# ADVANCES IN MECHATRONICS AND BIOMECHANICS TOWARDS EFFICIENT ROBOT ACTUATION

EDITED BY : Jörn Malzahn, Navvab Kashiri, Monica Daley and Nikos Tsagarakis PUBLISHED IN : Frontiers in Robotics and AI

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# ADVANCES IN MECHATRONICS AND BIOMECHANICS TOWARDS EFFICIENT ROBOT ACTUATION

Topic Editors:

Jörn Malzahn, Istituto Italiano di Tecnologia, Italy Navvab Kashiri, Istituto Italiano di Tecnologia, Italy Monica Daley, Royal Veterinary College, United Kingdom Nikos Tsagarakis, Istituto Italiano di Tecnologia, Italy

Image: sdecoret/Shutterstock.com

Citation: Malzahn, J., Kashiri, N., Daley, M., Tsagarakis, N., eds. (2019). Advances in Mechatronics and Biomechanics towards Efficient Robot Actuation. Lausanne: Frontiers Media. doi: 10.3389/978-2-88945-911-7

# Table of Contents

*05 Editorial: Advances in Mechatronics and Biomechanics Towards Efficient Robot Actuation*

Jörn Malzahn, Navvab Kashiri, Monica A. Daley and Nikos Tsagarakis

Svetlana Grosu, Carlos Rodriguez–Guerrero, Victor Grosu, Bram Vanderborght and Dirk Lefeber

*74 Efficiency and Power Limits of Electrical and Tendon-Sheath Transmissions for Surgical Robotics*

Christopher R. Wagner and Evangelos Emmanouil

*91 The Making of a 3D-Printed, Cable-Driven, Single-Model, Lightweight Humanoid Robotic Hand*

Li Tian, Nadia Magnenat Thalmann, Daniel Thalmann and Jianmin Zheng

Stefan S. Groothuis, Gerrit A. Folkertsma and Stefano Stramigioli

*137 Highly-Integrated Hydraulic Smart Actuators and Smart Manifolds for High-Bandwidth Force Control*

Victor Barasuol, Octavio A. Villarreal-Magaña, Dhinesh Sangiah, Marco Frigerio, Mike Baker, Robert Morgan, Gustavo A. Medrano-Cerda, Darwin Gordon Caldwell and Claudio Semini

# Editorial: Advances in Mechatronics and Biomechanics Towards Efficient Robot Actuation

Jörn Malzahn1 \*, Navvab Kashiri 1 , Monica A. Daley 2 and Nikos Tsagarakis 1

1 Humanoids and Human Centred Mechatronics Lab, Department of Advanced Robotics, Istituto Italiano di Tecnologia, Genova, Italy, 2 Structure and Motion Laboratory, Royal Veterinary College, London, United Kingdom

Keywords: energy efficient actuation, actuator design, actuator control, energetics of human locomotion, energetics of animal locomotion, bioinspired control, bioinspired design

**Editorial on the Research Topic**

### **Advances in Mechatronics and Biomechanics Towards Efficient Robot Actuation**

Biological systems such as animals and humans can be energetically autonomous for several days and some species endure even longer. Today's robotic systems aim to match the physical capabilities of their biological counterparts in terms of strength, agility, and dexterity, yet fail to display untethered operating times any longer than few hours. Changing this situation is challenging and likely requires fundamental shifts in the current paradigms for robot designs.

Today, new and promising paradigms have evolved from the recent advances at the interface of robotics and biomechanics. Robotics has become a prominent tool for validating and testing biomechanical models of animal locomotion, allowing direct testing of hypotheses about the mechanisms behind locomotion in nature. The physical implementation of the biomechanical models in robotic systems allows quantitative evaluation of theory and comparison between replicated movement and force patterns to those observed in biology. This approach has recently advanced our understanding of nature's locomotion principles, in particular for the integration of neural control and actuation for agile locomotion.

These new biomechanics insights are now being turned into novel mechatronic paradigms and solutions for dynamic and efficient walking robots and robust and lightweight robotic prostheses and orthoses. Conventional robot designs have been dominated by chains of rigid links with high transmission ratio non-backdrivable joints. The integration of intrinsically compliant components into robot designs has been researched for more than two decades now. However, we have only recently gained sufficient understanding to effectively exploit passive springs and intrinsically backdrivable low transmission ratio actuators for low inertia designs, with force sensing and control for efficient and impact resilient actuation. Impact resilience is especially important because impacts on the mechanism represent normal operating conditions for legged locomotion in unstructured environments and realistic terrain. Further insights on neural control in biological systems continues to spawn new paradigms for hierarchical and hybrid local/distributed control architectures. These bio-inpsired control advances help to tackle the task complexity involved in enabling robots to robustly perform in real-world scenarios outside the lab. Recent findings in this realm suggest that, in some cases, control loops need not run at high rates (> 1 kHz) to achieve robust performance. Sometimes closing a loop, with the associated delays and efforts to ensure stability, might not be advisable at all. Instead feedforward actions along with carefully shaped natural dynamics can lead to simpler, more robust and efficient solutions.

Edited and reviewed by: Giuseppe Carbone, University of Calabria, Italy

> \*Correspondence: Jörn Malzahn<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Humanoid Robotics, a section of the journal Frontiers in Robotics and AI

Received: 21 January 2019 Accepted: 04 March 2018 Published: 26 March 2019

#### Citation:

Malzahn J, Kashiri N, Daley MA and Tsagarakis N (2019) Editorial: Advances in Mechatronics and Biomechanics Towards Efficient Robot Actuation. Front. Robot. AI 6:19. doi: 10.3389/frobt.2019.00019

The present Research Topic joins research efforts from the robotics, control, and biomechanics communities toward novel robot design and control paradigms. The joint efforts included the organization of a physical work meeting in the form of a joint workshop on the energetic economy of robotics and biological systems during the International Conference on Intelligent Robots and Systems (IROS) on September 24, 20171 .

Given the interdisciplinary nature of the Research Topic, it is organized under the sections "Humanoid Robotics" and "Robotic Control Systems" within Frontiers in Robotics and AI as well as the "Bionics and Biomimetics" section with Frontiers in Bioengineering and Biotechnology. The collection of articles in this Research Topic captures a wide-angled perspective on the current state-of-the-art in robotic as well as biodynamic actuation modeling, analysis, design and control toward enhanced robot energy efficiency.

The wide-angled perspective is initialized with an overview article by Kashiri et al. on fundamental principles of locomotion inspired from natural biological systems, and principles for the design and control for efficient robot locomotion. As a foundation, Lee and Harris present and discuss a framework for quantitative evaluation of locomotion efficiency in animals and robots. The Research Topic further elaborates on some of the locomotor principles outlined in the overview with dedicated articles on minimally actuated walkers (Schroeder and Bertram) and articulated compliant parallel actuation arrangements (Roozing).

Nature demonstrates elegant solutions to minimize the inertia of moving limbs through remote tendon driven actuation. Several articles in the Research Topic are devoted to the potential and the challenges encountered during the technical implementation and application of such principles (Grosu et al.; Tian et al.; Wagner and Emmanouil).

Urbina-Meléndez et al. model and study how observability and state-estimation in balancing skills depends on the physical location of sensory organs. Nguyen et al. investigate the activation and response behavior of biological muscles. Engineers seeking to find suitable target functions for actuator designs or optimal sensor placements in their robots can greatly benefit from these insights, which emerge from millions of years of natural evolutionary design iterations.

Nature seems to effortlessly manage complexity, not only concerning growing and self-regenerating biomechanics, but also considering efficient and effective control of millions of cells, sensors and muscle fibres. In this Research Topic Groothuis et al. address this topic in the context of energy aware control across distributed control hierarchies as observed in biology and—with the aim to manage system complexity—also applied to technical systems (Barasuol et al.).

Apart from mobile and legged robots, the direct beneficiaries of the mutual insights in biodynamics and robotics engineering are humans. This Research Topic includes examples of robotic rehabilitation systems (Ghannadi et al.) as well as assistive robotic devices such as passive and active prostheses (Jeffers and Grabowski; Tahir et al.) to improve or recover the quality of life.

The editors hope that the results presented in this Research Topic will catalyze the advent of new robots and assistive robotic devices with enduring energetic autonomy, which will help us tackle the upcoming societal and economic challenges. At the same time the presented works report unique and invaluable experimental data that help verifying and refining theories as well as hypotheses striving to understand the nature of the species living on our planet (Nguyen et al.; Urbina-Mele'ndez et al).

## AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

## ACKNOWLEDGMENTS

We gratefully acknowledge the kind support of the Frontiers Editorial Team during all stages of this Research Topic. Moreover the authors would like to thank all authors for submitting their high class works, which have truly rendered this Research Topic an all-inclusive image of the current state-of-the-art in efficient robotic actuation. Last but not least, we would like to express many thanks to all reviewers, who have contributed their time and effort to provide valuable suggestions and enhancements to the articles presented in this Research Topic.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Malzahn, Kashiri, Daley and Tsagarakis. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

1https://energeticeconomyrobotics.wordpress.com/

# An Overview on Principles for Energy Efficient Robot Locomotion

Navvab Kashiri 1 \*, Andy Abate2 , Sabrina J. Abram3 , Alin Albu-Schaffer 4 , Patrick J. Clary 2 , Monica Daley 5 , Salman Faraji 6 , Raphael Furnemont 7 , Manolo Garabini 8 , Hartmut Geyer 9 , Alena M. Grabowski 10, Jonathan Hurst 2 , Jorn Malzahn1 , Glenn Mathijssen7 , David Remy 11, Wesley Roozing1 , Mohammad Shahbazi 1 , Surabhi N. Simha3 , Jae-Bok Song12, Nils Smit-Anseeuw11, Stefano Stramigioli 13, Bram Vanderborght 7 , Yevgeniy Yesilevskiy 11 and Nikos Tsagarakis 1

1 Humanoids and Human Centred Mechatronics Lab, Department of Advanced Robotics, Istituto Italiano di Tecnologia, Genova, Italy, 2 Dynamic Robotics Laboratory, School of MIME, Oregon State University, Corvallis, OR, United States, 3 Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, Canada, 4 Robotics and Mechatronics Center, German Aerospace Center, Oberpfaffenhofen, Germany, 5 Structure and Motion Laboratory, Royal Veterinary College, Hertfordshire, United Kingdom, 6 Biorobotics Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 7 Robotics and Multibody Mechanics Research Group, Department of Mechanical Engineering, Vrije Universiteit Brussel and Flanders Make, Brussels, Belgium, 8 Centro di Ricerca "Enrico Piaggio", University of Pisa, Pisa, Italy, 9 Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, United States, 10 Applied Biomechanics Lab, Department of Integrative Physiology, University of Colorado, Boulder, CO, United States, 11 Robotics and Motion Laboratory, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, United States, 12 Department of Mechanical Engineering, Korea University, Seoul, South Korea, 13 Control Engineering group, University of Twente, Enschede, Netherlands

#### Edited by:

Francesco Becchi, Danieli Telerobot Labs, Italy

#### Reviewed by:

Wiktor Sieklicki, Gdansk University of Technology, ´ Poland Giovanni Stellin, Danieli Telerobot Labs, Italy

> \*Correspondence: Navvab Kashiri<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Humanoid Robotics, a section of the journal Frontiers in Robotics and AI

Received: 18 March 2018 Accepted: 01 November 2018 Published: 11 December 2018

#### Citation:

Kashiri N, Abate A, Abram SJ, Albu-Schaffer A, Clary PJ, Daley M, Faraji S, Furnemont R, Garabini M, Geyer H, Grabowski AM, Hurst J, Malzahn J, Mathijssen G, Remy D, Roozing W, Shahbazi M, Simha SN, Song J-B, Smit-Anseeuw N, Stramigioli S, Vanderborght B, Yesilevskiy Y and Tsagarakis N (2018) An Overview on Principles for Energy Efficient Robot Locomotion. Front. Robot. AI 5:129. doi: 10.3389/frobt.2018.00129 Despite enhancements in the development of robotic systems, the energy economy of today's robots lags far behind that of biological systems. This is in particular critical for untethered legged robot locomotion. To elucidate the current stage of energy efficiency in legged robotic systems, this paper provides an overview on recent advancements in development of such platforms. The covered different perspectives include actuation, leg structure, control and locomotion principles. We review various robotic actuators exploiting compliance in series and in parallel with the drive-train to permit energy recycling during locomotion. We discuss the importance of limb segmentation under efficiency aspects and with respect to design, dynamics analysis and control of legged robots. This paper also reviews a number of control approaches allowing for energy efficient locomotion of robots by exploiting the natural dynamics of the system, and by utilizing optimal control approaches targeting locomotion expenditure. To this end, a set of locomotion principles elaborating on models for energetics, dynamics, and of the systems is studied.

