapes on-site into the pre-programmed double-curved geometry (Fig. 1). The shape can then be locked by constraining the edges or inter parts of the structure to avoid further deformation.

**Fig. 1.** (a) A lightweight, self-shaped double-curved shell structure manufactured additively from 3D-printed bio-composite metamaterial patterning (MMP) and integrated wood actuators. (b) Detail of the stiffness-tunable patterning and actuator connection

# **1.1 Self-shaping Structures**

The development of self-shaping systems is a growing field of research in material science and engineering. Geometric self-shaping mechanisms in planar lattices have been demonstrated on smaller scales [5, 6]. At a similar scale, prestressed reinforced elastic membranes have been used for deployable elements that spring from flat to curved when released [7]. These systems are scalable but require control of high stresses at deployment.

**Self-shaping Wood.** In the form of a bilayer, wood becomes a natural actuator that generates curvature. It is both hygroscopic and anisotropic, which makes it respond to its surrounding relative humidity (RH) with shape changes depending on its grain direction and wood moisture content (WMC) [8, 9]. When used for shaping large curved timber elements, wood bilayers are fabricated flat and self-shape during drying [10]. Although single curvature can be achieved from wood bilayers, the creation of double curvature in solid wood plates is only achievable to a limited extent and difficult to predict [11]. Self-shaping wood gridshells have also been investigated with finite element (FE) models and tabletop prototypes but have limited design freedom so far [12]. The principle of self-shaping wood actuators combined with a 3D-printed structure for single-curved geometries has been studied with prototypes on a similar scale [13].

# **1.2 Large Scale Additive Manufacturing (LSAM)**

Large Scale Additive Manufacturing (LSAM) is a high-resolution additive fabrication method that enables tuning on a local level. Lightweight, filigree structures can be designed and printed with specific local bending properties and bent into shape. These properties allow for the creation of shell structures with little to no waste production but still require extensive and coordinated physical shaping on-site [14].

### **1.3 Bending-Active Metamaterial Surfaces**

Auxetics are a class of metamaterials that show unusual behavior when stretched or compressed due to their engineered geometry that causes negative Poisson's ratio [15]. Unlike most other bending-active plate materials that create single curvature when bent [16], these materials can create double curvature [17]. By carefully designing these MMPs, the resulting bent geometry can be pre-programmed to exhibit anticlastic, single curved, and synclastic areas [18]. The potentials of this principle for building structures have so far only been explored on a small scale due to the significant forces required to bend larger structures.

# **2 Methods**

Our approach focuses on the computational design and fabrication of a 3D-printed auxetic MMP with integrated wood bilayer actuators to achieve self-shaping shell structures at a large scale. The concept is investigated through the development of a computational design workflow (Fig. 2), validated with a 1:10 scale physical prototype, and a full-scale demonstrator.

### **2.1 Design and Analysis**

The computational design workflow starts with the design of a double-curved shell geometry in which surface curvature is adjusted within a range related to the bending stiffness of the materials. The design intent is evaluated through curvature and structural analysis: While the structural analysis is used to determine where to reinforce the geometry with increased stiffness through a gradient in structural depth, the curvature analysis plays a key role in designing the MMP and determining the actuator locations and orientations.

Since predictingthe behavior of a hybridmaterial systemis complex, physicaltests are used to understand the relationship between the wood actuators and the 3D-printed MMP.

**Fig. 2.** Computational design workflow overview: defining the system parameters, hybrid additive manufacturing (AM) of the prototypes, self-shaping through drying and evaluation

A simulation is also developed as a design tool allowing for quick design iterations with the feedback of both structural and shaping parameters. In parallel, scaled physical prototypes (1:10) are produced to test the simulation accuracy and to validate the self-shaping of the structure. The scaled physical prototypes are geometrically compared to the outcome of the simulation, and the self-shaping parameters are calibrated until satisfactory results are achieved. Based on a chosen configuration, the wood actuators are produced and the fabrication instructions for the LSAM are generated.

# **2.2 Physical and Digital Testing**

While physical tests (Fig. 3) are essential to study the complex relations between different design parameters, they are time and material-consuming. The simulation tool developed for this research combines Timoshenko's bimetal theory [19] and a latticebased model with varying expansion coefficients [20, 21] using an incremental solver for large deformation analyses in Karamba 3D [22]. Restrictive and active layers of the actuators are represented by a lattice of beams, rigidly connected in each node. The external stimulus for shrinkage in the active layer is represented by changes in the thermal load with the corresponding thermal expansion coefficient. The radius achieved by the bilayers in the simulation is compared and calibrated to actuated physical wood bilayers. The 3D-printed pattern is modeled as a system of vertically oriented shell elements with mechanical properties matching that of the printed material, rigidly connected to the lattice structure of the bilayers.

# **2.3 Hybrid Additive Manufacturing**

First, the wood actuators are produced from passive layers and active layers that were equalized at 92% (RH) for a month. Subsequently, they are CNC milled into their final shapes and once again put back into the moisture chamber until the start of the hybrid additive manufacturing process.

**Fig. 3.** Initial cm scale tests showing variable MMPs' influence on curvature. (a) Physical tests with variations in cell geometry to produce anticlastic, single curved, and synclastic bending with a desktop fused deposition modeling (FDM) printer, polylactide (PLA) filament, and a wood veneer bilayer actuator. (b) Initial digital tests with variations in cell geometry (T = angular parameter determining concavity)

To 3D-print the MMP, a single continuous polyline is created for the G-Code generation [23]. The base layers are the first to be 3D-printed using robotic LSAM, leaving pockets for the actuators. Then, the actuators are inserted into the MMP, and enclosure layers are printed on top.

### **2.4 On-site Self-shaping**

Once the fabrication is completed, the structure is wrapped in airtight packaging and flat-transported to the deployment site. There, it is allowed to dry in ambient humidity conditions, gradually decreasing the WMC and self-shaping into the final structure.

# **3 Prototyping and Results**

Before upscaling the system, the developed workflow was tested using a small-scale physical prototype (1:10) to ensure that the design parameters could meet the geometrical and behavioral expectations. After this preliminary study, the design was scaled up ten times and a full-scale demonstrator was produced to prove the scalability of the material system.

### **3.1 Small Scale Prototype**

A shell geometry was designed to self-erect from the ground as much as possible from a 60 cm × 20 cm flat pattern while exhibiting areas of anticlastic, single, and synclastic curvature (Fig. 4). The pattern was printed in three pieces and embedded with eleven actuators made from 3 mm thick beech-maple bilayers. The three pieces were assembled by using glue and were left in interior ambient conditions (40% RH) to self-shape as a single structure in 36 h (Fig. 4c). The resulting self-shaping geometry achieved reasonable approximations to the simulation prediction, although continuous curvature was not achieved most likely due to the gradient being interrupted between the pieces.

**Fig. 4.** Small scale prototype. (a) Gaussian curvature values of the goal geometry are used to adjust the MMP, actuators are placed on the cells with the highest first principal curvature. Depth gradient is applied to ensure curvature continuity. (b) FE simulation of self-shaping structure. (c) Results of self-shaping in 1:10 physical prototype

### **3.2 Large Scale Demonstrator**

The significant shift in the scale and self-weight required recalibration of the parameters in the computational design workflow. The cell sizes and actuator placement were adapted for the workspace (3.0 m × 1.5 m table) of a robotic LSAM setup incorporating a 6-axis industrial robot (Kuka KRC420) equipped with a Fused Granular Fabrication extrusion system (CEAD GB.V.). To achieve a stable geometry, local utilization values from the structural analysis were used to inform the depth gradient that reinforces the structure. The simulation was also adjusted to the increased cell size and pattern depth, as well as the new nozzle diameter (3 mm) and printing material, a cellulose-filled plastic bio-composite (UPM Formi 3D 20/19 - UPM). Two 3D-printed MMP specimens were subjected to a deflection test and compared to the simulation for calibration. The same approach was used to calibrate the model to the wood bilayers. A 16 mm thick bilayer, consisting of 12 mm beech conditioned to a WMC of *>*25% and 4 mm white wood was considered most suitable. For calibration, a sample actuator was left to dry unbound in indoor ambient conditions (ca. 25 °C/50% RH). The final actuator placement was based on the comparison of simulation outcomes with the design intent.

The demonstrator was robotically fabricated in four sequential steps (Fig. 5a) within which the actuators were placed and encased during 15 consecutive hours.

The demonstrator with the overall dimensions of 250 cm × 150 cm was produced in one piece using eleven embedded actuators (Fig. 5). The completed demonstrator was then left to self-shape in indoor conditions (ca. 21 °C/RH 35%–47%). After 72 h, only minimal shape change was achieved due to the large self-weight of the prototype. To aid in the shaping process it was then supported from its center of gravity. In the next 80 h, the hanging demonstrator bent to the intended geometry and remained in the

**Fig. 5.** Demonstrator fabrication. (a) MMP structure and sequential printing steps. (b) Detail of variations in the MMP and associated printing tool paths. (c) LSAM of the base layers. (d) Integration of the wood actuators within the tuned MMP before printing the enclosure layer

shaped configuration under its self-weight (Fig. 6a)**.** Structural supports were added at the ends of the structure post shaping to prevent any further movement in the structure due to ambient condition changes. The shape retention was verified by 3D scanning the demonstrator (Fig. 6d) after over four months in ambient conditions and comparing the point cloud to the simulation.

**Fig. 6.** Demonstrator. (a) Self-shaping sequence of the large-scale demonstrator over 152 h. (b) Predicted geometry from the simulation. (c) Self-shaped structure in the actuated state. (d) 3D laser scan of the self-shaped geometry with areas of synclastic (+/+), anticlastic (+/-) and single curved (0) bending

# **4 Discussion**

The large-scale demonstrator showcases the potential of scaling up self-shaping wood and 3D-printed MMP to achieve double-curved shell geometries. We developed a computational design workflow for pre-programming self-shaping surfaces with goalgeometry-oriented auxetic pattern generation and actuator orientation, resulting in a structure with embedded self-shaping information. Our simulation proved to be capable of predicting both the self-shaping process (Fig. 4) and the final geometry (Fig. 6b, d), serving as a useful design tool. Finally, we implemented an optimized printing sequence for the auxetic metamaterials, used during the robotic LSAM process. While the preprogramming of geometry with the developed workflow and upscaling of this material system were successful, the self-shaping process did not occur entirely as intended. The most notable issue resulted from the separation of the actuators and the MMP which caused stress-related failures and deviations from the model. This could have been avoided if the prototype was supported from the start of actuation, and by better integration of the actuators.

To improve the accuracy of the model, future research could incorporate moisture dependency of the mechanical properties of wood. The presented model was developed by relying on the inherent structural benefit of double-curved surfaces, therefore further work is needed to verify that the self-shaping is compatible with structural design requirements. Form stability after actuation is a known requirement of self-shaping processes applied in construction. The addition of supports at the edges of the structure or the usage of tension cables to lock areas of the geometry as used in gridshell structures could increase the structural stability after self-shaping. Another interesting approach is to lock the geometry using integrated snap-fit locking mechanisms (Fig. 7) that could be included in the printing of the MMP.

**Fig. 7.** Initial development of an integrated 3D-printed snap-fit locking mechanism. (a) Flat state diagram. (b) Bent state diagram. (c) Physical prototype flexible state. (d) Physical prototype locked state. (e) Locking mechanism detail

# **5 Conclusion**

A computational design workflow was developed for designing and predicting selfshaping hybrid structures. The framework was tested through two physical prototypes at different scales, demonstrating how MMP can be used for self-shaping architectural scale double-curved structures. This system can be adopted for the construction of shells that are typically structurally well-performing, but which are usually avoided due to the difficult production and erection processes. We envision a construction approach that achieves complex 3D geometries from simplified 2.5D fabrication, with the potential of reducing carbon footprint through flat-packed transportation and decreasing labor and scaffolding by self-shaping on-site (Fig. 8). With further improvements to the fabrication setup, the research presented offers a low-impact solution for the construction of complex architectural structures. In this way, it contributes environmentally and technologically to the way we build, taking a step towards more sustainable construction methods.