Keywords: variable impedance actuators, energy efficiency, energetics, cost of transport, locomotion principles, bio-inspired motions

## 1. INTRODUCTION

The recent development in design and control of active or intrinsically controlled Variable Impedance Actuators (VIA) has demonstrated remarkable advancements in safety, robustness and peak power performance. However, despite the above, considerable performance improvements and progress made in the past 20 years in mechatronics and control, the motion/locomotion efficiency of even the most energy efficient robots still remains many times smaller than that of humans or animals. Due to these deficiencies there are several untethered applications (humanoids, manipulators, assistive and power augmentation exoskeletons, prostheses) where the limited power autonomy prevents their full practical exploitation. The advancement on robotic economy will therefore substantially impact the viable exploration of robotics in all applications requiring untethered operation. To enable this progress, new design principles and technologies are needed.

This paper1 reviews the recent advancements in new robot design principles and control that target to reduce their energy consumption and lead to robots that are more efficient. The main objective is to present an overview of recent activities on the development of these new robot machines. Emerging topics to improve energetic performance of these robotic systems include novel joint-centralized variable impedance actuation, energy neutral intrinsic load cancellation and lock/release mechanisms, variable recruitment actuation principles, bioinspired distributed compliance actuation, embedded energy buffering and high efficiency power transmission concepts. The exploration of control principles for effective energy recycling and load cancellation during motion is also fundamental for improving the energy efficiency of these machines and will also be discussed with an emphasis on techniques for the exploitation of intrinsic resonance modes and energy efficient impedance regulators for under-actuated variable impedance or multi-articulated robots. Contributions on the biological side, particularly on the energy economy of humans and animals as well as on the biomechanics of locomotion efficiency, are complimentary and will provide the ground reference for today robot efficiency as well as set the energy efficiency goal of future robotic machines. In summary, we aim at demonstrating recent developments in mechatronics and control with a focus on the energy economy of robotic systems, to advance the understanding of actuation and control principles contributing to energetic economy in biological systems, humans and animals.

To clarify the energy efficiency of current robotic systems, we compare the Specific Resistance2 (SR) of biological systems with that of robots. For instance, a horse trots with a SR of 0.2, and humans walk with a similar SR of 0.2. Based on the data reported by Tucker (1975) for Cost of Transport (CoT) of humans and animals, passive walkers (see the work by McGeer, 1990) are considerably more efficient than humans as shown by Collins et al. (2001), although they possess very limited flexibility in terms of functioning versatility and demand carefully dynamics tuning of operating conditions e.g., initial states. Humanoid robots that are capable of replicating human-like motions and executing human tasks, however, render fairly larger CoT/SR as compared to humans: Asimo presented by Sakagami et al. (2002) exhibits an SR of 2 (1.8 KW for 1.5 m/s, with a mass of 54 kg) and Durus introduced by Reher et al. (2016) targets an SR of 1. These are amongst the most efficient humanoids robot while the CoTs of them are ten and five times larger than human CoT, respectively. Similarly, the hydraulically actuated Big Dog operates with an SR of 15 that limits the autonomous operation time to about 30 minutes given the fuel capacity limitation (15 L of fuel for 20 Km, with a mass 110 kg). On the other hand, mammalian skeletal muscle exhibits a power density of 0.041 W/g and has about a 25% efficiency for concentric muscle action, while a motorized actuator can render higher values. An individual motor can possess a power density of 0.5 W/g and about 80% efficiency, although theses values may drop to 0.17 W/g and 40% when combined with a typical gearbox, respectively. Yet, the MIT cheetah actuators that exploit electrical energy regeneration/recycling demonstrate an SR of 0.5.

To understand efficient motion, we analyse human walking/running. Human locomotion comprises mostly unforced motion, where back-drivability significantly enhances the efficiency, and presents considerable energy storage due to recycling. Power consumption of the Walk-Man robot developed for performing disaster response tasks as the primary target, introduced by Tsagarakis and et al. (2017) requires about 387 W for electronics (45 W for perception system, 62 W for two processing units, and 280 for 36 motor driver electronics), and the total power consumption for standing is about 420 W. Slow walking (20 cm per second) requires a total power of 510–755 W in the most demanding condition. This shows that the maximum consumption includes an actuation power of 368 W; thereby representing an SR of 1.35. This describes an SR seven times higher than that of human walking only for actuation, while the total consumption expresses an SR of 2.8 which is 14 times larger than that of human walking. However, the lack of efficiency in comparison with humans is expected as the energy storage capacity of the system is limited to passive compliant elements with small deflection, that leads to large energy consumption for moving/accelerating joints. The other significant cause is the high gearing that renders large reflected inertia and results in a strict need for forced motions.

By incorporating the passive dynamics, as well as kinematic and actuator optimizations, the energetics performance of the robot can be significantly improved. Preliminary experiments on the bipedal robot CASSIE show that the 30 kg robot can walk at 1.0 m/s using a total of 200 Watts of power while performing different locomotion behaviors such as squatting, thereby rendering an SR of 0.7. This efficiency is owed to not only added compliance, but also to a leg design that (i) selects actuator/transmission through a joint-level actuator work minimization for performing walking tasks, see Rezazadeh and Hurst (2014); (ii) designs minimal toe inertia to reduce ground impacts, see Abate et al. (2015); (iii) utilizes a leg kinematics configuration which balances net task power among involved actuators (see Abate et al., 2016). Advancement in energy efficiency of robotic systems requires attention in various aspects of the robot operation problem, ranging from actuation and limb design to motion control. **Table 1**3 presents a comparison between the energetics of biological systems and current robotic

1Contents of this paper are mainly based on the presentations of IROS 2017 workshop titled "On the Energetic Economy of Robotics and Biological Systems: a challenging handicap to overcome".

2 Specific resistance is an index used to evaluate the energy efficiency of a mobile robot. It is defined as the ratio of the total energy consumption E for a travel of a distance d to the gravitational potential energy when the robot is lifted by the distance d, i.e., E Mgd with M and g representing the robot mass and gravitational acceleration; reported also by Kajita and Espiau (2008). This measure is equivalent to Cost of Transport (CoT).

3biological systems data is extracted from https://en.wikipedia.org/wiki/Muscle, Basalmetabolicrate,Humanbrain,Foodenergy

systems. This paper reviews recent advancements in design and control of robots, to elucidate the energetic state of current robotic and mechatronic systems in comparison with biological systems, and to derive insights and features for the development of more energy efficient robots. The rest of the paper is structured as follows: section 2 reports the variety of compliant actuators propounded for enhancing energy efficiency of robots, (see **Figure 1**). Section 3 discusses the importance of limb segmentation in design, dynamics and control, and how the robot design should rely on this information. Section 4 discusses a set of state-of-the-art energy efficient control methods on the basis of bio-inspired and optimal control principles. Section 5 describes a set of cutting-edge concepts initiating novel directions for robot locomotion. Finally, the paper summary is described in section 6.

## 2. COMPLIANT ACTUATION

Despite the potential of most electric motors for electrical energy regeneration, it is not often used in robotic systems, except for highly dynamic robots using direct drives e.g., cheetah robot presented by Seok et al. (2015). The lack of use is likely due to substantial losses in high gear reduction systems typically used in robotics requiring high torques, as discussed by Verstraten et al. (2015), thereby rendering significant copper losses (heat produced by electrical currents in motor windings) and leading to trivial energy regeneration. Furthermore, the actuation systems typically suffer from having the link and motor in a series chain. As a result, all torques pass from the motor, and even in stationary conditions, i.e., zero mechanical power, there is a non-negligible electrical energy consumption. Mechanical storage mechanisms/methods are therefore exploited in robotic machines, which often rely on integration of passive elastic elements into actuation units. Nevertheless, a suitable choice of a mechanical storage system cannot be based only on the mechanical energy domain. As discussed in Verstraten et al. (2016), the dynamics of reduction system and motor dynamics, as well as the operating position and range of motion, influence the optimal compliance and whether series and/or parallel

compliance is more beneficial. As shown in Beckerle et al. (2017), while the use of compliance in series with the motor can often be more energy efficient, compliance in parallel may become more beneficial when the operating point changes (therefore more static force).

As animal structure and motion have simultaneously evolved to be specifically designed to perform desired tasks efficiently and effectively, it is essential to account for both morphology and motion in robot design and control. Yesilevskiy et al. (2015, 2018a) discussed the effect of morphological variations in legged robots, and showed for a one-dimensional monoped hopper that is driven by a geared DC motor, with the correct choice of the transmission parameter, a hopper with Series Elastic Actuators (SEA) is more energetically efficient than one with Parallel Elastic Actuator (PEA). It is mostly due to the fact that, for a hopper with PEA, the motor inertia contributes to energetic losses due to the ground contact collisions. The energy saving capacity of this kind of compliance arrangement had been shown not only when used in legs, but also when used in torso structure as shown by Folkertsma et al. (2012). In all these cases, the natural mechanical dynamics connect the motion of a robot or animal to its morphology, thereby inherently coupling control and design of such systems.

## 2.1. Compliance in Series

The incorporation of built-in compliance into robot joints was primarily introduced to enhance the shock tolerance capacity via generation of inelastic collision force spikes, system responsivity due to higher force control bandwidth, and energy efficiency by cycling the energy flow; as well as amplifying output power. To address the limited storage capacity of the passive compliant component, various designs enabling larger deflection were proposed, e.g., by Tsagarakis et al. (2009). As presented by Verstraten et al. (2016), the inclusion of compliance in parallel or in series allows a decrease in both peak power and energy consumption provided that the stiffness of the elastic element is tuned properly, and substantiates the development of variable stiffness actuators, see Vanderborght et al. (2013).

Nevertheless, compliant systems exhibit unwanted vibrations that require inclusion of active, semi-active and passive damping. While active impedance control has been widely studied, e.g., by Ferretti et al. (2004); Kashiri et al. (2014b), the active dissipative action is often limited by the control-loop bandwidth, and suffers from feedback noise and phase-lag problems. The semi-active and passive damping therefore proved to be more effective as presented by Laffranchi et al. (2014) and Kashiri et al. (2017a). However, the inclusion of damping amplifies the complexity and total mass of the system. The former escalates the development and maintenance costs, and the latter reduces the energy efficiency. Moreover, semi-active solutions require additional controllers that intensify the complexity of the system, e.g., see works by Kashiri et al. (2014a), Kashiri et al. (2015), and Kashiri et al. (2016). As a result, despite the proven energy consumption reduction achieved by such systems, the utilization of variable impedance solutions, when considering the additional hardware/software complexity, requires careful attention to the application requirements.