**Fig. 8.** Concept for the self-shaping of a component based double-curved shell structure

**Acknowledgements.** This research was conducted as an M.Sc. thesis in the framework of the Integrative Technologies and Architectural Design Research (ITECH) program at the University of Stuttgart, led by the Institute for Computational Design and Construction (ICD), and the Institute of Building Structures and Structural Design (ITKE). The research was supported by the Sino-German Center for Research Promotion: DFG and NSFC through the project Performative Design Methodology based on Robotic Fabrication for Sustainable Architecture (GZ 1162). T. Cheng, S. Leder, D. Wood, A. Menges acknowledge the support of the German Research Foundation under Germany's Excellence Strategy - EXC 2120/1 – 390831618. Printing materials were sponsored by UPM Formi. The authors especially thank Riccardo La Magna for his advice on auxetic metamaterials, Michael Schneider and Michael Preisack for their help in the faculty wood workshop, Urs Basalla and the Institute for Engineering Geodesy for laser scanning, Zied Bhiri, and BEC GmbH and Lucas Janssen of CEAD GB.V. for their extended efforts in robotic extrusion integration.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Additive Manufacture of Cellulose Based Bio-Material on Architectural Scale**

Yimeng Wei1,2(B) , Areti Markopoulou1, Yuanshuang Zhu2, Eduardo Chamorro Martin1, and Nikol Kirova1

<sup>1</sup> Institute for Advanced Architecture of Catalonia, Barcelona, Spain<EMAIL_ADDRESS>
<sup>2</sup> Shanghai Digital Fabrication Engineering Technology Center, Shanghai, China

**Abstract.** There are severe environmental and ecological issues once we evaluate the architecture industry with LCA (Life Cycle Assessment), such as emission of CO2 caused by necessary high temperature for producing cement and significant amounts of Construction Demolition Waste (CDW) in deteriorated and obsolete buildings. One of the ways to solve these problems is Bio-Material. CELLULOSE and CHITON is the 1st and 2nd abundant substance in nature (Duro-Royo, J.: Aguahoja\_ProgrammableWater-based Biocomposites for Digital Design and Fabrication across Scales. MIT, pp. 1–3 (2019)), which means significantly potential for architectural dimension production. Meanwhile, renewability and biodegradability make it more conducive to the current problem of construction pollution. The purpose of this study is to explore Cellulose Based Biomaterial and bring it into architectural scale additive manufacture that engages with performance in the material development, with respect to time of solidification and control of shrinkage, as well as offering mechanical strength. At present, the experiments have proved the possibility of developing a cellulose-chitosan- based composite into 3D-Printing Construction Material (Sanandiya, N.D., Vijay, Y., Dimopoulou, M., Dritsas, S., Fernandez, J.G.: Large-scale additive manufacturing with bioinspired cellulosic materials. Sci. Rep. **8**(1), 1–5 (2018)). Moreover, The research shows that the characteristics (Such as waterproof, bending, compression, tensile, transparency) of the composite can be enhanced by different additives (such as xanthan gum, paper fiber, flour), which means it can be customized into various architectural components based on Performance Directional Optimization. This solution has a positive effect on environmental impact reduction and is of great significance in putting the architectural construction industry into a more environment-friendly and smart state.

**Keyword:** Chitosan · Cellulose · Biomaterial · Performance directional optimization · Robotic construction · Additive manufacture

# **1 Methodology and Proposal**

### **1.1 Methodology\_A Multi-Scalar Approach**

This thesis will conduct material research and testing from three different levels: MICRO - MESO - MACRO, and finally applied to architectrual-scale application [4].

The MICRO research will focus on the microstructure of the crystallization reaction of chitosan-cellulose mixed materials, as well as the intermolecular reaction of other additives.

The MESO research will focus on the testing of various properties of the mixed material, including the mechanical properties of the dried sample and the printability of the mixed material in wet state.

The MACRO research, new structural forms suitable for additive manufacturing and robotic construction will be studied, and cellulose-chitosan based bio-material will be used to complete architectural-scale printing work (Figs. 1, 2, 3).

**Fig. 1.** MICRO: Intermolecular Mechanism and Reaction: (a) Cellulose with chitosan (1g chi in 1%w/w acetic acid). (b) Paper fiber with chitosan (1g chi in 1%w/w acetic acid).

**Fig. 2.** MESO: Material Innovation and Properties experiments: (a) Sample of Chitosan-Cellulose based Biomaterial in the dry state. (b) 3D-Printing accumulation test of Chitosan-Cellulose based Biomaterial.

### **1.2 Proposal**

Starting from the current issues in the construction industry, to the current academic research ideas in each field, it is not difficult to find an intersection: based on new materials (such as bio-materials), grafted to new productivity (Robotic Construction), and new construction methods (Additive Manufacturing), to practice new design concepts (BESO).

### **1.2.1 Proposal 1: Chitosan-Cellulose Based Biomaterial (Fig. 4)**

CELLULOSE and CHITON is the 1st and 2nd abundant substance in nature, which means significantly potential for architectural dimension production. Meanwhile, the mechanic properties can be enhanced with certain additives, such as pectin, Xanthan Gum, or even recycled paper fiber. Moreover, the printability of the mixture makes it possible to cooperate with robotic 3D printing.

### **1.2.2 Proposal 2: Large Scale Robotic 3D-Printing (Fig. 5)**

A proper fabricating method is strongly required once we have the proper biomaterial for architectural application. The way of this thesis focusing on is large scale robotic 3D printing. This kind of biomaterial can be used in a traditional manufacturing way, such as model casting. But with the help of robotic 3D printing, we can significantly speed up the construction efficient and achieve a more organic form.

# **1.2.3 Proposal 3: Bidirectional Evolutionary Structural Optimization [3] (Fig. 6)**

Once we decide the material and the fabrication method, we need to think about how we should design accordingly. This thesis is trying to explore the biomaterial application in architectural scale, which means it should be a structure part, like a beam or pillar. With the idea of BESO, we can figure out a reasonable and organic result.

**Fig. 4.** Proposal 1 **Fig. 5.** Proposal 2 **Fig. 6.** Proposal 3

# **2 Experimental Procedure**

# **2.1 Micro\_ Intermolecular Mechanism and Reaction**

# **2.1.1 Cellulose Based Biomaterial Innovation**

From the case study, we learned that Chitosan will combine all the fiber-like substances such as cellulose, wood fiber or paper fiber during the crystallization reaction. But also, even in the most proper ratio, such as 1:8 (chitosan : pure cellulose), Chitosan and Cellulose mixture will not have the proper mechanical strength for architectural structure application. In this MICRO state research, we gonna explore several additives to make an innovation to pure chitosan- cellulose composite. The aim is to enhance the strength and reduce the shrinkage.

# **2.1.2 Intermolecular Mechanism\_Optical Microscope Observation Research**

We made Chitosan solution (1g chi in 1%w/w acetic acid) as the base reference of MICRO level research. First, the molecule is all separate when there is only chitosan (Fig. 7), but once we add cellulose inside (Fig. 8), the molecule starts to turn to combine reactions (Fig. 9).

From here we can see the chitosan solution will combine all the fiber-like substances during the Crystallization reaction. Just like concrete and rebar, This is the basement of why chitosan-cellulose based biomaterial has remarkable mechanical properties.

# **2.2 Meso \_ Material Innovation and Properties Experiments**

# **2.2.1 Additives Research**

In order to strengthen specific characters of Cellulose-Chitosan composite, additives will be necessary. The current problem of pure composite is mainly low mechanical strength

**Fig. 7.** Cellulose only (1g chi in 1%w/w acetic acid)

**Fig. 8.** Cellulose with chitosan (1g chi in 1%w/w acetic acid)

**Fig. 9.** Paper fiber with chitosan (1g chi in 1%w/w acetic acid)

and heavy drying shrinkage. To optimise these problems, we have to look into certain additives [5].

### **The Optional Additives**

Gelatine: To increase the mechanical strength and speed up the solidification process. Xanthan Gum: To make the composite more stable and homogeneous, and more suitable for printing.

Glycerin: To enhance flexibility and generate bio-plastic. it might not be structure but other architecture parts.

Flour: to decrease the dry shrinkage.

Paper Fiber: to decrease the dry shrinkage and enhance mechanical strength. Pine Resin: to speed up the solidification process.

### **Experiment Recording (Fig. 10)**

Sample 01: 1g cellulose + 1g chitosan (1g chitosan in 1%w/w acetic acid)

Sample 02: 1g cellulose + 1g gelatine + 1g chitosan (1g chitosan in 1%w/w acetic acid)

Sample 03: 1g cellulose + 1g glycerin + 1g chitosan (1g chitosan in 1%w/w acetic acid)

Sample 04: 1g cellulose + 1g Xanthan Gum + 1g chitosan (1g chitosan in 1%w/w acetic acid)

Sample 05: 1g cellulose + 1g Pine Resin + 1g chitosan (1g chitosan in 1%w/w acetic acid)

Sample 12: 1g cellulose + 1g flour + 1g paper fiber + 1g chitosan (1g chitosan in 1%w/w acetic acid)

### **Summary**

By setting up a control group experiment, we find some additives can greatly optimise the properties of chitosan- cellulose composite. Xanthan Gum will make the mixture more stable and easier for printing. Flour will enhance the mechanical strength and reduce the dry shrinkage. Paper fiber can significantly reduce the dry shrinkage since it offers a macro level fiber system to cooperate the micro level (cellulose).

**Fig. 10.** Sample 01–12

# **2.2.2 Ratio Research**

A proper ratio is necessary for this kind of composite to reach the best operating state. From the case study we learned that the most reasonable ratio of Chitosan : Cellulose is 1:8. But according to my experiments, this number will significantly change if the type of cellulose is different.

### **The Optional Cellulose**

Carboxymethyl cellulose: 1:12 Microcrystalline cellulose: 1:10 Nano fiber cellulose: 1:8 Pure fiber cellulose: 1:8 Lignocellulosic: 1:6

### **Observation**

To reach a similar density and viscosity, different cellulose required different ratios [6].

As is mentioned above, the ratio can be significantly different once the type of cellulose changed. Basically, the ratio will grow higher when the fiber size grows smaller.

# **Experiment Recording (Fig. 11)**

Sample 13: 10g cellulose + 1g flour + 1g Xanthan Gum + 10g paper fiber + 1g chitosan Sample 14: 8g cellulose + 1g flour + 1g Xanthan Gum + 8g paper fiber + 1g chitosan Sample 15: 6g cellulose + 1g flour + 1g Xanthan Gum + 6g paper fiber + 1g chitosan Sample 16: 8g cellulose + 1g flour + 2g Xanthan Gum + 8g paper fiber + 1g chitosan Sample 19: 8g cellulose + 3g flour + 1g Xanthan Gum + 8g paper fiber + 1g chitosan Sample 20: 8g cellulose + 2g flour + 1g Xanthan Gum + 8g paper fiber + 1g chitosan (Sample 13–20: 1G CHITOSAN IN 3%W/W ACETIC ACID)

### **Summary**

According to the sample testing result, the best ratio for now is 8g cellulose + 2g flour + 1g Xanthan Gum + 8g paper fiber + 1g chitosan. In this state the shrinkage is min and the printability is the best.

**Fig. 11.** Sample 13–24

# **2.2.3 Properties Test**

**Lightweight Test Based On Water Absorption And Evaporation (Fig. 12):** When we finished the material making process, we got a wet, printable composite. Here is an experiment of how much the weight will reduce after it dries. We made 6 groups of samples, weighed it before and after it dry, calculating the weight change.

**Conclusion:** 70% weight lost after dry. This kind of material has a significant advantage for architectural application, that it is super light material.

**Shrinkage Test (Fig. 13):** There is a problem for all biomaterial shrinkage. After dry, the cell structure loses water, and the original form can never be maintained. Here we also create 6 groups for this testing. We measure and record the size in 3 dimensions before and after it dry, and calculate the shrinkage rate.

**Conclusion:** Around 5% size shrinkage after it dries. This is an average number. During the testing we noticed the shrinkage direction and size can be slightly different on one sample in different positions. Meanwhile, the model material and the dry environment will significantly influence the result, which means a proper way to do the drying process is the key to control shrinkage and final form.