## 2.2. Compliance in Parallel

## 2.2.1. Asymmetric Configuration

To develop a robotic actuator that combines high power and physical robustness with energetic efficiency, Tsagarakis et al. (2013) proposed an asymmetric compliant antagonistic joint concept, and developed a 1-DOF knee-actuated prototype leg. The novel design featured variable quasi-static load compensation, moderate gearing, large energy storage capacity, and controllable energy storage/release. It includes two branches working in parallel to each other: a high power branch, and an energy storage branch. The first branch embodies a series elastic actuation system, with an elastic element serving as a bi-directional coupling between the drive and the output link, protection of the drive unit, and torque sensing as demonstrated by Kashiri et al. (2017b). The second branch includes a low power motor coupled with a high reduction efficient linear transmission in series with a passive elastic transmission, and an elastic element with large energy storage capacity. To achieve this, it uses an elastic band similar to bungee cords, instead of metal springs. The coupling between the low power drive and the elastic element is done using a non-backdrivable transmission component, and a two-way overrunning clutch module, to remove the effort for maintaining pretension of the elastic element. On the basis of this concept, Tsagarakis et al. (2014) demonstrated the efficiency benefits of the large energy storage capacity in cyclic motion operations and in static load compensation in a unit with Series Parallel Elastic Actuator (SPEA). Roozing et al. (2016b) further expanded the work and proposed an integrated control strategy that actively utilized both branches, and experimentally demonstrated a 65% reduction in electrical power consumption when compared to conventional SEA.

Roozing et al. (2018) presented the development of a semi-anthropomorphic 3-DOF leg design, where series elastic actuation units are complemented with parallel high efficiency energy storage branches. Based on the earlier work in Roozing et al. (2016a), three exchangeable actuation configurations were described, where the energy efficiency achieved by parallel elasticity branches in mono- and bi-articulated configurations is demonstrated, as compared to a series-elastic-only configuration as a baseline. In biomechanical systems, biarticulated muscles span multiple joints and thereby allow the transfer of mechanical power between joints. Similarly, in the bi-articulated actuation configuration, the energy storage branch allows the transfer of mechanical power between the robotic knee joint and ankle joint. The multi-DOF energy storage branch system can thus provide a desired torque profile over the range of motion in an efficient manner to obtain minimal energy consumption and/or maximum gravity compensation. Additionally, it can increase peak torque output and assist in explosive motions such as pushoff during running. The leg presented in Roozing et al. (2018) performed a set of squat motion in three different configurations: without parallel elastic storage, and with parallel elasticity in mono-articulated and in bi-articulated configurations, with overall masses of 7.57, 9.14, and 9.21 kg, respectively, and exhibiting 33.1, 15.4, and 13.2 W electrical motor power when lifting 20 kg by 25.6 cm. On the other hand, humans4 consume approximately 41, 53, and 54 W to perform a similar squat motion, for the overall mass of afore-mentioned configurations. If we account for efficiency of actuation in both cases (20% in muscles and 40% in robotic drives), the mechanical output power of the robotic leg is 13.2, 6.2, and 5.3 W, while that of humans is 8.2, 10.6, and 10.8 W; confirming the importance and effectiveness of parallel elasticity units.

## 2.2.2. Symmetric Configuration

Due to a strong demand for energy-efficient, yet low-cost, robotic arms, it is necessary to minimize the torque required to operate a robot while maintaining high performance. Considering robots developed for interaction purposes often operate at low speeds, the dominant torque is to carry the robot weight, especially when the payload to robot mass ratio is low. Gravity compensators can therefore save a significant amount of mechanical energy. It is therefore beneficial to counterbalance the gravitational torques resulting from robot mass, and accordingly employ the motor efforts for gravitational torque of varying payload and the inertial torques. Despite several advancements toward such efficient robotic manipulators using spring-based counterbalancing, the majority of such systems are often bulky and heavy, with a small range of rotation, and their utilization is limited to a one or two DOFs, see designs proposed by Koser (2009),

4We used the relation extracted in Robergs et al. (2007); however, we used twice the mass value, i.e., 55.14, 58.28, and 58.42 kg, as the formula was extracted from data corresponding to two legs (and significantly larger mass than the prototype), and then we divided the output power by two. Moreover, we subtracted a basic metabolic power of 80 W from the overall value as we compare with the prototype's electrical motor power.

Nakayama et al. (2009), and Lacasse et al. (2013). Passive gravity compensation using a counterbalance spring-based mechanism can rely upon various concepts, including (1) Wire-based systems, e.g., the service robotic arm proposed by Kim and Song (2014); (2) Gear-based devices; (3) Linkage-based mechanisms, such as the slider-crank based system developed by Kim et al. (2016). Given a multi-DOF manipulator, it is necessary to deal with continuously varying gravitational torques that depend on the robot configuration, thereby increasing the need for multi-DOF counterbalancing.

A possible solution to this problem is the development of a mechanism with a reference plane corresponding to each link, so that the spring counterbalancing the gravitational torques connects the link to this reference plane, and accordingly compensates for the gravitational torque of each link independently. Such a reference plane therefore is required to automatically align with the gravity direction, and enables proper linking with neighboring reference planes in a way that the compensated torque is transmitted to the ground, and the motion of one link does not affect others. On the basis of this concept, Korea University developed a series of spatial robots with multi-DOF counterbalancing features: including SCORA-H, SCORA-V, and KU-WAD. The latter employs a counterbalance mechanism based on two sections: (1) Spring and wire: to generate the compensation torque exhibiting zero counterbalance error; (2) Timing belt and pulley: to provide a suitable reference plane interconnection, and render a wide operation range without dead points. Experiments on SCORA-V (with six DOFs, 49 kg mass and 8 kg payload capacity) show significant mechanical and electrical energy savings thanks to the mechanical gravity compensation feature. Without using the gravity compensation system, the robot requires about 160 W for maintaining a high gravity posture and consumes 170 Wh for 1 h of operation (a repetitive task), while these values reduce by 34 and 30% by exploiting the counterbalancing mechanisms, respectively. Such a reduction in electrical energy consumption enables the use of smaller motors and gearing transmission systems in the design process, and saves a considerable amount of energy in the long-term use of a robot.

## 2.3. Compliance in Series/Parallel With Locking Mechanism

Another solution addressing actuation inefficiencies was presented by Plooij et al. (2016); Geeroms et al. (2017), that exploits Lockable Parallel Elastic Actuator (LPEA), as well as series elasticity. Experiments on a knee prosthesis powered by this actuator showed an energy consumption of 65 J/stride and peak power of 100 W, which are considerably lower than those generated by the same system powered by a direct drive (400 W and 156 J/stride) and SEA (200 W and 98 J/stride). Mathijssen et al. (2016) proposed another potential solution: the use of redundancy in actuation when a set of lockable SEAs (LSEAs) are set in parallel, to show a clear difference in mechanical energy consumption due to parallel springs that can be loaded with respect to any desired position. However, Verstraten et al. (2018) discussed the advantages of exploiting actuation redundancy in a more generic case, i.e., a multi-motor drive as compared to a single drive, to present smaller size and mass, and more importantly, a considerably higher efficiency for slower speeds, and larger static operation range; although it shows lower maximum efficiency, and slightly lower bandwidth. Mathijssen et al. (2017) discussed a similar concept for development of a discrete muscle-inspired actuator, presenting how this approach allows overpowering binary drive units (solenoids).

Chen et al. (2013) presented the employment of a locking mechanism in parallel with compliance in series, in order to store and release energy at the right time. Malzahn et al. (2018) discussed the employment of locking mechanisms (clutch) in series with the drive train possessing compliance in series, i.e., Lockable SEA (LSEA). The work is inspired by human muscle activity in different phases of running. As presented by Novacheck (1998), while the stance phase requires highly active motion of the joints to overcome gravitational torque, motion of the joints during the swing phase is passively driven by gravitational and inertial link torques. It is therefore more efficient to relax the muscles during the swing phase of running and exploit the passive dynamics of the system. However, the high transmission ratios used in conventional electric robot actuation do not permit such an operation. The transmission ratio trades the high speed of electric drives for increased output torques, which enable high torque density actuator designs. But, the transmission ratio steps up the motor as well as gearing friction torques, which render the actuation barely backdrivable by gravitational and inertial torques. Unlike in the human example, the motor therefore has to actively drive and overcome the intrinsic friction throughout any motion phase. As an alternative to direct drives, a clutch mechanism in series between the transmission and the link can be utilized so that the conventional mature high torque density drive unit can be partially/fully disengaged when the passive dynamics can partially/fully generate the required motion. The energy saving potential of the series clutch approach depends on the motion dynamics and the ratio between the link gravitational and motor friction torques. The theoretical savings range between 20 and 60 % of the mechanical energy required to perform the same motion compared to the identical drive without series clutch actuation.

## 2.4. Purely Passive Compliance

While robotic platforms often utilize active joints, with and/or without Passive Elasticity (PE) integrated as discussed above, fully passive compliant joints are not often used except for endeffectors such as feet. However, they are commonly used in leg prostheses, where metabolic and biomechanical effects of people with lower extremity amputations is of utmost importance. Herr and Grabowski (2012) presented a powered prosthesis (BiOM) that enables people with a transtibial amputation to achieve normative metabolic costs, preferred walking speeds, and step-to-step transition work while walking over level ground across a wide range of speeds. D'Andrea et al. (2014) showed that use of the BiOM enhances the regulation of whole-body angular momentum, and therefore reduces fall risk. Grabowski and D'Andrea (2013) found that use of the BiOM reduces unaffected leg knee loading and thus osteoarthritis (OA) risk. Jeffers et al. (2015) compared changes in metabolic power and mechanical power during step-to-step transitions while nonamputee subjects walked on a range of slopes at different velocities. They found that at faster velocities, metabolic power increased, the leading leg absorbed more power, and the trailing leg generated more power compared to slower velocities. Moreover, with increasing slopes, mechanical work of the leading leg became more negative while mechanical work of the trailing leg became more positive. Jeffers and Grabowski (2017) also found that use of the powered prosthesis (BiOM) compared to a passive-elastic energy storage and return (ESAR) prosthesis, improves biomechanics and metabolic cost on uphill slopes.

To discuss the effects of compliance and geometry of a class of passive-elastic running-specific prostheses in series with the leg, a set of this class of prostheses developed by manufacturers based on subjective stiffness categories was studied. Beck et al. (2016) found that the prosthetic stiffness values of these manufacturer recommended stiffness categories varied between prosthetic models. They also found that the force-displacement profiles of such prostheses are curvilinear, indicating that prosthetic stiffness varies with the magnitude of applied force. Beck et al. (2017) investigated the effects of running-specific prosthetic stiffness, height and speed on the biomechanics of a set of athletes with bilateral transtibial amputations. They found that with use of stiffer prostheses, athletes could apply greater peak and stance average vertical ground reaction forces, increase overall leg stiffness (inversely associated with running speed), decrease ground contact time and increase step frequency; although these effects were reduced at faster running speeds. The effects of ±2 cm changes in prosthetic height on biomechanics (inversely associated with step frequency) were unchanged. It was also shown that J-shaped running-specific prostheses often outperform C-shaped prostheses in terms of both metabolic CoT and maximum speed in athletes with transtibial amputations.

## 3. SEGMENTED LIMBS

Periodic motions such as crawling, walking, and running, are typical tasks in which energy storage and release frequently occur; where muscle and tendon elasticity plays the most important role in biology. Efficient generation of such motions requires realization and characterization of periodic oscillations. Eigenmodes of linear dynamics have been widely used for rendering such motions based on the classic generalized eigenvalue problem (see works by Blickhan, 1989; Geyer et al., 2006; Kashiri et al., 2017c).To approach the performance and efficiency of the biological archetype, it is crucial to employ physical elasticity in drive units. To exploit the full dynamics of segmented legs, Lakatos et al. (2017) described eigenmodes of non-linear dynamics. Such a complete modal model can enhance the system performance as the robot design targets match the segmented leg dynamics with a desired dynamics set based on template models, e.g., Spring-Loaded Inverted Pendulum (SLIP), and desired motion considerations. While the robot structure design relies primarily upon geometry specifications, statics requirements, and actuation principles; design of kinematics, elasticity and inertial parameters respecting the above-said matching dynamics initiates a mechanical system with an embodied modal task, as discussed by Duindam and Stramigioli (2005). Such a design can significantly facilitate the robot control; similar to humans who excite the resonance by means of timed and directed motions.