**Fig. 12.** Lightweight test based on water absorption and evaporation

**Fig. 13.** Shrinkage test

**Fig. 14.** Moisture test

**Fig. 15.** Compression test

**Fig. 16.** Bending test

**Moisture Test (Fig. 14):** Here we also create 4 groups r oisture testing. We measure and record the size in 3 dimensions for all samples and put them in the testing box, with the temperature setting in 27, humidity in 80% and put them there for 2 month. Every 15 days we measure the size and calculate the deformation ratio.

**Conclusion:** The deformation is 0%. According to the testing result there is no significant deformation on the testing sample. This means, at least for form keeping, this kind of material is quiet humidity resistant.

**Compression and Bending Test (Fig. 15/Fig. 16):** Here we use the air pressure device to do the compression and bending testing. This device is developed by IAAC and the maximum air pressure is 8 pa. We put one full dried cubic sample for compression and bending testing. When the air pressure goes to the max there is still nothing happening to the sample. After that we tried to put weight on the sample to reach the compression/ bending limitation, but even 100kg weight on it there is still not even one crack on surface.

The air pressure testing calculation is based on the following formular: F = P (pressure in bars) \* Area (related to piston diameter in cm2) <sup>F</sup> <sup>=</sup> p\*A *<sup>&</sup>lt;*=*<sup>&</sup>gt;* <sup>F</sup> <sup>=</sup> P\*{<sup>π</sup> \* 1.62} *<sup>&</sup>lt;*=*<sup>&</sup>gt;* <sup>F</sup> <sup>=</sup> (P \* 8.03) kg RTF <sup>=</sup> (3 \* F \* L) / (2 \* b \* h2)

**Conclusion:** The compression/bending resistance is remarkable. According to the formula calculating we figured out the number is *>*10 N/mm2, which is a significant advantage for the application in architecture, especially for the architectural part.

# **2.2.4 Data Recording**

Here is the data recording for all the sample testing. From the Sample 2 we figured out that Xanthan Gum is super important for viscosity. From Sample 3 we found flour influences consistency a lot. From Sample 4 we learned that Paper fiber is the key to control the shrinkage.

As for ratio testing recording, from sample 13 we found the best ratio for chitosan and microcrystalline cellulose is 1:10. From Sample 14–17 we learned the amount of xanthan gum and flour is 1:2. And finally, in sample 20, we got the best ratio of this kind of Chitosan-Cellulose base biomaterial composite.

# **2.2.5 Summary of Each Additive's Fuction**

**Fig. 17. Sample 20 parameters:** Dry time: 48 h (80 °C)/7 days (25 °C), Lighting weight: 60%-70%, Shrinkage: 5%, Humidity resistance: 0%, deformation: (80% hum/2w), Compression resistance: *>*10 n/mm2, Bending resistance: *>*10 n/mm2, Biodegradability: 100%, Recyclability: 100%

### **2.3 Macro\_Architectural Scale Application**

### **2.3.1 Geometry Design–Research Strategy**

This part is focusing on the application of biomaterial on architectural structure. Here we assumed a specific pavilion structure, and used ameba to do the beso analysis to figure out the most reasonable state of all the bearing elements, and thereby generated the skeleton of this pavilion (Fig. 20).

This process is focusing on the combination of the advantages of BESO and Additive Manufacture (like robotic 3D printing on architectural scale), and the possibility of Advanced Architecture Design- Construction Workflow which is super different from the Traditional Construction Methods.

BESO is a form-finding theory developed by Ameba research team, the leader is Xie Yimin, from RMIT. Ameba is a plug-in software based on Grasshopper.

Here in the following chart (Fig. 18), we can see the iteration information and the analysing state. Finite element is growing fewer and fewer while the Total energy is growing higher and higher. The result of analysis can be displayed in real time once there is an updated calculation (Figs. 19 and 20).

**Fig. 18.** Iteration information **Fig. 19.** MISES

diagram.

**Fig. 20.** Displacement diagram.

**Fig. 21.** Generation process

### **2.3.2 Generation Process**

Here we have the BESO analysis interaction (Fig. 21). there is 45 times interaction in total. We recorded here every 5 Iterations. BESO is an analysis system based on Finite element. In each iteration it will automatically remove some low-efficient elements and put more elements in the weak part.

The left elements will grow fewer and fewer since the iteration is building up. Usually when we do the architectural analysis, the iteration will meet up the most reasonable state when the iteration comes to 40–60.

Here in this tree pavilion design (Fig. 22), at the iteration of 45 we got the ideal analysis result. The next step is to modify this basic form accordly, and optimise it into a more logic, smooth state that can be fabricated.

# **3 Additive Manufacture**

### **3.1 PC - Extruder - 3D Printer Workflow and Extruder Fabrication**

In the early stage of Bio-material printability test, we developed a small-scale printer suit based on ANYCUBIC KOSSEL 3D printer. This series of processing equipment can fully meet the printing requirements of pneumatic/motorized extrusion and continuous breakpoint printing, and the small size is suitable for house office.

**Fig. 22.** Tree pavilion

### **3.1.1 Delta Extruder (Fig. 23)**

This delta extruder is developed for small scale 3D printing. The Function of this device is mainly to make sure that there is no bubble inside the material, instead of pushing material out.

To make sure the material comes out in the right direction instead of goes up, we put two bearing washers to clap the bearing.

# **3.1.2 Robotic Extruder (Fig. 24)**

This robotic extruder is developed for large scale 3D printing. The length of the material tube is 60 cm, which means the printing distance is remarkable.

To make sure the step motor outputs the right speed to cooperate the motivation of the robot arm, we add a gearbox to match the speed.

# **3.2 Biomaterial Printability Testing**

This part is printing testing with biomaterial. There are three different testing aspects: First is the extrudability of biomaterial. Secondly is the accumulability and Third one is Decline Angle limitation testing.

# **3.2.1 Prototype 3D Printing Test Summary**

The operation process is smooth and the stability of the prototype is good. Quantitative analysis of the carrying capacity will be followed up. Based on the current research results, it is initially determined that the cellulose-chitosan-based Biomaterials are feasible for 3D printing structural members in the construction field (Figs. 25, 26 and 27).

**Fig. 23.** Delta extruder

# **3.2.2 Form Optimization for Large Scale 3D Printing**

### **Optimization 1 \_Opening Printing**

Limited by the conditions of the site equipment, this time it was not possible to do opening printing. However, based on the previous printing experience, opening printing can be used for this kind of bio-material (Fig. 28).

### **Optimization 2 \_Decline Angle Limitation**

The angle setting for this test was relatively conservative, and a 40-degree safety angle was selected. However, based on the previous testing results, the upper limit can reach about 60 degrees, thereby creating a more efficient structure (Fig. 29).

### **3.2.3 Large Scale 3D Printing Test Summary**

This version is a buildability test conducted in the middle of the design. The selected form is relatively conservative, with a maximum tilt angle of only 40 degrees. In addition, due to the site and equipment conditions during the epidemic and the difficulty of material transportation, the selection of the test material for this time was the cellulose-pla-based ecological material provided by a third party. This material is basically the same as the early composition of this research, and the characters are also relatively close. So using this as an alternative version of the final material, the deviation of the test results will be comparable (Fig. 30).

**Fig. 24.** Robotic extruder

**Fig. 25. Extrudability testing:** The extrudability of this kind of material is quite good. According to the air pressure powered extrude testing, the operating gas pressure is 2 pa, which means it is quite easy to extrude and the operation condition is quite safe.

**Fig. 26. Accumulability testing:** This testing version is focusing on accumulability of this composite. According to the test result, the accumulability is significant. We accumulated more than 100 layers and it remains super stable.

**Fig. 27. Decline angel limitation testing:** The decline angle limitation testing shows that, while the material is in wet state, the angle limitation is around 20 degree. But once we blow it with hot wind to speed up the water evaporation, the angle limitation is significantly improved.

**Fig. 28.** Large scale form optimization **Fig. 29.** Printing process

**Fig. 30.** Printing parameters. Prototype height: 1 m. Max decline angle: 40 ° Prototype Weight: 3.25 kg Total Routine Length: 202 m Nozzle Diameter: 4 mm Material Amount: 8080 cm Printing Time: 6 h 25 min

# **4 Conclusion**

# **4.1 Combination: Biomaterial + Additive Manufacture + Beso**

This thesis research is focusing on the economic problems and natural issues caused by today's construction industry [7], and coming up with a possible solution in the aspects of Biomaterial, Additive Manufacture and Bi-direnctional Evolutionary Structural Optimisation (BESO).

### **4.1.1 Biomaterial**

Cellulose and chitosan are the first/second abundant materials in this world, with natural characteristics such as biodegradability and renewability. Moreover, this thesis proved the mechanical character [8] can be enhanced or oriented optimised with specific additives [9], which means it is of great potential for architectural application.

### **4.1.2 Additive Manufacture**

With the cooperation of a new booming construction ideal, robotic labor and data oriented management, "printed house" is coming to this real world step by step. Additive manufacture is definitely one of the best ways to cooperate with biomaterial. This thesis proofed the possibility of 3D printed biomaterial on architectural scale, which can be a meaningful inspiration for further research.

### **4.1.3 BESO**

Here in this thesis, we use BESO as a theory to generate structures. What should be stressed here is just one ideal of many. How do we use new material, as well as fabrication tools and methods, is always a multidisciplinary innovation. it can be BESO, it can be FGM [10], it can be any possible or seems-impossible way. We tried BESO in this thesis because we want to confirm this thinking is possible, and more important, to share an inspiration for further innovation.

**Acknowledgments.** I would like to express my gratitude to my thesis advisors Areti Markopoulou. This thesis would not be possible without her guidance, dedication and inspirational insides on the intersection of architecture, biology and additive manufacture. I would like to thank Eduardo Chamorro Martin, a genius mechanist, and Nikol Kirova, a worm-heart supervisor and friend. Their support and remarks were quite essential for the development of the thesis.

I would also like to thank Ricardo Mayor for his guidance on digital fabrication, robotics and computation. I would like to thank Ankita Alessandra Bob, Surayyn Selvan and Megan Yates Smylie. Their willingness to give time so generously has been very much appreciated.

Next, I would like to thank Anton Koshelev for his support on robotic extruder. And Seçil Af¸sar, for her generous sharing of chitosan-cellulose work experience. Also, I would like to express my special gratitude to my Classmate Doruk Yildirim for sharing the in-house knowledge on robotics and additive manufacturing with clay.

Finally, I will be forever grateful to my family and friends who have supported me for the last 9 years throughout different countries and continents, their encouragement has made all this possible.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Imprimer La Lumiere – 3D Printing Bioluminescence for Architectural Materiality**

Mette Ramsgaard Thomsen1(B) , Martin Tamke1, Aurelie Mosse2, Jakob Sieder-Semlitsch1, Hanae Bradshaw2, Emil Fabritius Buchwald1, and Maria Mosshammer<sup>3</sup>

<sup>1</sup> CITA, Royal Danish Academy, Copenhagen, Denmark<EMAIL_ADDRESS><sup>2</sup> ENSAD, Paris, France<EMAIL_ADDRESS><sup>3</sup> University of Copenhagen, Copenhagen, Denmark<EMAIL_ADDRESS>
**Abstract.** 'Imprimer la Lumière' examines the making of a bioluminescent micro architecture. The project positions itself inside a sustainability agenda. By exploring the use of light-emitting bacteria as a material for architecture it asks what are the concepts, methods and technologies needed for designing with living materials. The project devises new means by which to design with the luminescent vibrio fischeri bacteria in a 3D printing manufacturing process based on extrusion principles. By combining the study of these living organisms and their appropriation through advanced robot-controlled 3D printing technologies, we establish a conceptual, material and technological framework for a bio-controlled bacteria growth and 3D extrusion process and a printable material based on agarose and gelatine.