Geyer et al. (2006) discussed the significance of segmented leg dynamics, which are often ignored, thereby creating untapped potential for improved mechanical energetics and control. Exploring point mass models whose legs are reduced to force laws shows that increasing the number of leg segments helps to reduce the mechanical advantage of leg force with less burden on joint actuators, i.e., lower joint torques; however, it also increases the design complexity. In addition, multiple segments create internal degrees of freedom, which introduce joint buckling in elastic stance leg behavior. Seyfarth et al. (2001) showed different strategies to mitigate this destabilizing effect from segment length changes (non-equal lengths) to non-linear joint elasticities to biarticular actuation. Such remedies enlarge the design complexity. In addition, studies on human locomotion revealed the swing leg dynamics are double-pendulum like and appear nearly passive, as reported by Mochon and McMahon (1980). However, the motion of a double-pendulum is chaotic if not properly restrained. Potential field calculations of the foot point (using energy neutral coupling springs) show that the double pendulum can be suitably restrained by passive bi-articular coupling, resulting in natural and comparably robust swing leg behavior. Overall, these two examples show leg segmentation introduces significant challenges to locomotion dynamics, which if they are ignored, lead to increased control effort and actuator energy expenditure.

The knowledge gained from studying the effects of leg segmentation can benefit the control of robotic limbs. Desai and Geyer (2012, 2013) showed the influence of incorporating active bi-articular coupling into nonlinear swing leg control to generate natural swing leg motions without pre-recorded reference trajectories. Moreover, the resulting control approach can position the leg into a wide range of target postures with robustness to large swing disturbances. On the basis of this concept, Thatte and Geyer (2016) formulated a control policy for powered knee-ankle prostheses. Simulation results suggest this policy generates human-like leg behavior in steady walking, and responds to disturbances to the swing leg with experimentally observed elevation and lowering strategies. Furthermore, a comparison with the performance of an impedance controller shows the proposed policy enables a computer model of an amputee to walk over rough terrain and recover from larger disturbances.

## 4. ENERGY EFFICIENT CONTROL

Efficient motion of robotic systems can be based on various principles. A majority of studies in this area employ optimal control techniques and bio-inspired approaches. Another paradigm for the control of such systems is energy-aware robotics that targets energy flows, especially in interactions. This provides a basis to constructively tackle issues of stability during interaction and methods to analyse energy storage and consumption in robotics systems. Stramigioli (2015) and Folkertsma and Stramigioli (2017) elaborated the basis of this concept to present a universal framework that models drive and interacting robotic systems, as the basis for energy-limited control, so that the actuation controllers can expend an energy budget to execute a given task, without injecting more energy. Below, we discuss a set of state-of-the-art optimal/bio-inspired approaches.

## 4.1. Natural Motion

Development of systems capable of executing efficient cyclic motions requires the exploitation of the robot's natural dynamics (McGeer, 1990; Collins et al., 2005; Ferris et al., 2007). Mechanisms for efficient natural dynamics have often been inspired by studies of the agile and efficient dynamics of human and animal locomotion (McMahon, 1985; Ferris et al., 1998, 2007; Full and Koditschek, 1999; Daley and Biewener, 2006; Geyer et al., 2006). A bio-inspired Central Pattern Generator (CPG) approach is one commonly-used method for rendering cyclic motions, as explored by Ijspeert (2008). However, the method relies upon an isolated unit to generate a periodic motion pattern. The control structure is thus open-loop as the controlled system feedback is not considered in the control. Furthermore, the oscillatory dynamics of the elastic body (robotic or biological) system are not exploited. To identify/realize the resonance excitation mechanism of humans, Lakatos et al. (2014) carried out a set of psycho-physical experiments including a human in the control loop; when the human is asked to excite a simulated elastic limb to a limit cycle in minimum time or with minimum effort, and the force feedback device displays to the human the forces from simulation. To estimate human adaptability, the limb parameters are arbitrarily varied in simulation. The results revealed a bang-bang control law switching the position reference around an equilibrium point when the force feedback changes direction. Lakatos and Albu-Schäffer (2014b) exploited this switching control approach for generating limit cycle motions. In order to excite a multidimensional, non-linear elastic multi-body system, Lakatos and Albu-Schäffer (2014a) proposed to apply the bang-bang controller in the torque transformed direction, and compute the corresponding reference joint positions from the modal coordinate. Lakatos et al. (2014) showed the functionality of this approach in generating cyclic motions on a DLR variable stiffness arm, which can elaborate the modal coordinate transformation from a neuroscience perspective as "dynamics synergies", see the work of Stratmann et al. (2016).

## 4.2. Minimal Energetics

Legged locomotion in nature can be observed to happen in a variety of different gaits that can be characterized by their different footfall patterns and contact forces, as discussed, for example, by Hildebrand (1989). Biomechanical experiments have established a clear relationship between running speed, choice of gait, and energy consumption in humans by Minetti and Alexander (1997) and horses by Hoyt and Taylor (1981). These data suggest that animals may change gait as a function of locomotion speed based on metabolic CoT. To capture the effect of gait in robotic systems, Xi and Remy (2014); Xi et al. (2016) employed optimal control for motion generation of conceptual models of bipeds and quadrupeds. The approach generated motions that minimized positive mechanical work (normalized by distance traveled) while being subject to realistic robot dynamics and locomotion constraints such as foot non-penetration or actuator limits. By varying forward speed and contact sequence, the results show that changing gait as a function of locomotion speed can substantially increase mechanical economy. The optimal behavior in bipedal locomotion is to walk at slow speeds and run at high speeds and in quadrupedal robotic locomotion to walk at slow speeds, trot at intermediate speeds and gallop at high speeds. It is notable that there was only a small mechanical energetic difference between trotting and toelting, which may explain why the toelt is part of locomotion repertoire of some horses. In contrast to biological quadrupeds, galloping did not significantly outperform trotting in simulations. This might be attributed to the lack of an articulated spine in the original quadrupedal model Yesilevskiy et al. (2018b).

Smit-Anseeuw et al. (2017) extended this approach to discuss optimal motions for the bipedal robot RAMone, and investigated the results of comparing two different footfall sequences (a walking sequence with a double support phase and a running sequence with aerial phase) and two different orientations of the knee joints (pointing forwards and backwards). It showed the optimal gait switches from ballistic walking with an instantaneous double-support to spring-mass running with an extended aerial phase at a speed of around 1 m/s. That is, at slow speeds nearly no elastic energy is stored in the actuator springs, while at high speeds almost all of the mechanical energy fluctuations within the robot are conducted through the springs. Switching from ballistic walking to spring-mass running reduced metabolic energy consumption by up to 88%. This is comparable with studies on the metabolic cost of human walking.

Donelan et al. (2001) showed, when humans walk, they prefer a particular step width, and execute this preference with remarkably small variability. In arriving at this preference, the nervous system may seek to minimize an objective function composed of a weighted sum of objectives. One such objective may be metabolic cost. Toward understanding how the nervous systems of able-bodied people weight this objective in walking, Selinger et al. (2015) measured people preferred gait in different cost landscapes, defined as the relationship between metabolic cost and a given gait parameter, and demonstrated that people can continuously optimize step frequency to minimize metabolic energy. Abram et al. (2017) evaluated results on several ablebodied subjects and found that preferred step width in a new landscape was determined by continuous energy optimization. Using step frequency as that gait parameter, Selinger et al. (2016) found the key features that describe this energetic cost optimization process, which can also be partially reproduced using a simple reinforcement learning algorithm, as shown by Simha et al. (2017).

Human motor control relies on central loop control, synergies, learning and peripheral loop (reflexes) as core principles, while robot motion control for transport (locomotion) is typically based on a decentralized position/torque/impedance controller and motion generation via simple models such as cart-table and SLIP. Such classical methods cannot exploit the full-body robot dynamics to obtain efficient motions. A possible solution to address this problem can be to determine the robot trajectories based on whole-body dynamics using a trajectory optimization approach targeting minimum CoT. Gasparri et al. (2018) formulated an optimal control problem in a way that robot dynamic parameters such as joint impedance may also be optimized, in addition to typical state and control variables. Once the locomotion constraints defining periodic change of contact phases (single and double supports) are set, in addition to the robot dynamics and conventional constraints e.g., joint limits, the optimal control problem is solved using a direct method. It is, however, a computationally highly demanding problem that cannot be solved in real-time. To address this issue, a library of optimized trajectories is generated off-line, and then it is searched in real-time for the trajectory associated with the current robot states/conditions. Nevertheless, it is demanding to manage the trajectory library size for robotic hardware with a large number of DOFs. A feasible remedy to this problem is to decipher the trajectory library.

The method is applied to a six-Degree-Of-Freedom (-DOF) planar biped powered by compliant actuators. Based on Principal Component Analysis (PCA), 99% of the variance of 500 optimized trajectories can be explained by three principal components that can also be expressed/fitted by second order polynomials. The results of this implementation on various walking speeds render a CoT around 0.5, which is on average about five times more efficient than the CoT resulting from a Zero-Moment-Point- (ZMP-) based approach rendering the trajectory based on the cart-table model. Results show that the swing leg joint torques of the two techniques are comparable. However, the stance leg joint torques using the optimized locomotion are negligible while the ZMP-based locomotion render substantial joint torques due to the non-straight leg configuration. To realize the effect of compliance on CoT in walking/running, the optimization based approach is employed for two cases, when the robot is rigid and soft. The results show that the slow walking CoT in the two cases are similar, although the soft system exhibited considerably lower CoT for fast walking. In addition, the rigid system renders a CoT approximately twice as great as the soft system when running. Moreover, using the soft system reduces the walk-to-run transition speed, and increases the maximum feasible running speed.

## 5. LOCOMOTION PRINCIPLES

When comparing different animals in nature, as well as the above robotic optimization studies, it is remarkable that despite substantial differences in structure, legged systems of all kinds rely only on a small set of different gaits. One potential explanation could be that these gaits are a manifestation of the underlying mechanical natural dynamics of the legged system. Gan et al. (2016) explored this idea by reducing the models to be completely lossless. Even with such conservative models, all common bipedal and quadrupedal gaits can be represented as passive periodic orbits, suggesting that gaits are merely different dynamic modes of the same structural system. Gaits manifest themselves as different non-linear elastic oscillations that form distinct (yet connected) limit cycles that passively propel an animal or robot forward. It therefore implies that different phenomena observed in such systems should rely upon common models and principles. Below, we discuss a set of recent propositions on these concepts.

## 5.1. Metabolic Cost Model

Faraji et al. (2018) proposed a simple cost model to predict metabolic cost trends under general walking conditions. A 3D linear walking model (called 3LP) developed by Faraji and Ijspeert (2017) is used to predict swing and torso balance costs in the sagittal and frontal planes. The vertical collisional loss and recovery work missing in the 3LP model are included via a Center of Mass (CoM) velocity redirection cost. To account for walking with a non-zero amount of leg lift, a ground clearance cost is incorporated. A weight support cost is also added to account for the energy consumed by leg extensor muscles preventing the stance leg from collapsing under body weight. The resulting cost model is the sum of all four individual costs, scaled by a constant muscle efficiency to convert from positive mechanical work to metabolic input. To evaluate the model, a set of walking conditions from several studies are simulated, including variations in step frequency, step width, added mass, extra ground clearance, crouched walking and reduced gravity conditions. For example, while Donelan et al. (2001) found that the metabolic cost increases at a rate of 6.40 W/kg per meter squared of step width, a quadratic fit to the proposed model reveals a close rate of 5.21 W/kg per meter squared of step width. Overall, the proposed linear combination of four major costs can predict (within the data's 95% confidence interval) the metabolic cost of increasing step width and many other walking conditions. It also provides a detailed metabolic contribution of each component, which is valuable for improving or augmenting performance.