**Keywords:** New materiality · Architecture · Bio-design · Robotic fabrication · Bioluminescence · 3D printing

# **1 Introduction**

As we enter an era of resource scarcity, architecture and design communities are urgently rethinking their material practices. New conceptual frameworks allow us to consider a bio-based material paradigm as an inspirational model (biomimetics), a co-worker (biodesign) or a technological platform (bio-technology) allowing to reprogram the living (Collet 2013).Whether natural or synthetic, the development of biological manufacturing processes plays an increasing role in this context (Franklin and Till 2018; Terranova and Tromble 2017; Brayer and Zeitoun 2019), leading to the conceptualisation of a metabolic-driven material paradigm that challenges the perception of our surroundings as inert to something essentially living (Ramsgaard Thomsen 2019) (Fig. 1).

'Imprimer la Lumière' is an interdisciplinary research enquiry sitting at the intersection of architecture, design and microbiology exploring the use of light-emitting bacteria

**Fig. 1.** Micro-architecture of 'Imprimer la Lumière'.

as architectural materiality. By investigating the 3D printing of bioluminescent bacteria, we are questioning how architecture can be host for an ecology of species in symbiotic coexistence (Beesley 2014). Widely occurring in marine life, some mushrooms and insects, bioluminescence in architecture and design remains an under-explored territory of investigation, essentially used to date to imagine and probe more sustainable ways of lighting. In this paper, bioluminescence is used as a mean to question the critical thinking and appropriation of bacteria as an architectural material and how this is changing the practice of architectural design and fabrication.

Our aim is to investigate the critical thinking and appropriation of living bacteria as an architectural materiality. To do so, we explore bioluminescence: a chemical form of light produced by many marine organisms, some insects and mushrooms. While bioluminescent genes are used as markers and for imagining in biology and medicine bioluminescence, recent experiments in the bio-design community have explored bioluminescence as an alternative to public and domestic lighting (Myers 2012; Brayer and Zeitoun 2019). Here, successful experiments have predominantly focused on bioluminescent algae (Van Dongen 2014; Rodriguez 2016, Douenias 2015), we extend this research to bioluminescent bacteria.

In 'Imprimer la Lumière' we use bioluminescent bacteria to examine the metabolism of a living architecture. As any living organism, luminescent bacteria have a limited lifespan. Their appropriation into the built environment therefore induces an intrinsically temporal dimension to the conception, fabrication and experience of architecture, which implies not only the development of a new conceptual framework but also new processes, tools and know-how adapted to microbiologic life that are inseparable from a set of ethical challenges.

As a consequence, this paper asks what are the conceptual, material and technological framework for bio-based architecture and how does designing for living systems challenge our current models of design, registration, specification, fabrication and inhabitation. What are the new models by which we can support the design of metabolistic systems of living organisms and capture their limited lifespans and how does living and nurturing become part of a new vocabulary for how we build?

The project is an interdisciplinary collaboration between architecture, design and marine biology undertaken by: CITA (Centre for IT and Architecture, KADK), Soft Matters group, Ensadlab (ENSAD) and Department of Marine Biology (Copenhagen University) (Fig. 2).

**Fig. 2.** Micro-architecture performance: the light emitted by the bacteria.

# **2 New Methods for a Living Architecture**

'Imprimer la Lumière' presents a set of 3D printed structures acting as a constellation of self-illuminating micro architectures. These micro architectures act as design probes (Ramsgaard Thomsen and Tamke 2009; Mossé 2018) that reflect on the actualisation of architecture as a host for an ecology of species in symbiotic coexistence. The method of the design probe positions the research across conceptual and technological investigations challenging the way we understand the material and performance of contemporary architecture while simultaneously questioning the technologies by which the design and fabrication of living systems can be studied.

Design can be understood in a generic sense as a cultural process of technological appropriation, meaning 'a way of adopting technology in our culture by accepting its influence as well as by influencing it' (de Winter 2002). To question how microbiology can become a new technological platform for architecture, we adopt a practice-based approach informed by the design probe culture (Gaver and Dunne 1999). In this context, a variety of design probes are developed to critically question how to create acceptance for new technological evolutions and discuss whether these changes are desirable. The micro-architectures discussed in this paper sit more specifically at the intersection of conceptual and material probes (Mossé 2018). As a conceptual experiment, they are probed to develop a speculative inquiry or narrative addressing the implications of future desirable cultural patterns. As a material probe, their primary role is to explore the crafts, materials and techniques through which this cultural pattern can be shaped as well their performance as an architectural materiality (Fig. 3).

**Fig. 3.** Vibrio Fischeri cultures in nutritional solution over time from initial activationa.

# **3 Developing 'Imprimer La Lumiere'**

The project is conceived over a series of experiments appropriating techniques for growing luminescent bacteria and developing the technologies for 3D printing the extrusion of their medium. 3D printing is explored as a means of liberating the forming processes of the medium to investigate how topology and surface treatment can drive the life cycles and therefore the light performance of the bacteria. In 'Imprimer la Lumière' we use a collaborative robot with a bespoke micro dispenser. This allows us to address an architectural scale of fabrication distinct from dedicated bioprinter that operate at smaller scales. The building of new 3D printing methods for collaborative robots also allows us to interface with programmable design environments, allowing a higher degree of control and steering of both the design and fabrication process.

# **3.1 Ethical Considerations**

With biodesign, ethical considerations become an intrinsic part of the design project. Designing with bacteria as a material for architecture means designing for and with the life cycles of living organisms, and allowing co-inhibition within our environment. Where bacteria do die as part of this new architecture, they are also nurtured and invested into a new habitat. In 'Imprimer la Lumière' we work with biosafety level 1 bacteria meaning that they are not genetically modified, do not pose a danger to their surroundings and are fully biodegradable.

In designing with Vibrio Fischeri, we delocalise a marine bacteria to the new host environment of the medium. In doing so we provide a monocultural environment which both optimises its living conditions but also makes it less resilient to change.

### **3.2 Designing the Medium for 3D Printing**

The first task is to understand the optimal living environment for the bacteria and design the medium in which it lives. The medium provides nutrition and holds oxygen for the bacteria to metabolise. In 'Imprimer la Lumière' the design of the medium is tailored to the fabrication process and incorporate the requirements for 3D printing. Through experimentation we developed a recipe to control the rheological properties of the medium consisting of Agar, Gelatin, Glycerin, Nutritive media and Water (to 3.2%, 1.8%, 2.8%, 6.5% respectively). The recipe is developed in order to control the viscosity of the medium during the printing process and final state and use for fusion deposition. Agar is used as the basis of the medium for its melting and gelation properties. The amplitude between both temperatures gives the medium durability and firmness (Whistler 1985). Due to this, it is widely used as microbiological media (Dhanapal et al. 2012). We use a common household agar for cooking which enables us to print with additional height, compared to lab grade agarose media otherwise used in direct ink writing technologies (Kilian et al. 2017) (Fig. 4).

**Fig. 4.** Fabrication process in 'Imprimer la Lumière'.

In 'Imprimer la Lumière', we require the medium to be kept above the gelation point at all times during printing. To keep the medium cartridge that stores the material at constant temperature before the 3D printing process, we developed a self-regulating heating unit. Gelatine is added to lower the gelation temperature of the mixture to 40°C. This reduced temperature conserves energy, enables faster gelation and smooths the surface for a more homogeneous appearance. Additionally, glycerin is used as a plasticizer that increases the flexibility of the intermolecular connections between the Agars polymer chains (Arham et al. 2016). The medium is extruded through a high precision micro-dispensing unit (ViscoTececoPen700) with self-sealing rotor-stator arrangement. The dispensing unit is carried by a 6 axis collaborative robot (UR5e). This allows the robot being used inside laboratory conditions and to be moved to sterile environments for inoculation.

Through this design process, we built a strong understanding of the requirements for the medium and the 3D printing process. The medium needs to perform as a hybrid of scaffold and nutrition where the containing walls allow dispersion of nutrition and oxygen. During experimentation, we learnt that controlling the surface of the medium was crucial to promote the light-emitting capacity of the cultures. By having a high surface to volume ratio the bacteria is better exposed to oxygen, propagates better and its emitted light becomes easier to perceive. The parallel effort to control the structural capacity of the medium in a gelled state allowed us to develop design criteria for the probes as having a large surface, interior cavities and to build high (Fig. 5).

**Fig. 5.** Changing the composition of medium radically affects the living conditions of the bacteria, the structural capacity and surface quality of the structure

### **3.3 Designing a Living Architecture**

The design of the micro-architecture probes employs a differential curve growth algorithm. This allows us to maximise the surface to volume ratio of the structure and optimise the bacteria's light emitting capacity. The line differential growth algorithm also allows us to generate the robot print path as an intrinsic part of the design process allowing greater unity between processes of design and processes of making.

The generative algorithm employs strict form-generating rules to generate complex topologies. In 'Imprimer la Lumière', we adjust the rules to addressing structural and fabrication-based constraints such as maximum overhang, interconnectivity, layer heights and structural performance as a result of wall undulation.

The algorithm follows the logic of differential curve growth. Here, a base curve is iteratively subdivided in selective increments. The curve sections are form found using a physics engine to simulate forces between the subdivision points on the curve. On the subdivision points, sphere colliders force these segments to elongate, resulting in the differential growth of the geometry.

In order to achieve a suitable degree of surface complexity and to ensure a balanced distribution of complexity, we employ the differential growth algorithm in two stages: firstly to generate a satisfactory base geometry and secondly to grow the topology in three dimensions. Narrow passages, emerging from the generative process are detached allowing the probe geometry to branch. The splitting is conditioned by a straight skeleton calculation evaluating local surface area. The single branches are then calculated within the incremental growth process as individual objects within a unified system. This process ensures that the overall forces driving the form finding process apply equally to the topological whole and that structural and fabrication requirements are fulfilled. The process can be locally varied to account for structural support and gravity.

The branching structure generates a complex interior section with distributed hollows that act as vessels for bacterial growth. The complexity of the micro-architecture probes allow us to steer the emission of light through topology.

# **3.4 The Inoculation Process**

Lifecycle optimisation and the strict environmental requirements of the cultures demand new fabrication processes bringing new challenges and opportunities (Dade-Robertson 2019; Colette 2007; Pasquero and Poletto 2014). In 'Imprimer la Lumière', the manufacturing process requires the nurturing of the bacteria culture and its shielding from impending contamination. Activated from lyophilized state, the culture is pre-grown within nutritive media suspension while the printed probe is inoculated with a microdispenser. This allowed for stronger recognisable glow, which can be attributed to the reintroduction of oxygen through diffusion. The inoculation process uses the robot for precise positioning. A digital model of the probe is used to compute the access-path for the robot. The probe is then injected with the bacteria suspension and filled into its vessels (Fig. 6).

**Fig. 6.** Bacteria culture growing on medium over time with luminescence analysis.

During tests we observed an activation time of an average of three days. For the colony to survive, a sterile environment containing sufficient oxygen and nutrition needs to be ensured. Prior experiments have shown that the gelation of the agar prohibits diffusion of additional oxygen, which renders active air exchange obsolete. To understand the life cycle of the probes, the timeframe of the culture's growth and propagation needs to be considered.

### **3.5 Evaluation**

The probes are evaluated using two processes of observation and oxygen sensing. The first process uses imaging to register the bacteria growth and propagation patterns across the surface in time. The images are taken in the dark to allow best understanding of the bacteria's light emitting properties. The colony is observed across 12 days in which we observe firstly the growth of the colony around the inoculation point and the strengthening of the light emitted (day 2–4) and secondly a move of the light emitted away from the inoculation point (day 5–12). Our assumption is that the colony propagates into new medium as nutrition and oxygen is consumed. To test this assumption a second evaluation is undertaken using optical oxygen sensing based on the dynamic quenching of an oxygen sensitive indicator dye by oxygen. Here, an optical oxygen meter (FireStingO2) with a retractable needle-type sensor (OXR230) from Pyroscience (pyroscience.com) is used for measurements of dissolved oxygen. Oxygen is measured at the surface of the bacterial culture and different depths through the culture and the medium towards the bottom of the petri-dish. Additional measurements are done at the interface of the bacterial culture and medium, and stepwise further away from the bacterial culture at approximately 1 mm depth within the medium. A clear gradient in oxygen concentration became apparent, as oxygen depleted gradually from the medium (approx. 100% air saturation) towards the bacterial culture, which was completely anoxic (0% air saturation). An oxygen profile measured from the surface of the culture through the medium to the bottom of the petri-dish showed similar results. The bacterial culture proved to be anoxic, and the medium below increased in oxygen concentration the further away from the bacteria measurements were conducted (Fig. 7).