## 5.2. Bioinspired Insights

To realize principles of leg control for robust and economic locomotion over rough terrain, Daley (2017) focused on use of comparative biomechanics as a tool to derive insights into how mechanics and control are integrated to achieve agile, stable and economic locomotion. Birds serve as a useful bipedal animal model, because ground birds such as quail,fowl and ostriches use walking and running gaits that are similar in wholebody dynamics, limb trajectory and ground reaction forces to gaits of humans (Daley, 2018). To understand the principles of bipedal gait, it is essential to combine perspectives from biomechanics, sensorimotor control and engineering. Recent studies have focused on measuring movement biomechanics over simple terrain features, such as obstacle negotiation and single downward steps (Birn-Jeffery et al., 2014; Blum et al., 2014), gait transition dynamics of ostriches moving freely in an open field (Daley et al., 2016), and leg loading during kicking and locomotion in the snake-hunting secretary bird (Portugal et al., 2016). These studies provide insight into locomotor control strategies by comparing steady and transient movement tasks, and investigating potential trade-offs among factors such as speed, stability, robustness and economy.

Birn-Jeffery et al. (2014); Blum et al. (2014); Hubicki et al. (2015) compared bird running biomechanics to model predictions, using reduced-order models and trajectory optimization of bipedal locomotor dynamics, to directly test hypotheses about the priorities and mechanisms underlying bipedal locomotion control. Studies of obstacle and step negotiation revealed that running birds prioritize consistent leg loading (injury avoidance/safety), as the dominant control objective (Birn-Jeffery et al., 2014; Blum et al., 2014). These studies also revealed that the optimal leg trajectories to regulate leg loading (to maintain consistent forces) are similar to the optimal trajectories to minimize mechanical work. These findings highlight that control priorities for economy (minimal work) and safety (consistent forces) are closely aligned. Birds use a three-step recovery strategy over obstacles that reflects priority for economy and safety, but does not directly prioritize trajectory stabilization to maintain the nominal steady-state body center-of-mass dynamics. Running birds achieve stability through passive-dynamic mechanisms, so stability is not required as a direct target of actuation control, due to integration of passive-damping and (multi-articular) intrinsic compliance.These studies revealed that robustly stable and agile locomotion over uneven terrain can be achieved through a simple control strategy of prescribing a leg trajectory (and therefore foot landing conditions) to maintain desired leg loading as modeled by a simple point-mass spring-loaded inverted pendulum (SLIP) model. During stance, leg dynamics are asymmetric and consistent with work-minimizing control of an intrinsically damped leg model. These studies also found that the control strategy used by running birds was similar across many conditions, including unexpected (invisible) potholes, visible obstacles, single steps and multiple steps. Despite varying ability to anticipate the upcoming terrain, leg dynamics and control strategies remain consistent across contexts.

The principles from these studies have been implemented as control policies in the bipedal robot ATRIAS at Oregon State University (Hubicki et al., 2016b), resulting in robustly stable bipedal gaits that are dynamically similar to those of ostriches and humans. These studies have also provided insight into the similarities and differences between humans and birds as bipedal animals. Humans and birds share similar wholebody dynamics of walking and running gaits and similar ground reaction force patterns. However, humans and birds use different stride length and frequency characteristics that reflect their different leg morphology. Humans and birds also use different sensorimotor control strategies. Humans rely heavily on "cephalized" (brain-dominated) control, involving extensive learning and high reliance on predictive planning; however, these processes suffer from long control delays. In contrast, birds have specialized to more heavily rely on "spinalized" (spinal-cord dominated) control, primarily using spinal rhythm generation coupled to robustly stable intrinsic leg mechanics (Daley, 2018). Rehabilitation and control of prosthetic devices might benefit from bird-inspired control mechanisms to achieve robust stability using simple control algorithms and intrinsically stable leg mechanics.

## 5.3. Underlying Concept

Real-world applications require reasoning and decision-making higher-level control, for which complete perception data is necessary, in order to select suitable behavior and motion planning schemes. Patrick et al. (2018) discussed their research on planning for efficient reactive legged locomotion. Prior planning architectures for legged robots generally rely on either finding state trajectories with an on-line optimization process (see Feng et al., 2015; Kuindersma et al., 2016), or using a specific walking controller formula that allows for analytic approximations of the stance dynamics (see Arslan and Saranli, 2012; Englsberger et al., 2015). These reactive control methods are, however, poorly compatible with common robotic motion planning methods that rely on regulating the robot trajectory through its state space. To address this, Patrick et al. (2018) presented that an alternative way of planning legged locomotion is to plan through the action space of efficient reactive legged behaviors which is similar to the controllers shown by Hubicki et al. (2016a). The elements of this space consist of controllers for different periodic gaits and transient actions that can arbitrarily trade off efficiency and robustness. Motion planning using this action space makes the planner choose which behaviors the robot should execute at any given time. When disturbances occur, the behavior executing in the control layer takes immediate action to keep the robot from falling, and after some latency the planning layer can react by specifying a new plan that accounts for the new situation. As a result, the robot can be more robust to real-world disturbances, while also allowing the use of arbitrary energyoptimized gait controllers. However, to navigate through such a dynamic space, it is necessary to understand the underlying principles of locomotion.

Jonathan et al. (2017) adopted legged locomotion as a dynamical phenomenon, inspired by its analogy to a clock, to discuss the periodic attractor underlying most natural gaits.This expounds the dynamical phenomenon of legged locomotion including walking, running, skipping, hopping and jumping. However, it excludes decision-making and path-planning of the system, as well as balancing, gaits that maintain a center of pressure within a polygon of support, and slow one-foot-infront-of-the-other gaits. This concept can be described as a cycle of energy between internal potential, gravitational, and kinetic energy, given compliant interaction5 renders bouncing due to discrete footsteps observed in bird experiments discussed above. The energy exchange cycle can therefore describe different

5Due to the compliance of the locomotor and the environment/world, foot contact is a process, rather than an event, in which the tangential foot forces cannot be applied at the contact instance. The robot interactions with terrain should then be compliant since compliant oscillations are insensitive to external disturbances and can eliminate inelastic collisions. Interactions can accordingly be robust with respect to ground height and/or impedance changes resulting from the lack or imperfection of world models. Additionally, prevention from rigid collisions avoids large impact forces and unnecessary energy consumption.

locomotion modes, e.g., a specific shift in the cycle defines walking and running, and one can find damped oscillation a key to stabilization. It can then suffice for dynamics of legged locomotion and just relies on on-board proprioception similar to blind walking/running for humans, which requires only an inertial measurement unit (IMU).

Inspired by the evaluation of bird running over uneven terrain (Birn-Jeffery et al., 2014; Blum et al., 2014; Hubicki et al., 2015), the fundamental locomotor functionality of a legged system can be independent of environmental conditions such as light, and recovery from small terrain variation need not require exteroceptive sensory information and/or large processing. It is then important to integrate compliance carefully into the system. In addition to passive compliance that was discussed earlier in section 2, the employment of active compliance (impedance control) enables the replication of different (linear or non-linear) compliant behavior, in addition to the adjustment of damping for variable energy dissipation, inspired by damping/energy dissipation regulation of birds for robust stability in uneven terrain. Moreover, integration of compliance improves the Markov Decision Process (MDP) of expected response, especially when set-point trajectory is given through feed-forward approaches.

## 6. SUMMARY

This paper reviewed recent progress in design and control of robotic systems from different perspectives, to indicate the current state of robotics in terms of energy efficiency, and to highlight solutions advancing this criterion. It includes a review of various robotic actuators exploiting compliance in series and in parallel for energy recycling, and discusses the importance of limb segmentation in design, dynamics analysis and control of dynamical systems. A set of energeticallyestablished control approaches are explored, and compared with human behaviors/controls. In addition, a set of cutting-edge topics initiating new directions in locomotion are reported. Overall, we can briefly conclude that:

## REFERENCES

## AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

## FUNDING

The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 644839 (CENTAURO) and 644727 (CogIMon).

disturbance rejection. PLoS ONE 9:e100399. doi: 10.1371/journal.pone.01 00399

efficiency in coupled compliant joints via PCA. Front. Neurorob. 10:2. doi: 10.3389/fnbot.2016.00002

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Kashiri, Abate, Abram, Albu-Schaffer, Clary, Daley, Faraji, Furnemont, Garabini, Geyer, Grabowski, Hurst, Malzahn, Mathijssen, Remy, Roozing, Shahbazi, Simha, Song, Smit-Anseeuw, Stramigioli, Vanderborght, Yesilevskiy and Tsagarakis. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Linking Gait Dynamics to Mechanical Cost of Legged Locomotion

David V. Lee1 \* and Sarah L. Harris 2

1 School of Life Sciences, University of Nevada Las Vegas, Las Vegas, NV, United States, 2 Department of Electrical and Computer Engineering, University of Nevada Las Vegas, Las Vegas, NV, United States

For millenia, legged locomotion has been of central importance to humans for hunting, agriculture, transportation, sport, and warfare. Today, the same principal considerations of locomotor performance and economy apply to legged systems designed to serve, assist, or be worn by humans in urban and natural environments. Energy comes at a premium not only for animals, wherein suitably fast and economical gaits are selected through organic evolution, but also for legged robots that must carry sufficient energy in their batteries. Although a robot's energy is spent at many levels, from control systems to actuators, we suggest that the mechanical cost of transport is an integral energy expenditure for any legged system—and measuring this cost permits the most direct comparison between gaits of legged animals and robots. Although legged robots have matched or even improved upon total cost of transport of animals, this is typically achieved by choosing extremely slow speeds or by using regenerative mechanisms. Legged robots have not yet reached the low mechanical cost of transport achieved at speeds used by bipedal and quadrupedal animals. Here we consider approaches used to analyze gaits and discuss a framework, termed mechanical cost analysis, that can be used to evaluate the economy of legged systems. This method uses a point mass perspective to evaluate the entire stride as well as to identify individual events that accrue mechanical cost. The analysis of gait began at the turn of the last century with spatiotemporal analysis facilitated by the advent of cine film. These advances gave rise to the "gait diagram," which plots duty factors and phase separations between footfalls. This approach was supplanted in the following decades by methods using force platforms to determine forces and motions of the center of mass (CoM)—and analytical models that characterize gait according to fluctuations in potential and kinetic energy. Mechanical cost analysis draws from these approaches and provides a unified framework that interprets the spatiotemporal sequencing of leg contacts within the context of CoM dynamics to determine mechanical cost in every instance of the stride. Diverse gaits can be evaluated and compared in biological and engineered systems using mechanical cost analysis.

Keywords: biomechanics, energetics, economy, walking, running, bipedal, quadrupedal, comparative

## INTRODUCTION

As with any structural or functional animal feature, it is important to consider locomotion through the lens of organic evolution. In nature, the process of natural selection replaces the forward design used in engineering. As emphasized by Vogel (2013), instead of being optimized through a design process, biological designs emerge to be just good

#### Edited by:

Monica A. Daley, Royal Veterinary College, United Kingdom

#### Reviewed by:

Daniel Schmitt, Duke University, United States Peter Eckert, École Polytechnique Fédérale de Lausanne, Switzerland

> \*Correspondence: David V. Lee<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Bionics and Biomimetics, a section of the journal Frontiers in Robotics and AI

Received: 25 May 2018 Accepted: 05 September 2018 Published: 17 October 2018

#### Citation:

Lee DV and Harris SL (2018) Linking Gait Dynamics to Mechanical Cost of Legged Locomotion. Front. Robot. AI 5:111. doi: 10.3389/frobt.2018.00111

**20**

enough so that the organism can survive, compete, and reproduce in its ecological niche. In addition, natural selection is constrained by phylogenetic, constructional, and developmental factors. Leg number (Shubin et al., 1997), the composition of the skeleton (Currey, 2002) or cuticle (Hopkins and Kramer, 1992), as well as muscles and their innervations (Diogo and Abdala, 2010) are generally conserved within taxa. For example, when considering leg number, true crabs (Decapoda) have ten legs, insects (Hexapoda) have six, and terrestrial vertebrates (Tetrapoda) have four (except when lost in certain lineages). Crabs and insects (Arthropoda) also have an exoskeleton made of a chitin composite, whereas vertebrates have an endoskeleton made of bone. Such fundamental features are conserved within a given phylogenetic group and therefore place limits on the mechanical solutions that might emerge. Phylogenetic, constructional, and developmental features of an animal's biology, as well as body size, lifespan, and other characteristics, impose severe constraints on the structural and functional "design solutions" available. As extreme examples, biological constraints make it so that we cannot replace our bones with a jointed exoskeleton or develop longer sarcomeres for greater force production. Hence, the locomotion and neuromusculoskeletal function observed in any species should not be seen as "optimal" but simply as a competent solution emerging from the highly constrained process of natural selection. Here we review key features of nature's strategies for terrestrial locomotion, focusing on gait and center of mass dynamics with a view toward informing the design of legged robots.