**Fig. 7.** Particle system simulating the progress of bacteria propagation through the medium.

# **3.6 Simulation of Bacteria Behaviour**

In order to understand the lifecycle of the bacteria, we develop a simulation of propagation through the medium. Herefore, we use a simple particle engine to approximate the printed geometry. These are equipped with a density attribute computed by the proximity to their neighbours. The particles closest to the inoculation points are activated as live particles. This attribute is used to control and call the propagation of neighbouring particles by counting up a 'life-time' attribute across each time-step of the calculation. Neighboring particles are then 'activated' in subsequent iterations. When a particles 'lifetime' surpasses a defined maximum value, it transitions into a 'dead' particles, simulating the state where all oxygen and nutrition is consumed. No additional particles can be activated from this point. The simulation of propagation speed and lifespace is calibrated using the observed imagining data from the physical probes.

# **4 Conclusion**

'Imprimer la Lumière' sits at the intersection of biodesign and digital fabrication. It opens up new perspectives for the design and appropriation of bioluminescence as an architectural materiality. At a conceptual level, the project asks what happens when the material of architecture becomes living: what are the new concepts, methods and technologies that are needed to design for and with living materials?

The first step in 'Imprimer la Lumière' is to link bio-design agendas with digital fabrication and 3D printing. Our application of collaborative robots for 3D printing of microbiologic organism allow us to extend the scale of fabrication and speculate upon the design criteria. In 'Imprimer la Lumière', the probes are informed by both the optimal living environment for the bacteria and the fabrication criteria for 3D printing. By controlling the rheological properties of the medium and its gelling, we can steer the light-emitting performance and design its structural capability to build complex topologies with interior cavities and vessels that optimise the living environment for the bacteria.

The second step is to build assumptions about how the geometry of the microarchitecture affects performance. These assumptions are made through empirical observation studies and evaluated through localised oxygen sensing. The assumptions are used as a basis to build prototypical models that can simulate and capture the light emitting performance and propagation of the bacteria as it moves through the medium, 'Imprimer la Lumière' speculates on what the nature of futures representations can be. Where traditional architectural representation emphasises the description of form through the geometry of extension, 'Imprimer la Lumière' develops volumetric models that change across time steps. These descriptions allow architects and designers to specify and describe the design and steering of material lifecycles and their associated performances.

The probes in 'Imprimer la Lumière' look like towers or dense cities in small scale. Conceived as micro-architectures, their aim is not to solve an architectural performance such as public or domestic lighting, but instead to probe what a living architecture could mean.

**Acknowledgment.** 'Imprimer la lumière' is a cross-disciplinary collaboration between CITA (Centre for IT and Architecture, KADK), Soft Matters group, Ensadlab (ENSAD) and Department of Marine Biology (Copenhagen University). The project has benefited from the support of the IFD sciences programme of Institut Français du Danemark (2018) and subsequent funding from the Danish Arts Foundation (2019). We thank Leuchtlabor GbR, Weiherhammer, Germany for their kind support. We thank the students of CITA Computation in Architecture (Aroni Roy,Tessira Reyes Crawford, Claudia Colmo, Izabella Banas, Kawtar Al Akel, Ke Lin, Nikhila Vedula, Youcheng Li, Carolin Feldmann) for their contribution to observational studies.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Bio Scaffolds**

N. Alima1(B) , R. Snooks1(B) , and J. McCormack2(B)

<sup>1</sup> School of Architecture and Urban Design, RMIT University, Melbourne 3000, Australia<EMAIL_ADDRESS><sup>2</sup> Sensi Lab, Monash University, Melbourne 3000, Australia

<EMAIL_ADDRESS>
**Abstract.** 'Bio Scaffolds' explores a series of design tectonics that emerge from a co-creation between human, machine and natural intelligences. This research establishes an integral connection between form and materiality by enabling biological materials to become a co-creator within the design and fabrication process. In this research paper, we explore a hybrid between architectural aesthetics and biological agency by choreographing natural growth through form. 'Bio Scaffolds' explores a series of 3D printed biodegradable scaffolds that orchestrate both Mycelia growth and degradation through form. A robotic arm is introduced into the system that can respond to the organism's natural behavior by injecting additional Mycelium culture into a series of sacrificial frameworks. Equipped with computer vision systems, feedback controls, scanning processes and a multi-functional endeffector, the machine tends to nature by reacting to its patterns of growth, moisture, and color variation. Using this cybernetic intelligence, developed between human, machine, and Mycelium, our intention is to generate unexpected structural and morphological forms that are represented via a series of 3D printed Mycelium enclosures. 'Bio Scaffolds' explores an interplay between biological and computational complexity through non anthropocentric micro habitats.

**Keywords:** Mycelium · Feedback systems · Material agency · Adaptive fabrication

# **1 Introduction**

In this paper, we present a novel cybernetic relationship entwining robotics and Mycelium growth. Through an adaptive feedback system of biological and computational agencies we explore the robotic infusion of Mycelium into biodegradable scaffolds. To orchestrate natural growth and decay over time, we posit a strategy where the degradation of form is catalyzed by robotic interaction between material, natural and computational agency. Our aim is to develop design techniques where biological materials influence the robot's movements and thus become a co-creator within the design process. We therefore examine the design tectonics that occur when enabling nature to co-direct the construction of architectural form. The methodology presented here draws from the adaptive processes of biology within a broader ambition to consider how our buildings can grow, adapt, self-repair and biodegrade. As László Moholy-Nagy stated,

**Fig. 1.** Universal Robot injecting mycelium liquid culture into 3D printed biodegradable scaffolds.

"architecture will only be brought to its fullest realization when the deepest knowledge of biological life is available" [2]. Within this context, we examine natural materials and demonstrate new relationships between form and environment to speculate on their architectural potential. Our research is therefore interested in the biological process of formation and ways in which it can contribute to design. We encourage other designers to rethink current relationships with nature by enabling a negotiation between biological growth and architectural intention. To demonstrate such a dialogue, here we present *BioScaffolds*: a sustainable approach and demonstration of novel feedback strategies for architects working with living materials (Fig. 1).

The integration of biological systems within the architectural design and construction processes has a significant lineage and historical precedence. Many disciplines, from engineering through to design and computer science have drawn on natural systems and processes as a rich source of design inspiration. Common methodologies of incorporating nature into design include biomimetics, biophilia and sustainability. Often these methodologies result in a mimicry of nature's forms or its simple application onto existing building structures, without engaging with the agency of material throughout the design process. In this paper we argue that working with nature requires a radical shift toward a new era in which nature is incorporated in both the design and construction processes [11]. An era in which natural growth becomes the catalyst for robotic intervention, 3D printing and computational design.

Within the innovative field of design, Mycelium is increasingly being used for the fabrication of products and buildings. Mycelium is the vegetative part of a fungus bacterial colony and is characterised by mass branching of growth [16]. Mycelium's long, branching filaments, known as *hyphae* are collections of one or more cells surrounded by a cellular wall [3]. Mycelium is often referred to as 'the web of life' as it plays an important role in the decomposition of plant material and pollutants, making them important ecosystem engineers. As Paul Stamets asserted, "I see the mycelium as the Earth's natural Internet, a consciousness with which we might be able to communicate" [4]. We too view mycelium as an integral part of our planet and have therefore become fascinated in enhancing our relationship to nature through design; specially through the creation of form and robotic orchestration.

Today, mycelium is increasingly being used in the fabrication of products and sutainable solutions to building materials. Mycelium's chemical characteristics include, its ability to remove toxins from water, act as a natural binder, act as a good insulator and a moldable and biodegradable substrate [5]. Due to its proven compressive abilities, projects such as Philippe Block's *Mycelium Tree* demonstrate structural use of the materials, despite its modest compressive capacity of around 30 psi [16]. Designers including Phill Ross have demonstrated that mycelium can be grown and transformed into building blocks of different shapes that are 100% organic and compostable [7]. Showcased in David Benjamins HiFi tower, mycelium bricks where fabricated in order to showcase sustainable solutions to our design and construction industry. Inserting a Mycelium mixture within a mold, it hardens over time, taking the shape of the desired form. It is then dried to become inactive and no longer a living material [8]. Companies such as 'Myco Composite' are currently utilizing the material as an agricultural bio-product for packaging by moulding the material into predetermined forms to be utlised for human purposes [6].

While Mycelium is increasingly being used in the field of architecture and design, its application is generally subservient to a priori form. What has yet to be explored within the field of design is utilising Mycelium within its live state and exploring its complex patterns of growth. We are therefore interested in the organism's ability to consume and eventually decompose an organic substrate, in order to receive its nutritious properties [8]. This chemical reaction occurs as Mycelium grows by releasing enzymes from the hyphal tips to absorb and digest the surrounding nutrients. As a result Fungi attain energy from their surroundings by branching out and building filamentous Mycelial networks [16]. Due to the material's ability to biodegrade through a range of substances in order to receive its nutrients and fibrous minerals, our original contribution to this field is harnessing the organism in its live state in order to enable natural patterns of growth and agency to contribute to the design and fabrication process. Rather than molding Mycelium to preexisting architectural forms and drying it out [18], this research exploits natural growth, enabling the living material to become a co-creator within the design processes. 'Bio scaffolds' examines Mycelium's ability to biodegrade and destroy architectural forms and host systems. By exploring the potential of natural Mycelium growth within the architectural context, our ambition is to engage nature and material agency within the design process rather than deferring material behavior directly to form. We therefore present a series of design methodologies that emerge from the interaction of living (material) and non-living (machine) behaviors, which currently remains underexplored within the field of Architecture. 'Bio scaffolds' explores the fusion between computational and biological intricacies, resulting in a series of non-anthropocentric Mycelia enclosures. Hacking into the degradation rates of natural material, sacrificial frameworks act as architectural habitats for Mycelium to grow and eventually biodegrade. In this research paper, we explore robotic intervention as a tool for maintaining and choreographing's the organisms homeostasis and patterns of growth. In order manipulate natural growth, we explore dynamic feedback system in which machine, nature and computational form are in constant dialogue with one another. As the organism begins to grow within the designed geometry, the robot detects and responds to this data by injecting additional mycelium culture into the sacrificial formworks. This cyclitic process occurs over a seven day period, resulting in a computationally and robotically orchestrated process of natural growth. By fusing technologies and existing processes from the natural, robotic and computational fields, this research invites a multidisciplinary approach to architecture. Architect and academic, Marcos Cruz has said that "A notion of design is emerging whereby interdisciplinary work methodologies is traded between designers, engineers and biologist; giving rise to hybrid techniques, new materials and hitherto unamenable living forms" [10]. In order to truly rethink our relationship with nature, 'Bio Scaffolds' adopts a series of trans-disciplinary techniques from the architectural, medical and scientific disciplines.

### **1.1 Medical Bio Scaffold**

This ability to intertwine robotic 3D printing with living materials in the fabrication of biodegradable forms was originally derived from the medical bio-scaffold. Our research draws on techniques from the field of biomedicine, such as tissue engineering, 3D printed artificial organs and bio-scaffolds. Specifically, we have been investigating the processes of medical bio-scaffolds where cells are implanted in order to adopt the geometry of the scaffold. This process occurs by 3D printing a structure, then seeding it with native cells and proteins to encourage cell adhesion and tissue generation [12]. Being a biocompatible and bioresorbable material [13], the scaffold is designed to degrade over time (see Fig. 2). Our research explores how these characteristics of biodegradability and biocompatibility may occur within an architectural context.

# **1.1.1 Mycelium: Bio Scaffold**

Adopting an approach similar to the medical bio-scaffold, our research explores the decomposition process of Mycelium. However, rather than allowing this process of growth and biodegradability to occur naturally and randomly as it would in nature, we conducted a series of experiments to influence and disrupt the Mycelium's existing behavioral characteristics through robotic intervention, form and materiality. Using computer-designed geometries, we direct the growth of mycelia by hacking into its existing patterns of growth through complex, nutrient rich scaffolds. Mycelium excrete enzymes to break down resources in their surroundings and assimilate the nutrients to build up their fungal network [17]. This absorption process occurs when fibrous, organic substrates are fed to the organism including, wood chips, coffee grounds, sawdust, biodegradable plastic, cardboard and paper [17]. With this knowledge we tested the organism's ability to biodegrade a wood plastic composite material, comprised of corn starch and wooden fibres. The organism was attracted to the fibrous properties contained

**Fig. 2.** Far left image (sourced from Computer-Aided Designed, 3-Dimensionally Printed Porous Tissue Bioscaffolds For Craniofacial Soft Tissue Reconstruction Journal) showcases a medical bio scaffold before implantation. Middle image and far right showcases computational forms designed by authors incorporating this time based process of decay

within a wood-based PLA filament, and was therefore capable of growing on scaffolds composed from this material. The following experiments explore 3D printed, biodegradable, nutrient rich scaffolds which manipulate the growth of mycelium through form and materiality. As shown in Fig. 3, this 3D printed geometry demonstrates a successful process of degradation. Mycelium was injected into the wood-based plastic composite forms, eventually degrading the structure and adopting to the set geometry provided. As the Mycelium grows along the scaffold it decomposes and consumes the geometry, replacing the structure with a network of fibrous growth. Growth occurs largely at the tips of the hyphae [5], allowing the Mycelium to spread directly over complex geometric structures as they consume the scaffold.

**Fig. 3.** Far left image showcases growth of organism, middle image showcases bio scaffold printed out of wood based plastic composite material before mycelium inoculation. Far right images showcases mycelium bio degrading wooden scaffold.

### **1.2 Designing with Living Matter**

In order to integrate this unique form finding method with biological growth, our research aims at applying scientific knowledge of Mycelia growth to achieve novel architectural forms. Bio scaffolds entails a layered iterative design process that combines techniques of digital software, fabricated experiments and robotic feedback. Through this fusion of operations, a true hybrid between computation, nature and machine is achieved, as the architect can orchestrate natural growth through form and robotic intervention. Through this nonlinear framework, a singular design process becomes undetectable as the architect's aesthetic and the organism's natural growth become intertwined. Rather than treating nature as a decorative element applied to objects, our approach explores a design and robotic response to Mycelia's natural growth.

Utlising accessible Mycelia cultures, we experimented with the organism and studied its natural growth patterns, in order to manipulate this process through design. This raised the question of how would robotic interference and architectural aesthetic modify the growth of mycelium to achieve a specific growth aesthetic? And what types of geometries would result in the selected biological patterns of growth? Our objective was therefore to study how mycelium propagates over specific forms and surfaces that arise from computational design and robotic fabrication.

During this process, a series of computational experiments were devised to control Mycelium's patterns of growth and behavioral growth characteristics. Each computational form was digitally fabricated and tested by infusing Mycelium culture at key points over the scaffold. This process began with a with a series of computational heterogeneous skins that selectively encourage and hinder the growth of the organism. These features varied in porosity, density and shape and density of internal chambers for the mycelium to seep through. Each geometry was 3D printed using a wood-based PLA filament, composed of approximately 20% sawdust. Once the scaffold has been fabricated, liquid culture mycelium was robotically injected into it at specific insertion points. We studied the organism's compatibility and rates of degradation, in order to gain a comprehensive understanding of its process of growth and decay. Each experiment was judged and reflected upon in order to examine the ideal forms for successful Mycelia growth. Through these designed experiments, we discovered that Mycelium grows at its most rapid pace along smooth puros surfaces that provide a series of micro valleys for the organism to seep through (shown in Fig. 6). Through this process, we cataloged the inherent qualities of mycelia growth, which included characteristics of branching, bridging and web like strands (see Fig. 4). Each experiment explored a series of intricate weaves and designed obstacles that the Mycelium would grow around, resulting a unique set of growth that would otherwise not occur in nature. Through this interface between machine- and biological-fabricated forms, Mycelia growth therefore became the performative aspect within design, resulting in a series of non-anthropocentric biological enclosures.

However, in order to enable a true co-design between designer and nature, the architect's aesthetic must remain an important contributor to the design process. The preservation of design identity showcases a true duality between nature and architect. Through a series of digitally designed geometries, the designer aims at creating unusual forms that showcase biological material in new and innovative ways. Whilst the geometry has

**Fig. 4.** Computational forms: smooth surfaces designated from mycelium growth

evolved from an understanding of the relationship between digital tools and Mycelium growth, the designer's vocabulary of creating 'mystical creatures' remains an integral part of this process. This co-existence between the architect's design vocabulary and biological agency ultimately exposes a new relationship between computational and biological complexity.

Whilst this research encouraged Mycelia growth through digital tools and robotic fabrication, it also explores an intervention and orchestration of growth. We therefore attempt to also hinder the growth of Mycelium in particular sections of the geometry through a series of articulated forms. Rather than allowing the organism to grow wildly and degrade the entire form, we are interested in a controlled processes, as sections of the geometry are designed to remain or fossilize. In order to achieve this gradience of growth, the scaffolds are comprised of heterogeneous skins what both encourage and hinder life through form. Whilst mycelium latches to smooth surfaces, it is repelled from climbing up vertical antenna lattice systems (Showcased in Fig. 6). We therefore tested a series of scaffold designs that would hinder the growth of mycelium and allow sections of the scaffold geometric integrity to remain. Through a time-based process of decay, we designed fractal components that would remain uneaten by the organism once majority of the scaffold had degraded (Fig. 6).

A series of self-organising generative algorithms were deployed in the design of the scaffolds, including a behavioral design strategy that draws on the logic of swarm intelligence. This multi-agent process, based on the Behavioral Formation approach developed by Roland Snooks, encodes design intention within a population of agents that interact to generate a self-organised design intention and emergent formal assemblages. This algorithmic logic distributes a series of components that create complex topologies and intricate, heterogeneous surface articulation [19].

This contrast between the fibrous intricate details that hinder the growth of mycelium and the smooth valleys that encourage Mycelia growth, enables the designer to orchestrate both the growth and decay of nature. This juxtaposition between designed intricacy and simplicity exposes a contrast between computational and biological complexity. Whilst the smooth surface offers a blank canvas for the Mycelium to spread its growth,

**Fig. 5.** 3D printed scaffolds from wood based biodegradable plastic infused with corn starch and natural fibers.

the intricate scaffold details enables the architect's aesthetic to be preserved, showcasing a true hybrid between biological and design agencies. Showcased in Fig. 6 nature is working with and against the geometry. Whilst it follows the architectural pathways provided, it also separates from it: affirming its own distinction, independence and individuality. This duality between surface and component enables an ecosystem of interactive geometries, counterbalancing both the biological and computational intricacies.

**Fig. 6.** Image on far left showcases computational model with smooth surface for mycelium to inoculate and designed intricacy that would hinder the growth of mycelium. Middle image showcases this computational model printed out of a wood based bio plastic material. Far left image showcase mycelia growth being orchestrated through these designated forms.

**Fig. 7.** Universal Robotic customized tool rotating to extract data from mycelium. This tool contains a robotic syringe and Arduino moisture sensors on the opposite end effector.

### **1.3 Technical Workflow: Robotic Intervention**

In order to detect and respond to the organism variations of growth, robotic vision systems where implemented that combine form generation, digital fabrication, and material computation into a seamless integrated processes. In addition to orchestrating biological degradation through form, robotic intervention enables us to further intervene on the 'living' with immediate response [1]. As a result, we explored methodologies in which complex fungi behaviors and material data informed robotic feedback. As Mycelium growth may often take place over months or years, robotic intervention seems ideal, since a robot never tires and can act over timescales inconvenient or impossible for human designers. These long-term temporal interventions react to the organism's unpredictability and change over time. During the course of the mycelium's development, the battle and symbiotic tension between machine, organism and form become apparent. As the mycelium begins to spread throughout the sacrificial framework, multiple computational behaviors mutually negotiate to orchestrate the organism's growth. As a result, the robot detects and responds to the organism's properties, including variations in colour, and moisture qualities and responds through systematic feedback loops.

Mycelium, similar to some plants, displays distinct signs when in a flourishing live state in contrast to its dead, dried out state. Visually, these signs include its colour and its moisture content. According to Mitchell P. Jones if the organism is dying, it will display signs of a brown exterior with minimal moisture [8]. In order to keep the organism alive, it requires moisture that maintains its white fibrous exterior. Consequently, we have developed an approach where colour, moisture data and patterns of growth are extracted from the mycelium through robotically controlled scanning and sampling, which then influences the robot's behaviour. The robot reads and responds to this data establishing a symbiotic feedback system where fabrication techniques, robotic intervention and organic development all contribute to the overall design process. Our initial experiments, which hack into nature via robotic intervention, began examining Mycelium's patterns of growth and its ability to biodegrade through a range of complex scaffolds.

The technical components of this research include a computer vision system, 3D scanning process, sensing, and feedback control, 3D printing, and robotic infusion of liquid culture, have been included in the co-creation process between human, machine, and mycelium intelligence. Equipped with customised sensors that track the organism moisture qualities, patterns of growth and colour variation, the technical workflow for*Bio* *Scaffold* involves a feedback system between the robot, customised tools, material behavior, the vision system and computational form. This series of design experiments used a Universal Robot UR10 controlled by Grasshopper, and 3D printed wood-plastic composite scaffolds, an Arduino moisture sensor, webcam, a customised multi-tool including robotic syringe. These techniques were combined into a single end-effector to scan, read and respond to Mycelium growth in a unified way (see Fig. 7).

**Fig. 8.** Technical workflow showcasing the robot scanning, extracting and computationally recognizing this data from the organism

# **1.3.1 Feedback System: Computation, Robotic and Material Agencies**

In order to maintain the mycelium's homeostasis, the UR robot operated on the organism over an extended period of time, a process which we refer to as 'slow-botics'. This long-term intervention offers an alternative to the common conceptions of robotics that concentrate on speed and efficiency. Over a 7-day period, the robot waits patiently to receive new data and then acts accordingly [9] (see Fig. 8). Rather than treating the robot and organism as two separate mediums, the robot remains a permanent fixture within in this system, where the behavior of organism and machine support growth and coexistence. The following experiments demonstrate processes in which the robot interpreted data provided by the organism, by identifying the contrasting living conditions of the material, quality of life and areas of nourished or dying mycelium. This feedback system occurred through the following process (see Fig. 9). **Process:**

**Fig. 9.** Technical cyclitic feedback workflow showcasing the robot scanning, extracting and computationally recognizing this data from the organism

6. According to the data received from the moisture sensor, a set of computational rules and restraints are implemented. The algorithm instructed the robot how to respond to the organism. (see computational *Logic* bellow) **If** the robot detected that the area was lacking in nutrients and therefore 'barren' it would respond by rotating the singular tool, infusing 30ml of mycelium. In contrast, **if** the robot extracted 'living' data and was therefore in a nourished moist state, it would 'do nothing' and proceed to take the next value of its neighboring cell.

During the scanning process, an algorithm is implemented instructing the robot how to react.

*Logic:*

**If** value received was 0 *>* 50 **then** infuse 30 ml of Mycelium

This indicated that the mycelium was extremely dry and was in need of additional moisture.

**If** value received was 50 *>* 80 **then** infuse 10 ml of Mycelium

This indicated that the mycelium was in a stable condition and required minimal moisture to maintain this condition.

**If** value received was 80 *>* 120 **then** do nothing.

This indicated that the mycelium was extremely moist, do not deposit additional moisture in order to prevent drowning the organism and bacteria.