## GAIT

Locomotion is fundamental for foraging, prey capture, predator evasion, securing territory, finding mates, and migration. Animals use various modes of locomotion called gaits as defined by their movement patterns. Gait is conventionally defined by temporal footfall patterns and, for terrestrial animals, the footfall sequence is the primary identifier of gait. Footfall sequence is quantified by the phase relationships of individual legs, expressing the time of foot contact as a fraction or percentage of stride period. For example, for walking, one foot lands at the beginning of the stride (0%) and the second foot lands at mid-stride (50%).

Yet a phase-based definition of gait is often incomplete and can fail to distinguish different gaits because they may have similar or even identical phase relationships. For example, bipedal walking and running show the same left-right-left sequencing of footfalls, with phases of initial contact of alternating feet at 0% and 50% of the stride period (**Figure 1A**). Hence, the distinction between walking and running traditionally relies upon the duty factor, which represents the duration of a given footfall as a fraction of stride period. On this basis, human running is distinguished from walking by its duty factor of <0.5, which specifies an aerial period in the case of bipedal running but not necessarily in quadrupedal or multilegged running, where footfalls with duty factors <0.5 may be sequenced such that there is no aerial phase. In contrast to humans, birds are bipedal striders that blur the distinction between walking and running. Using duty factors >0.5, they exhibit exhibit "grounded" running without an aerial phase. But how do we know that grounded running is indeed running as opposed to walking? Despite the convenience of separating running from walking on the basis of duty factor, it is clear that criteria beyond temporal footfall metrics are needed to distinguish the underlying physics of gait. This section focuses on the broad utility of temporal patterns in the definition of gait, and section Center of Mass Dynamics addresses similarities and differences in the underlying dynamics of various gaits.

## Symmetrical vs. Asymmetrical Gaits

Legged gaits are broadly characterized as symmetrical or asymmetrical according to the phase relationships of left-right pairs of legs. If the left and right legs of a pair are one-half stride cycle out of phase with one another, the gait is defined as symmetrical—if not, the gait is asymmetrical. This convention spans animals of different leg number. For example, bipedal running of humans, quadrupedal trotting of dogs, pacing of camels, and hexapedal trotting of cockroaches are all symmetrical gaits because left-right pairs of fore-, mid-, and hind-legs are onehalf cycle out of phase with each other. Regardless of leg number, gait symmetry is defined by this half-cycle phase relationship of the left and right legs at a given cranio-caudal position.

The number of legs limits the number of leg sequencing options, such that gait possibilities for bipeds are restricted to symmetrical striding gaits (walking and running) and asymmetrical hopping and skipping. Quadrupeds use five symmetrical gaits (lateral and diagonal sequence walking, trotting, pacing, and ambling) and six asymmetrical gaits (lope, transverse and rotary gallops, half-bound, bound, and pronk). These are broad definitions, and it is important to note that phase separations between foot contacts show substantial variation within gaits, as illustrated in (Hildebrand, 1965, 1968) plots for the gaits of horses and dogs.

## Bipedal Gaits

Bipedal striding gaits, including our own walking and running, are symmetrical by definition (**Figure 1A**). These gaits are used by birds and historically by theropod dinosaurs, which comprise the greatest diversity of bipedal striders. Humans and birds (except small songbirds) walk at slow speeds and run at fast speeds (Small songbirds typically use hopping rather than striding gaits). Some great apes and monkeys are facultative bipeds, occasionally walking or running for short distances. Lizards and cockroaches may run bipedally at their fastest speeds by pitching their body into a more upright attitude and straightening their legs as they transition from a quadrupedal (Irschick and Jayne, 1999) or hexapedal trot (Full and Tu, 1991). This seemingly odd behavior increases speed by increasing stride length. In general, bipedal striders achieve greater absolute stride lengths than quadrupeds of the same body mass (Reynolds, 1987), and this has been argued to be an advantage for endurance runners of our own genus—for example, in persistence hunting

of quadrupeds or aggressive scavenging in competition with quadrupeds (Carrier, 1984; Bramble and Lieberman, 2004).

Although the presence of only two legs allows relatively few sequencing options, two asymmetrical gaits—hopping and skipping—are used by bipeds (**Figure 1C**). Bipedal hopping gaits are common in mammals and birds, particularly at small body size. It may seem counterintuitive that the paired contacts of right and left hind limbs should indicate an asymmetrical gait, however, this deviates from the symmetry criterion that right and left contacts be one-half stride cycle out of phase. Bipedal hopping is found convergently in several groups of rodents, including springhares, kangaroo rats, and jerboas and the only large bipedal hoppers are the wallabies and kangaroos, with male red kangaroos equaling human body mass (reviewed by McGowan and Collins, 2018). Bipedal skipping, a gait occasionally used by children and sometimes in reducedgravity conditions, is the only asymmetrical gait used by humans (Minetti, 1998, 2001a,b; Ackermann and van den Bogert, 2012). Monkeys and apes with forelimbs specialized for brachiation in arboreal environments sometimes use side-ways bipedal skipping gaits on the ground, and this is typified by the fast, dance-like gait of the gibbon/siamang (Vereecke et al., 2006). Bipedal skipping gaits are thought to be akin to the asymmetrical galloping of quadrupeds and this is supported by similarities in relative phase of the hindlegs (**Figures 1C,D**), as well as by the analysis of CoM dynamics (Minetti, 1998).

## Quadrupedal Gaits

The symmetrical gaits of quadrupeds include the walk, trot, pace, and amble. Quadrupedal mammals, crocodiles, lizards, and salamanders normally walk at slow speeds and trot at intermediate speeds, while the pace and amble are used by just a few mammals. During walking, leg contact phases are typically separated by about 25% and the order of contact is typically a hind foot, followed by the ipsilateral forefoot, followed by the contralateral hind foot and forefoot (**Figure 1B**). This most commonly used sequence of footfalls is called a lateral sequence walk. Yet most primates walk with a diagonal sequence, which is thought to provide better roll stability when walking on branches (Hildebrand, 1980; Cartmill et al., 2002). When walking on branches, however, this advantage of diagonal support may be diminished by a relatively narrow stance compared to that of terrestrial locomotion. A full mechanistic understanding of this difference between primates and typical quadrupeds will likely require consideration of individual foot force and torque in addition to spatiotemporal considerations (e.g., Shapiro and Raichlen, 2005, 2007; Cartmill et al., 2007). Notwithstanding these distinctions, simple models have shown that the lateral sequence walking gait used by most quadrupeds provides a stable tripod of support, termed "static stability" (McGhee, 1976; Alexander, 1984), and a mathematical model of slow walking found this to be the most stable of the three possible gaits that can provide a continuous tripod of support (McGhee and Frank,

1968), while the other two solutions appear not be used by animals.

Quadrupeds use the remaining symmetrical gaits—the trot, pace, and amble—at intermediate speeds. Trotting is the symmetrical gait most widely used at intermediate speeds and its relative phases resemble those of bipedal striding (**Figure 1B**). During trotting, diagonal legs are in phase, providing a supporting leg on each side to resist rolling that may be induced by a sprawled posture. In contrast, ipsilateral legs are in phase during pacing, discarding roll stabilization but avoiding forehind interference in mammals with especially long legs, such as camels, as well as some dogs and horses (Hildebrand, 1968). The transition between walking and trotting occurs at a similar relative speed for all quadrupeds. However, the top trotting speed (i.e., trot-gallop transition speed) occurs at relatively faster speeds for larger quadrupeds. The gait referred to as an amble, tölt, or "running walk" is another symmetrical gait used by quadrupedal mammals including lemurs, monkeys, elephants, and some horses (reviewed by Schmitt et al., 2006). It is a fourbeat gait with phase relationships like those of walking but with speeds comparable to fast trotting. The amble reduces vertical oscillations of the center of mass and this relatively flat trajectory is thought to be advantageous for locomotion on branches (e.g., Cartmill et al., 2002) and as a fast gait that allows very large quadrupeds to avoid aerial periods (e.g., Hutchinson et al., 2003).

At intermediate to high speeds, quadrupeds use asymmetrical gaits, such as the gallop, half-bound, bound, and pronk. Sprawling quadrupeds like salamanders and lizards do not use asymmetrical gaits, although juvenile crocodiles are able to gallop with an upright posture (Zug, 1974; Renous et al., 2002). Asymmetrical quadrupedal gaits are linked with upright limb posture, where legs are retracted in the parasagittal plane. Because left-right pairs of fore- and hindlimbs may be kept more nearly in phase, asymmetrical gaits allow bending of the spine and pelvis to contribute to stride length, with the muscles of the trunk used to bilaterally dorsiflex and ventroflex the spine. The leftright phase separation during galloping is typically 10–35% in the forelimb pair and 10–25% in the hindlimb pair (Afelt et al., 1983; Alexander, 1984). During bounding, both left-right pairs are in phase, and, during half-bounding, the hind left-right pair are in phase while the fore left-right pair are somewhat out of phase. Deer, antelope, goats, and sheep use the bound and pronk for display or warning and in steep terrain. The pronk is a pronounced bouncing gait where all four feet strike the ground in unison. The half-bound is well-known in rabbits and is the fast gait most frequently used by rodents and other small mammals. Rodents tend to use the half-bound at speeds corresponding to the upper trotting range of larger quadrupeds.

The gallop is the most commonly used asymmetrical gait of quadrupeds larger than about five kilograms. Broadly defined, it includes loping or cantering—a slow, three-beat gait with one diagonal pair in-phase, being preceded by a single hindlimb and followed by a single forelimb. Wolves use the lope alternately with trotting when traveling long distances. Large mammals, that have longer forelimbs and a forward center of mass, such as hyenas and bison, have a reduced trotting range and switch to a lope at intermediate speeds where other quadrupeds would trot. The transverse gallop is a faster four-beat gait, introducing a phase separation in the lope's diagonal pair with the pair's forefoot following the hind foot. The rotary gallop is the fastest gait used by quadrupedal mammals and it changes the order of the forefoot contacts such that the contact sequence is circular rather than crossing in a figure-eight. Galloping typically has a single gathered suspension period but cheetahs and grayhounds add an extended suspension period between hind- and forelimb contacts that serves to increase stride length at the fastest speeds.

## Speed Effects

Animals choose a gait depending on their speed—they choose to walk at slow speeds and typically transition to symmetrical running or trotting at intermediate speeds and then asymmetrical half-bounding or galloping at fast speeds. The choice of symmetrical or asymmetrical gaits at faster speeds is related to leg posture (sprawling vs. upright), body mass, body mass distribution, rotational inertia of the body and appendages, leg length relative to body length, and fore-hind leg length differences. Gait choice and relative speeds at gait transitions may also change during uphill or downhill locomotion, or with varying substrate properties, or with uneven conditions in rugged terrain.

The analysis of phase relationships is generally effective for identifying and classifying gait, yet bipedal walking cannot be distinguished from running and quadrupedal walking from ambling based on foot sequencing alone. Thus, as introduced above, duty factor is typically used to distinguish these slower walking gaits from running and ambling. Greater duty factors are expected at slower speeds, and this provides a convenient method to discern gait differences using only temporal parameters. Despite its utility in gait analysis, duty factor cannot necessarily distinguish differences in gait dynamics. For example, walking and grounded running in birds have equal phase relationships and both have duty factors >0.5. Because duty factor decreases with speed, it can be associated with different gaits, as in the separation of walking from running of humans. Nonetheless, duty factor and footfall sequencing do not directly determine the dynamics underlying a particular gait and often lead to conflicting definitions of gait.