**Fig. 10.** Results showcasing the orchestration of mycelia growth through form and robotic intervention.

# **2 Conclusion**

Resulting from this symbiotic feedback system and form finding process, this research explores the ability to orchestrate natural growth through robotic intervention and Architectural form. Through this time-based process of growth and decay, Mycelia growth is showcased in new and innovative ways that would otherwise not occur in nature. Designing through the interaction of natural systems and computational behaviors creates a complex feedback process that privileges volatility and the unknown. By researching through design, we examined various types of forms which encouraged biological growth. Demonstrated in (Fig. 10) skins that contain dense pours areas, enable the organism to seep through the built framework and degrade it at rapid speed. Similarly, geometries that where based on a branching system, encouraged the organism to extend its patterns of growth along the designated surface area. This research has established an approach where the interaction of these two domains – the physical and the digital, have the potential to generate new and unexpected structural and morphological formations. The interaction of these agencies offers the potential of creating new architectonic approaches, or as Philip Glass states, "A new language requires a new technique" [15]. In this paper we have demonstrated an approach to growing Mycelium through a set of hybrid digital and biological behaviors that interact with computationally generated scaffolds. We are interested in exploring how computational and material agency may work together through robotics feedback systems. 'Bio scaffolds' examines the design tectonics and adaptive living forms that may emerge from this process. Through this integration of a unique form finding technique with biological growth, this research aims at merging robotic technologies with living matter until the two become indistinguishable. Whilst the Mycelium enclosures presented are not yet architectural buildings or at architectural scale, they represent progress towards a developed system that engages with materials and addresses sustainability within Architecture.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# **Di-terial – Matching Digital Fabrication and Natural Grown Resources for the Development of Resource Efficient Structures**

Felix Amtsberg1(B) , Caitlin Mueller2(B) , and Felix Raspall3(B)

<sup>1</sup> ICD, University of Stuttgart, Keplerstrasse 11, 70174 Stuttgart, Germany<EMAIL_ADDRESS><sup>2</sup> Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA<EMAIL_ADDRESS><sup>3</sup> DesignLab, Adolfo Ibanez University, 2700 Diagonal Las Torres, Santiago, Chile

<EMAIL_ADDRESS>
**Abstract.** The research presented in this paper focusses on the concept of "Diterial" which aims to merge digital design and fabrication technology with natural materials such as bamboo poles and raw timber. It proposes a digital workflow that uses sensing techniques to gain individual material information of natural, unprocessed construction resources and identify their individual strengths and characteristics and therefore its potential in load-carrying structures. This information is then used to develop bespoke designs and fabrication concepts, bridging the gap between unprocessed material and automated fabrication setups. Two case studies, developed to prove this concept, are described and compared. Both cases focused on the development of spatial structures using node-bar combinations of local resources.

**Keywords:** Visual sensing · 3D-printing · Robotic fabrication · Node design · Material analysis · Bamboo structures · Timber structures

# **1 Context and Relevance**

Natural grown resources such as raw timber and bamboo poles are important construction materials with a long history in architecture but have been relegated in favor of the nowadays dominant materials concrete or steel. The building sector is the major contributor to climate change, accounting for over 30% of global green-house gas emissions, 40% of global energy use and 50% of global waste [1]. Due to the climate crises, the dominance of concrete and steel is being contested. Rising prices on the commodity markets make regrowing local resources an important factor for the near future in Architecture Engineering and Construction (AEC).

Currently, the construction industry is based on standardization. This determines how natural materials are processed and used: irregular logs and poles, for example, are usually cut into slats or strips, which are then re-joined via gluing. The resulting semi-finished goods include glue-laminated bamboo panels or timber, chipboards or LVL, among others. This standardization paradigm presents several drawbacks. First, during processing, the unique and highly efficient individual characteristics that trees and bamboos develop while growing in a specific natural environment are largely lost. Second, the processing of materials is machine- and labour-intensive and discards a significant amount of material due to offcuts. Third, the gluing results in a worse energy balance of the material. For example, Glulam, LVL, plywood and OSB used 8, 16, 19 and 28% respectively of total energy consumption for resin production [2]. Finally, the standardization of components influences, at least to some extent, the standardization of architectural concepts and may results in similar construction and building typologies.

# **2 Material Scanning in AEC Industry and Research**

Scanning natural materials to identify their geometry and properties exist in the AEC industry today. The timber/sawmill industry implements high performance analysis tools like 3D scanners or computer tomography for logs. These are used to gain information of each individual piece of lumber and generate cutting plans optimize the production of construction elements according to standards and to cut out any defect like knots, holes or pitch pockets [3]. In the research community, the use of material information obtained through computer vision has been tested in a large variety of applications: it has been used to upcycle scrap material and inform robotic assembly sequences [4], to assemble small scale structures or establish material libraries of natural grown resources i.e. timber crotches [5], to identify the best fitting element and use it only processed at the connection points to build a bis scale structure for a barn. These and other examples show the immense capacity of material scanning for a smart (re) use in digital fabrication processes.

# **2.1 Di-terial**

The concept "Di-terial" investigates smart design-to-fabrication systems that bring together cutting-edge digital technologies and raw, natural-grown resources. Aiming to develop highly efficient loadbearing structures in architectural scale, they use local resources. Di-terial uses material scanning as a tool to understand the individual material properties that each natural element has and take advantage of its unique qualities (Fig. 1).

### **2.2 The Central Role of the Node**

This research evaluates the concept of Di-terial in the design of space frames. Space frames combine bars-linear elements- and nodes -points where bars converge- into a three-dimensional structural system. They are notable for being lightweight and extremely efficient structures. The separation of the structure into relatively small nodes and bars simplifies prefabrication in a controlled environment using technology unsuitable for onsite use and eases transportation to the construction site. Space frames can

**Fig. 1.** Detailed individual material information investigated in this research: section geometry (bamboo) and fiber orientation (timber)

be configured to achieve structures of almost any shape, size and use, and to dis- and reassemble them for a second life cycle if needed. The node design is crucial for space frame's flexibility and efficiency. The joining concept with the bar, the valence of the system, the structural design of system and a corresponding node performance are the main questions to answer for a successful node-bar system. During the 20th century the influence of mass- and prefabrication concepts for standardized constructions, has produced various node concepts. Above all, the developments of Konrad Wachsmann with the General Panel System for housing and the USAF Node for industrial, have undertaken the effort to enable greatest freedom possible with standard components. However, the nodal joint was too complex to be economically successful [6]. The simpler MERO-Node which was developed in 1937 and is still in use today, enables multiple configurations of space frameworks but is still limited to the geometric constraints of the node.

The digital design-to-fabrication methods of the recent years have introduced new ways for efficient production of one-off components. CNC-technology like Industrial robots have been used for custom node fabrication and the recent advancements in additive manufacturing enabled an even higher degree of customization of structural connectors [7].

# **2.3 Case Studies**

Two separate case studies were developed with researchers from Singapore University of Technology and Design (SUTD) in Singapore and Massachusetts Institute of Technology (MIT) in Massachusetts using natural grown resources from the local environment (bamboo in South East Asia and timber in New England). Both projects developed customized node-bar systems based on the concept of Di-terial. It was important for this research to enable a maximum variety of design possibilities, deriving from the individual structural strengths of each material.

With a node-bar system identified as the construction system, the natural materials were used for the bars and for the node in Singapore and Cambridge, respectively. Both projects developed design-to-fabrication processes which could use the material as barely processed as possible and find their best possible fit in complex but efficient structural system. Digital design methods were used to produce the bespoke node geometries (Fig. 2).

**Fig. 2.** 36/12 bespoke and digitally fabricated nodes merge the individual strength of natural grown resources in spatial frameworks

### **2.3.1 Case Study "bamboo3"**

The project "bamboo3" investigates the combination of 3D-printing technology and unprocessed bamboo. Forming hollow straight tubes by nature, bamboo poles appear to be the ideal base material for trusses and bar-node systems. A simple 2D- scanning process is used to gain precise inner and outer contour curves of the bamboo section, which was then used to inform the geometry of the bespoke connectors (Fig. 3).

**Fig. 3.** Collected bamboo, scanning of the section geometry and digital representation

As mentioned before, 3D-printing enables the fabrication of almost any shape, but especially the chosen method FDM-printing of biodegradable PLA, results in limited structural performance. Thus, it was decided to focus on structural systems, where the node only must react to normal forces but not bending moments. Examples (Fig. 4) are trussed beam structures (a) and triangulated grid shells (b), but also spatial grids like tetrahedral meshes (c), which was chosen for the final design (d). These systems, especially if irregular request an efficient fabrication of one-off node due to unique angle combinations and various node valences in case of the realized structure 3 to 9.

**Fig. 4.** Spatial structures in 2D (a: trussed beam/valence 2–5, b: triangulated grid shell/valence 2–3) and 3D (c: tetrahedral mesh/valence 2-n) were investigated and led to the final design (d: Sombra Verde/valence 3–9)

A Grasshopper© script using Karamba© [8] was written to compare load carrying capacity of the bamboo pole and structural requirements of the design to identify the bamboo thickness (Fig. 5a). The results were categorized in bamboo diameter *>*30, 40 and 50 mm and used to inform the node diameter at the node-bar connection (b). Combined with the information of mesh angles and valence, this input is used to automatically generate the node design (c) and print (d) the nodes.

**Fig. 5.** Structural analysis of the designed bamboo gazebo (a) led to the node and dowel (red) geometries (b), their implementation in the structure (c) and production via 3D-printing of a node

Conventional PLA based 3D-printers were used to produce the 238 unique connectors and 36 nodes that joined the 117 bamboo poles. The fabrication time varied between 21 and 128 h for the node elements and 1.5 to 4 h for the dowels, respectively. These elements formed "Sombra Verde" a shade providing structure in Duxton Plain park Singapore. The 3-legged, 6 by 8 m spanning structure was installed for 3 months during the "Urban Design week 2018" (Fig. 6).

### **2.3.2 Case Study "Structural Upcycling"**

The project "Structural Upcycling" investigates the use of robotically subtractive fabricated timber crotches. The typically Y-shaped crotches of deciduous trees form natural

**Fig. 6.** Installed bamboo gazebo "Sombra Verde" and node close-ups

cantilevers and present a complex fiber orientation. For this reason, they are usually discarded during the fabrication of standard timber products despite their structural potential in structures with similar structural requirements as the original crotches [9]. This case study takes advantage of this natural structural design, using the crotches as bending stiff nodes in node-bar systems.

Low-cost consumer-grade 3D-Scanners are used to generate a 3D-mesh of the crotch surface. The meshes are simplified and the original branch vectors determined. A material library, an inventory of scanned crotches, is established and used to match a developed design concept (Fig. 7).

**Fig. 7.** Sourced crotches are 3D-scanned to establish the material library

Since the design system is based on the use of predominately 3-valence bending nodes crotches (Fig. 8) honeycomb meshes (a), more patterns like Voronoi (c) or certain Archimedean solids were investigated to establish the final design (d).

It is also essential for the morphology of the nodes in the structure to match the branch vectors as closely as possible, to benefit from the fiber orientations in the crutches. Large mismatches between designed structural node and the assigned crutch result in a decrease of the structural performance of the node [10]. Therefore, a matching algorithm was developed to assign the best-fitting crutch to each node in the structure and adapt the structure's morphology to the inventory of available crutches (Fig. 9 a). This matching concept has been explained in a separate publication [11]. In theory, the crotch achieves the best structural performance unprocessed, when no fibers are cut. However, this results

**Fig. 8.** Spatial structures in 2D (a: hexagonal grid shell, b: Voronoi) and 3D (c: truncated Icosahedra) were investigated and led to the final design (d)

in several disadvantages, when the unprocessed nodes are joined with the standard linear elements. Therefore, the node design was developed based on the logic of a convex hull (Fig. 9 b, c), a geometry which represent the smallest convex structure to cover the contact faces and generates a triangulated node. The convex hull has two key benefits: it creates a geometry that is compatible with the standard lumber sections of the bars converging in the node, and it creates a geometry without valleys, which can be manufactured using simple planar cuts with a band saw. This case study takes advantage of this natural structural design, using the crotches as bending stiff nodes in node-bar systems.

A second algorithm generates a node geometry which fills the scanned crotch mesh and expands its for to maximize the use of material available in the crutch. The rectangular contact faces fit the corresponding bars and establish a well-balanced compromise between maximized material use, minimal fabrication time and matches one-off and standard components. For the fabrication, a robotic work cell was developed, in which an industrial robot holding a crutch was located in front of a standard bandsaw (d). The script automatically generates the cutting sequence, resulting in a time-saving production of one-off component with just a few straight cuts (between 12 and 25 in the case study). Thus, the fabrication time of the convex hull took between 13 and 35 min depending on dimension of the node and the number of faces, cutting depth and hardness.

**Fig. 9.** Matching crotches were placed in the designed mock-up (a) a convex node geometry (b), their implementation in the structure (c) and production via robotic band sawing of a node

A full-scale mock-up was developed and installed at the MIT School of Architecture and Planning. The prototype demonstrated that the workflow, from scanning of crutches to node generation and allocation in the structure, to the robotic fabrication and assembly, are fully functional. The results of the mock-up also served as preparation for a permanent structure which is currently in the planning phase. The crotches were sourced from trees that had been felled during a renovation process in an urban environment. The pieces not collected by the researcher had no value and were chipped immediately. 12 crotches were processed and joined with 19 1 ½ × 1 ½ inch bars to form this 4 m × 2 m prototype (Fig. 10).

**Fig. 10.** Exhibition of the mock-up to test the case study "Structural Upcycling"

# **3 Comparison, Conclusion and Outlook**

As described, both case studies focused on specific implementations of Di-terial, but, in retrospect, they would significantly benefit from each other's innovations.

*Bamboo3:* The creation of an inventory of all scanned bamboo poles was used solely to create bespoke connectors. However, this information could be used for alternative strategies such as optimizing the structure based on the actual moments of inertia or cutting longer poles into shorter pieces. Additionally, the node printing orientation was determined to minimize printing speed, but could have been optimized for mechanical strength.

*Structural Upcycling:* Due to time constraints, the bar elements in the project had a fixed section. Applying different section geometries would result in a higher efficiency of the material use. The algorithm developed to generate the nodes already includes this functionality. Additional information like material hardness could generate more effective libraries. Alternative geometries beyond the convex hull could exploit more efficient material performance. Additional studies investigated the matching potential of different tree species for designed geometries, based on their typical ratio of branch angles [12].

The projects presented in this paper, show two different, successful approaches to Diterial. They analyze and identify individual strengths of *natural grown local resources* using *material sensing*. A *Structural system*, which takes advantage of these specific strengths is defined, designed and structural analysis software calculates the designed structure. That way, the *Material placement* happens were needed. *Digital Fabrication Concepts* are developed to join natural-grown construction materials seamlessly in a well-balanced resource efficient system.

One of the major challenges of the 21st century is the design, planning and construction of sustainable building and structures. Natural-grown resources show an immense capacity for application in digital fabrication and sustainable architecture. As data acquisition, storage and processing become increasingly affordable and ubiquitous, new digital workflows such as those described in this paper, can be developed to take advantage of non-standard materials with more complex structures. In this way, individual characteristics of each naturally grown material component are computationally analyzed and its features considered an opportunity rather than a disadvantage.

**Acknowledgements.** We would like to thank our sponsors, contributors and researchers:

*Bamboo3:* Urban Redevelopment Authority and Lope Lab, AIRLab, Yuxin Hu, Sourabh Maheshwari, Jenn Chong, Anna Toh, Aurelia Chan, and Sihan Wu.

*Strucutral Upcycling:* MIT School of Architecture Woodshop, Autodesk Build Space Boston, Yijiang Huang, Kevin Moreno Gata, Daniel M. Marshall.

# **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# **Application of 6-Dof Robot Motion Planning in Fabrication**

Hao Wu, Ming Lu, XinJie Zhou, and Philip F. Yuan(B)

College of Architecture and Urban Planning, Tongji University, 1239 Siping Rd., Shanghai, China<EMAIL_ADDRESS>
**Abstract.** In practical robotic construction work, such as laying bricks and painting walls, obstructing objects are encountered and motion planning needs to be done to prevent collisions. This paper first introduces the background and results of existing work on motion planning and describes two of the most mainstream methods, the potential field method, and the sampling-based method. How to use the probabilistic route approach for motion planning on a 6-axis robot is presented. An example of a real bricklaying job is presented to show how to obtain point clouds and increase the speed of computation by customizing collision and ignore calculations. Several methods of smoothing paths are presented and the paths are re-detected to ensure the validity of the paths. Finally, the flow of the whole work is presented and some possible directions for future work are suggested. The significance of this paper is to confirm that a relatively fast motion planning can be achieved by an improved algorithmic process in grasshopper.

**Keywords:** Motion planning · Robot · Fabrication · Brick · Grasshopper

# **1 Introduction**

### **1.1 Motion Planning**

With the increasing variety of architectural forms, more and more buildings need to rely not only on procedurally generated forms but also on the assistance of machines or robots to do bricklaying and wall painting. In the case of bricklaying, for example, many successful projects have been built, such as the curved facade of the West Coast Pool House (Fig. 1). Since most of these projects are built on-site, robot obstacle avoidance, or robot motion planning, needs to be considered. Robot motion planning is a longstanding problem that is still being studied today, and a balance between computational efficiency and reliability needs to be found in practical projects.

In traditional robot construction, robot path planning can be taught manually point by point, but this is very time-consuming and labor-intensive. Nowadays, the mainstream approach is to make the robot's motion in the simulation, adding auxiliary points to avoid the obstacles in the program, and then generate the offline program. However, in this case, the user still needs to manually add auxiliary points and check whether the whole

**Fig. 1.** XiAn Chi She brick wall

process encounters collisions. So a better approach is to automate the motion planning to do the job.

In building construction, real-time has a great impact on efficiency, but the algorithm of motion planning is a very time-consuming and complex task. There are a large number of papers that study motion planning algorithms, and there are also many software and libraries that implement most of the mainstream algorithms.

# **1.2 Previous Work**

The algorithms for motion planning are divided into sampling point-based and potential field-based. Most motion planning libraries use sampling-based algorithms. The most famous work is the OMPL library, which is based on PRM [1], RRT, EST, SBL, KPIECE, SyCLOP algorithms, and several variants developed from them. Also, the OMPL library can work with many software such as Openrave, MoveIt, etc. Similar to OMPL, there are also planners such as CHOMP and STOMP. All of the above need to be used in Linux systems and require a certain knowledge base.

Vrep has the OMPL library as a built-in plug-in, and RoboDK comes with its own PRM motion planner. However, most architects are familiar with these sorts of software, they use Rhino as a robot simulation environment and program using grasshopper, and use software such as Kuka PRC and FUrobot to control the robot to work. The work in this paper is to implement path planning in the FURobot environment.

# **2 Research**

### **2.1 Potential Field**

Obstacles and target poses are known, so a potential field is formed by setting the obstacles to exert repulsive forces on the robot and setting the target poses to exert attractive forces on the robot. This method is the potential field method. The potential field method obtains the gradient according to the external situation and descends step by step to the lowest point, which is the target point, according to the guidance of the gradient. The advantage of the potential field method is that it does not require extensive calculations, so it can be done in real-time.

However, after actual experiments, it is found that the potential field method needs to set at least the coefficients of attraction, repulsion, and descent rate to establish a suitable potential field, so setting these three coefficients is the key. In the case of ordinary moving path planning with a two-link robot arm, the robot's configuration space is twodimensional, so the potential field is three-dimensional, and it is possible to clearly see the three-dimensional shape of the potential field to adjust these three coefficients. However, in a high-dimensional configuration space, such as the six-dimensional configuration space of a 6-degree-of-freedom robot, the generated potential field is 7-dimensional, so it is difficult to adjust the three parameters to obtain a suitable potential field.

Finally, the potential field method has local minima, which will make the potential field method unable to reach the target point poses. In summary, PRM based on sampling points is chosen in this paper.

# **2.2 PRM**

PRM [1] first creates a series of randomly different poses and eliminates those poses that encounter external objects and keeps the collision-free poses. After establishing a certain number of sample points, PRM searches for neighboring sample points around each sample point and connects the two sample points when found. If the motion path between these two sample points is collision-free, the connection of these two sample points can be added to the whole sample point map. Once all the sample points are connected, the Astar algorithm can be used to find the shortest route.

Since rotating 0 degrees is the same as rotating 360 degrees (the angles are in degrees), the following distance function is needed:

$$Dist(\theta\_{goal} - \theta\_{start}) = \min(|\theta\_{goal} - \theta\_{start}|, (360 - |\theta\_{goal} - \theta\_{start}|))$$

Because the energy required to rotate each axis is different, distance weights can also be added to these six-axis joints (six-axis joints per pose Ang), with specific weight values C that can be set according to the energy consumption and range of influence of the rotation.

Dist*(*Anggoal <sup>−</sup> Angstart*)* <sup>=</sup> <sup>6</sup> <sup>i</sup>=<sup>1</sup> Ci <sup>∗</sup> Dist*(*θistart <sup>−</sup> <sup>θ</sup>igoal*)*.

# **3 Implement**

### **3.1 Collision**

As mentioned above, when building a map of sampled points, collision detection needs to be performed for each sampled point. In practice, using the mesh-to-mesh collision detection in Rhino is too time-consuming, so the method needs to be simplified. Specifically, the robot parts are simplified to simple geometry, such as cylinders or spheres, and the external collision objects are simplified to multiple points, and then these basic geometric objects are used for collision detection, which will greatly improve the detection efficiency.

The robot's A2, A3, A4, and A6 joint positions are extracted and connected to form three axes, and by setting a safety radius, such as 200 mm for each axis, a cylinder can be formed correspondingly. In collision detection, choosing the cylinder speeds up the calculation. The collision detection is calculated by detecting whether the shortest distance between the external collision point and the axis of the cylinder exceeds the sum of the radius of the cylinder and the radius of the external collision point [2]. The A1 joint is not included because in general work, the robot is stationary and the range of motion of the A1 joint is not large, so the detection can be ignored.

In addition to the robot's own parts, the tool head also needs to perform collision detection on external objects. But the shape of the tool head is rather irregular. By default, we use a line segment from the flange plate to the tool head coordinates as the axis and set a relatively large safety radius. However, this is not a good simulation, and it would be more appropriate to add multiple cylindrical axes and corresponding safety radius to the tool head (Fig. 2).

**Fig. 2.** Using different cylinders as collision detection objects for robots

After the sample points are created, it is necessary to find neighboring sample points for each sample point and then test the lines between them for collisions. It is not appropriate to test the entire line segment for a large number of collisions, but rather to test as few as possible to ensure that there are no collisions. Such tests are not even necessary when the distance between sampling points is small.

Once the sample points are created, they can be saved, since they are valid as long as no new obstacle objects are added and only the robot's starting and target poses are changed. It has been tested that the time required to create sampling points is typically three to five times longer than the time required to calculate the shortest path.

### **3.2 Trajectory**

### **3.2.1 By Grasshopper**

The shortest path derived by the Astar algorithm is not a smooth path, we can use a polynomial least-squares fit or use Rhino's spline curve to smooth it.

The specific steps to use rhino's spline curve are:

1. Take the components of the first three axes A1, A2, A3 of the robot arm as the x,y,z components of the first 3d point. Then take the components of the last three axes A4, A5, and A6 as the x,y,z components of the second 3d point.

The path through the fit will change the pose of the shortest path generation (Fig. 3), so it is better to check the collision again.

This trajectory smoothing approach is relatively easy to implement, but requires the use of Rhino's existing commands, and in general situations, other approaches may be choosed.

**Fig. 3.** Smooth path after fitting

# **3.2.2 Polynomial**

After check, it is feasible to use polynomials to find the smooth path.  Rows 2 and 7 of X represent the axial joint velocities at the starting and final pose, respectively, which are stationary at both poses, so they are 0.  This is one of the reasons why the X matrix is designed in this way. In this case, the number of known poses is 5, so the dimension of the X matrix is the number of known poses plus 2(two velocity constraints), and so on for different number of known poses from PRM.

In the case of real-time control of the robot, the advantages of this method over the previous ones are:

**Fig. 4.** Polynomial, PRM and curve interpolate