## CENTER OF MASS DYNAMICS

Identifying the temporal pattern of leg sequencing, as measured by relative phase and duty factor, is a critical first step in quantifying gait, yet it is often imprecise and is insufficient to reveal the physical basis of locomotion. The dynamics of a given gait can only be known by measuring the forces determining the motion of the center of mass (CoM). This section first describes the measurement of CoM dynamics to determine oscillations resulting from combined leg force. It then describes two conventional models of gait: the rigid inverted pendulum (RIP) model traditionally applied to walking; and the spring-loaded inverted pendulum (SLIP) model for running. We conclude the section with a discussion of mechanical cost analysis that evaluates CoM dynamics more objectively, without the a priori assumptions required by the RIP and SLIP models.

## CoM Measurements and Gait Patterns

Two approaches commonly used in the analysis of gait are a point mass model and a rigid-body model. The most basic measurement of gait dynamics treats the center of mass as a point mass, thus neglecting rotations about the center of mass (CoM). A point mass model of locomotion requires that forces exerted on all of the legs be summed and the instantaneous accelerations of the center of mass be determined throughout a complete stride (Cavagna, 1975). In contrast, a rigid-body model, requires separate measurements of forces exerted on each of the legs, as well as any torques, in order to consider not only the translation of, but also rotations about the center of mass. When more than one leg contacts the ground, as in the example of the diagonal limb pair during trotting, differential forces can produce force couples or "free moments," which act about the center of mass to resist rotation and contribute to balance (Gray, 1968; Murphy and Raibert, 1985; Lee et al., 1999). Torques exerted at the feet also influence rotation in a rigid body model but these are typically restricted to the yaw axis, unless the foot can adhere to or grasp the substrate. Here we focus on evaluating the dynamics of a point mass model of the center of mass, emphasizing the principal gaits of bipeds and quadrupeds.

During legged locomotion, forward progression is coupled with vertical oscillations of the CoM. This forward progression is achieved either by using one leg at a time, as during bipedal running with aerial phases, or by using more than one leg at a time, as during all other gaits of bipeds, quadrupeds, and multilegged animals. The net effect of the vertical and shear ground reaction forces summed across all legs, less the vertical force of body weight, is a cyclic redirection of the CoM. Hence, the summed vertical force always oscillates about body weight with equal variation above and below—otherwise, the CoM would have a net rise or fall during a stride. The summed foreaft forces exerted on the legs oscillate about zero with equal propulsive and braking impulse during steady-speed locomotion. At the beginning of stance, limbs are placed forward (protracted stance)—exerting force against the direction of travel, and at the end of stance, limbs are placed backward (retracted position) exerting force in the direction of travel. Thus, legs typically exert braking followed by propulsive force (Gray, 1968). When more than one leg is in contact with the ground, the summed vertical forces and the summed shear forces determine oscillations of the center or mass. The pattern of combined forces acting on the center of mass is influenced by the sequencing and duration of leg contacts—explaining in many cases the correlation of relative phase and duty factor with the dynamics of the center of mass.

For a given gait, the CoM will either oscillate once or twice per stride. Symmetrical gaits, such as bipedal walking and running, have two vertical oscillations per stride. These oscillations are achieved alternately by left and right legs of a pair, and each of these legs contributes to just one oscillation as long as each leg's duty factor is <0.5. During asymmetrical gaits, such as bipedal hopping and quadrupedal galloping, there is only one vertical oscillation of the CoM per stride. The legs of right-left pairs act either in unison or in a staggered sequence to achieve this single cycle of oscillation and an aerial phase separates the leg contacts of one stride from those of the next (Hildebrand, 1980). Exceptions to the rule of a single aerial phase include the fast gallop of grayhounds and cheetahs, as well as the fast halfbound of hares (Hildebrand, 1980; Bertram and Gutmann, 2008), which add a second aerial phase—an "extended suspension" between hind- and foreleg contacts—while preserving the typical "gathered suspension" between fore- and hind-leg contacts. Barring these exceptions, asymmetrical gaits include one vertical oscillation per stride and symmetrical gaits include two vertical oscillations per stride.

As already emphasized, total vertical force rises cyclically above and below body weight during the stride to achieve vertical oscillations of the CoM. This is true of both running and walking, although during bipedal walking the rise above body weight is achieved by simultaneous leg contacts during double support of the step-to-step transition (**Figure 2**), whereas a single leg contact achieves the rise above body weight during bipedal running. As a result of these differences between running and walking, vertical acceleration is downward during mid-stance of walking (**Figure 2**) and upward during mid-stance of running. Because acceleration is one-half cycle out of phase with its second derivative, position, the CoM reaches its lowest point during mid-stance of running and its highest point during midstance of walking. This traditional observation of the vertical

FIGURE 2 | Ground reaction forces of the left limb (gray) and right limb (black) during three steps of human walking (i.e., left-right-left)—showing vertical (solid lines) and fore-aft (dashed lines) components of force. This stride is defined from mid-stance of the left limb to the subsequent mid-stance of the left limb. Vertical ground reaction force (solid lines) is below body weight during mid-stance of single stance (SS) and peaks at values greater than body weight near the beginning and end of double stance (DS). Fore-aft ground reaction force (dashed lines) peaks during double stance (DS) for both positive (propulsive) force from the trailing limb and negative (braking) force from the leading limb.

position of the CoM at mid-stance is the basis for a long-standing dichotomy between walking and running (Cavagna et al., 1976, 1977).

## SLIP, RIP, and BSLIP Models of Locomotion

Running and walking have been characterized separately based on the phase relationships of their kinetic and potential energy oscillations which are typified by the spring-loaded inverted pendulum (SLIP) model and the rigid inverted pendulum (RIP) model. The view of kinetic and potential energy oscillations being either in phase, implying a SLIP model, or out of phase, implying a RIP model, remains the most influential construct in the field of gait analysis, including that of bipedal, quadrupedal, and multi-legged locomotion (reviewed by Dickinson et al., 2000). As explained in the previous section, patterns of vertical force dictate that the CoM reaches its lowest point (minimum potential energy) in mid-stance of running and its highest point (maximum potential energy) in mid-stance of walking. Despite this difference in potential energy at mid-stance, fluctuations in kinetic energy are determined primarily by changes in forward velocity, which follow the same pattern for running and walking. This is because braking occurs in the first half of a given leg's stance and propulsion in the second half. Thus, CoM velocity—and therefore kinetic energy—tends to reach a minimum near mid-stance in both walking and running.

In the case of running or other SLIP-like gaits, kinetic and potential energy both reach a minimum at mid stance making these energies more-or-less in phase. SLIP-like gaits include bipedal running and hopping, as well as quadrupedal and multilegged trotting, which are well-described as "bouncing" gaits because the greatest leg compression occurs at about the same time as the greatest vertical force (Blickhan, 1989; McMahon and Cheng, 1990). If physical leg springs are present, these spring-like dynamics provide some opportunity for energy savings by elastic storage and return of some portion of the absorptive and generative work done by muscles or robotic actuators. Current research hybridizes SLIP concepts with rigid body models and link-segment models (reviewed by Sharbafi and Seyfarth, 2017). For example, mass distribution away from the hip influences dynamics of the spring-loaded leg in a bipedal running model (Blickhan et al., 2015). This simulated biped is controlled using the virtual pivot point construct to direct the resultant force vector through a point above the CoM (Maus et al., 2008; Sharbafi and Seyfarth, 2017).

In contrast to SLIP-like gaits, potential energy tends to reach a maximum near mid-stance during walking—making kinetic and potential energies more-or-less out of phase. According to the conventional interpretation of "two basic mechanisms," this is sufficient to invoke a RIP model of walking dynamics. Nonetheless, experimental studies show that bipedal and quadrupedal walking dynamics (e.g., Lee and Farley, 1998; Griffin et al., 2004, Genin et al., 2010) do not match the RIP model. This is unsurprising given that an actual rigid inverted pendulum (i.e., a mass on a massless rod of fixed length) would show a peak vertical force instead of a minimum vertical force in the mid-stance position, as described by Geyer et al. (2006). The same authors propose an alternative compliant-legged model of walking called the bipedal SLIP or BSLIP, which reproduces the characteristic m-shaped force with a minimum at mid-stance by providing a spring-loaded leg that introduces compliance. The BSLIP also includes summation of leading and trailing leg forces during double support of the step-to-step transition. Although this revealing model is widely used and highly cited, the BSLIP has yet to upend the RIP model of walking in most textbook explanations. This may be partly because the BSLIP is more challenging to simulate and perhaps also because its conservative leg springs limit its ability to match the full range of human walking speeds (Lipfert et al., 2012). Nonetheless, a recent bipedal robot demonstrates SLIP-like running and BSLIPlike walking, using the same spring-loaded legs (Hubicki et al., 2018). In principle, the BSLIP model is more correct than the unrealistic impulsive step-to-step transition of the RIP model because it captures the m-shaped force profile and allows for double support.

## Mechanical Cost Analysis

Instead of focusing on phase relationships between kinetic and potential energies, mechanical cost analysis quantifies the mechanical cost of redirecting an animal's center of mass and reveals the underlying physics of that cost. This approach considers each instance of the stride. MCA reduces the observed center of mass dynamics to dimensionless parameters—the key amongst these being collision angle, which is equivalent to mechanical cost of transport (Lee et al., 2011). Using this approach, gaits are not constrained to a priori models that often invoke idealized gaits as ill-fitting approximations. Instead, mechanical cost analysis applies across gaits and species by focusing on the fundamental physics of the animal's interaction with the substrate. MCA provides further insight into not only the overall stride dynamics but also the individual events in the stride, indicating which phases of the stride are more (or less) costly.

The central concept of mechanical cost analysis is d'Alembert's (1743) "principle of orthogonal constraint," which shows that a mass can be redirected without mechanical work, as long as the constraint (force vector) is perpendicular to the path (velocity vector), such that their dot-product (mechanical power) is zero (**Figures 3D,E**). Considering the simple case of a flat trajectory, where the velocity vector is purely horizontal; the velocity of the center of mass would be increased by a forward-directed (propulsive) force vector or, decreased by a backward-directed (braking) force vector—these two conditions require generative or absorptive work, respectively, both incurring mechanical cost (**Figures 3A,B**). In contrast, a force vector (to resist gravity) does not change the velocity of the center of mass, thus requiring no work and moving with zero mechanical cost of transport (**Figure 3C**). In the latter example, the force and velocity vectors are kept perpendicular, matching the mechanics of an idealized wheel rolling on a flat surface. Although legged locomotion necessarily includes vertical oscillations, the benefit of moving without mechanical cost could be had as long as force and velocity vectors could be kept perpendicular throughout the vertical oscillations of the stride.

d'Alambert's theoretical redirection with zero work is not completely realized by legged systems because the ability to exert orthogonal forces is limited by a leg's position with respect to the CoM, its kinematic range of motion, and its force-torque capacity, amongst other factors. Nonetheless, certain gaits of bipeds, quadrupeds, and brachiators approximate orthogonal constraint. Deviations from orthogonal constraint require work. Specifically, work is required in any instance where force and velocity vectors deviate from a perpendicular relationship and the resulting mechanical power is non-zero (Ruina et al., 2005; Lee et al., 2011). Foundational studies in this area used mathematical models of discrete leg contacts to estimate the mechanical cost of redirecting the CoM for an entire stride of a given gait while considering leg number, step-to-step transition, or foot shape (McGeer, 1990; Kuo, 2001; Ruina et al., 2005). Mechanical cost analysis extends these previous models and captures the dynamics of the CoM not only for the entire stride but also at each instance of the stride by measuring the CoM velocity and ground reaction force on the CoM and then determining the instantaneous angle between these vectors. This analysis applies to both simulated models and experimental measurements.

Experimental data using mechanical cost analysis show that mechanical cost of transport is greater during running than during walking. Walking reduces mechanical cost by maintaining a more perpendicular relationship between force and velocity vectors throughout the stride. For example, during the stepto-step transition of human walking, also called double stance, the CoM (and thus, velocity) transitions from downward to upward while ground reaction force transitions from propulsive (forward) to braking (backward). Specifically during double stance, the force is first propulsive (dominated by the trailing leg) and then braking (dominated by the leading leg). In this way, force and velocity vectors are kept more nearly perpendicular during downward to upward redirection of the center of mass.

In contrast, SLIP-like gaits, such as running, cannot approach orthogonal constraint because they instead follow a brakingpropulsive pattern that simply aligns with the orientation of the support leg(s). Because bipedal running typically has only single-leg support, it cannot employ the propulsive and then braking pattern of the walking double stance. Instead, the SLIP-like pattern of a single leg's stance starts with braking (backward-directed force vector) with a large projection on the downward-directed velocity vector, followed by propulsion (forward-directed force vector) with a large projection on the upward-directed velocity vector (**Figures 3F,G**). In the SLIP construct, both early and late stance geometries deviate from orthogonal constraint, resulting in greater work during the downward to upward redirection of the CoM.

Mechanical cost analysis quantifies mechanical cost by measuring the collision angle φ , which is the deviation from perpendicular of the CoM force and velocity vectors. This angle is measured in each instance of the stride and is given by Lee et al. (2011):

$$\phi = \arcsin\left(|\mathbf{F} \cdot \mathbf{V}| / |\mathbf{F} \parallel \mathbf{V}|\right) \tag{1}$$

where F is the force vector and V is the velocity vector, either in two or three dimensions. The overall collision angle across the entire stride 8 is a weighted-average of φ , where the weights are the magnitudes of force and velocity vectors in each instance:

$$\Phi \sum |\mathbf{F} \parallel \mathbf{V} \mid \phi \rangle \sum |\mathbf{F} \parallel \mathbf{V} \mid \tag{2}$$

Substituting the small angle approximation of Equation (1) into Equation (2) then shows that stride collision angle 8 is approximately equal to the mechanical cost of transport:

$$CoT\_{mech} = \sum |\mathbf{F} \cdot \mathbf{V}| / n\overline{V\_{\mathcal{V}}} mg \implies \sum |\mathbf{F} \cdot \mathbf{V}| / \sum |\mathbf{F} \cdot \mathbf{V}| \tag{3}$$

where m is body mass, g is gravitational acceleration, Vy is the mean forward velocity, and n is the number of sampled points in a given stride. Mechanical cost of transport was originally derived using dimensional analysis and it gives the work to move a unit body weight a unit distance during steady-speed locomotion. However, only mechanical cost analysis reveals the physical basis for this cost. Specifically, the collision angle provides a physical basis for the mechanical cost of transport as well as a way to quantify the cost of individual events or phases within the stride. In contrast, CoTmech, in its original form, depends upon average forward velocity and only applies to a full stride of locomotion, without providing information about the costs of individual events or phases.

From the point mass perspective, SLIP-like bouncing gaits incur greater mechanical cost of transport—i.e., require more mechanical work to move the body weight a unit distance than walking gaits that reduce required work by targeting orthogonal constraint. In humans, for example, the mechanical cost of transport during SLIP-like running is three-times that of walking (**Figure 4**, compiled by Lee et al., 2013). Again, this lower mechanical cost of walking is achieved by summed forces on the trailing and leading legs during double support, providing propulsion while the velocity is directed downward, then braking while the velocity is directed upward. This is the opposite pattern of SLIP-like gaits, such as running, and it allows human walking dynamics to more nearly approach orthogonal constraint, thereby reducing required work and achieving oscillations of the CoM with reduced mechanical cost.

Work is also mitigated by brachiating siamangs (Michilsens et al., 2012) in the same way but to an even greater extent than in terrestrial walking. Instead of negotiating substrate interactions with one or more foot, as discussed so far, these apes use the overhead support of branches to achieve fast, smooth locomotion through the canopy. Brachiators are able to reduce required work using a single handhold because they can either pull or push on the handhold to keep force and velocity vectors more perpendicular, whereas terrestrial animals can only load their legs in compression. Hence, brachiating animals can achieve propulsion while their velocity is directed downward and braking while their velocity is directed upward—i.e., the same strategy of orthogonal constraint that is approached using two legs during the step-to-step transition of human walking or by four legs during quadrupedal galloping (Bertram and Gutmann, 2008; Lee et al., 2011). The astonishingly smooth movement of brachiating gibbons, in fact, helped initiate a resurgence of theoretical studies of collision mechanics, which model generative and absorptive events during locomotion (Usherwood and Bertram, 2003; Ruina et al., 2005; Bertram, 2016). While suspensory locomotion and inverted quadrupedal walking generally show a propulsive-then-braking pattern, (Ishida et al., 1990; Chang et al., 2000; Granatosky, 2015; Granatosky et al., 2016; Granatosky and Schmitt, 2017), mechanical cost analysis has yet to be applied to these data.

Mechanical cost analysis of animals can also be evaluated in light of theoretical predictions of how work can be mitigated by legged systems. A key finding of this mathematical approach is that mechanical cost of transport is reduced in proportion to the number of contacts used to achieve a given redirection of the CoM (Ruina et al., 2005). In other words, the mechanical cost of redirecting the center of mass is theorized to be divided by the number of sequenced leg contacts. For canine walking, as compared with human walking (see leg contact sequences in **Figure 1**), this prediction is borne out by mechanical cost analysis of experimental data, which shows about one-half the mechanical cost incurred for four sequenced leg contacts of a

SLIP-like "bouncing" gaits, having two- to five-times greater CoTmech at a given dimensionless speed. An apparent boundary zone (gray shading) suggests a discrete separation between SLIP-like gaits and those targeting orthogonal constraint.

dog as for two sequenced leg contacts of a human (**Figure 4**). The gallop and amble are faster quadrupedal gaits that use sequenced leg contacts to reduce mechanical cost of transport but not quite to the extent of quadrupedal walking (**Figure 4**). The concept of reducing cost by increasing the number of sequenced ground contacts has been extended to human walking by modeling contacts of the heel and toe as discrete "leg" contacts (Ruina et al., 2005). Just as for sequenced contacts of separate legs, this model predicts that sequenced heel and toe contacts halve the mechanical cost of transport during walking.

Another important theoretical prediction is that work can be reduced by increasing the length of the foot. Simulations show that a foot that extends forward the full length of the step and that is just slightly rounded (convex relative to the ground), as opposed to cupped (concave), achieves work-free redirections from one leg contact to the next during walking this case is likened to a polygon with convex surfaces rolling smoothly between pendular support phases at its vertices (Ruina et al., 2005). However, effects of the foot's length and its radius of curvature cannot be easily separated because, during singleleg stance, a rounded foot centered on a rigid leg prescribes the path of the center of mass in addition to lengthening the foot in both the "toe" and "heel" directions. The question of foot shape has been addressed in passive dynamic walking robots and simulations (e.g., McGeer, 1990; Kuo, 2001), as well as in human studies with experimental boots of different lengths and radii (Adamczyk et al., 2006). In the latter experiment, mechanical cost was reduced by simultaneously increasing the length and radius of curvature, a result that is similar to theoretical predictions based on foot length alone (Ruina et al., 2005).

It stands to reason that hexapedal and octopedal animals would have even lower mechanical cost than quadrupeds by using more than four sequenced leg contacts, however, mechanical cost analysis has not yet been applied to arthropods. The ideal of orthogonal constraint could be approached more nearly by eight sequenced leg contacts; however, arthropods primarily use alternating tripods to achieve SLIP-like trotting gaits (reviewed by Holmes et al., 2006). It is plausible that work reduction might not be as strongly selected in small arthropods—perhaps due to scaling of energetics, terrain interactions, or constraints on motor control. Whatever the explanation, mechanical cost analysis holds potential to further explore nature's solutions to multi-legged gait.

## Comparing Legged Animals and Machines

Legged robots designed for economy are typically slower than animals of similar size (e.g., Collins et al., 2005), with a few exceptions, such as the MIT Cheetah quadruped, which uses regenerative motors (Seok et al., 2015). Humans walk slowly (1.0 ms−1 ) with a mechanical cost of transport of ∼0.05 and a total cost of transport of ∼0.41 (Voloshina et al., 2013), so mechanical cost represents about one-eighth of the total cost. If we assume no co-contraction between antagonist muscle pairs and a muscle efficiency of 25%, the muscle energy needed for CoM oscillations would represent just one-half of the total cost of transport. Hence, the remaining half must be spent on muscle energy needed for co-contraction, work of the legs against one another, and work for swinging of the arms and legs. In comparison to humans, the world's most economical bipedal robot, Cornell Ranger, achieves a mechanical cost of transport of ∼0.08 (determined by doubling the cost of positive motor work) at a speed of 0.6 ms−1 (Bhounsule et al., 2014). After subtracting the energy used by its control system, Cornell Ranger has a total (electrical) cost of transport ∼0.11, and all of this energy is accounted for by positive and negative motor work with an average motor efficiency of 65%. Walking at a little more than one-half the speed of a human walking slowly, Cornell Ranger would need improved dynamics to both reach typical human walking speeds and achieve a mechanical cost of transport as low as 0.08.

## Summary

Legged gaits were first identified by the relative phases of leg contacts, which also identifies the sequence of leg contacts. A gait is defined as symmetrical when the relative phases of corresponding left-right pairs are separated by one-half stride cycle, such as in a striding biped or a trotting quadruped. When a left-right pair is used in unison (such as in hopping) or has staggered contacts (as in quadrupedal galloping), the gait is considered asymmetrical.

Locomotion is more correctly evaluated by measuring the dynamics of the center of mass (CoM). Traditional models have compared the phases of the CoM's potential and kinetic energy, using a spring-loaded inverted pendulum (SLIP) model when these energies are relatively in phase and a rigid inverted pendulum (RIP) model when they are out of phase. More recent work has introduced mechanical cost analysis that quantifies the work a gait requires by using the geometry of force and velocity vectors of the CoM.

All legged gaits include cyclic oscillations of the CoM; symmetrical gaits use two vertical oscillations, and asymmetrical gaits typically consist of only a single vertical oscillation per stride. SLIP-like "bouncing" gaits may be symmetrical (e.g., running and trotting) or asymmetrical (e.g., hopping and bounding), but they always couple braking with downward vertical velocity and propulsion with upward vertical velocity, resulting in mechanical work performed by the animal. Other symmetrical (e.g., walking and ambling) and asymmetrical (e.g., galloping and half-bounding) gaits, however, couple propulsion with downward vertical velocity and braking with upward vertical velocity, reducing an animal's mechanical cost of transport. This latter pattern takes advantage of d'Alembert's principle of orthogonal constraint by keeping force and velocity vectors more nearly perpendicular in each instance of the stride—thus reducing the mechanical cost of transport, which is zero in the idealized case of orthogonal constraint. Slow symmetrical walking gaits and faster asymmetrical galloping gaits exploit this principle to reduce work, and thus reduce the mechanical cost of transport. This reduction of mechanical cost of transport is a key feature of several gaits including bipedal and quadrupedal walking, fast gaits with multiple sequenced leg contacts, and brachiation. Theoretical mechanics show that increasing the number of sequenced leg contacts, dividing single foot contacts into multiple contacts, and increasing foot length are all mechanisms that can reduce mechanical cost of transport, as measured by mechanical cost analysis. Together with an increasing body of data from comparative animal locomotion, these principles hold substantial promise for the design and control of legged robots and prostheses that can achieve economical locomotion by reducing the mechanical cost.

## REFERENCES

## AUTHOR CONTRIBUTIONS

DL wrote approximately 60% of this review paper. SH wrote approximately 40% of this review paper.

## ACKNOWLEDGMENTS

We wish to thank André Seyfarth for valuable discussions of locomotion and physics, including d'Alembert's early work. DL was supported by an Alexander von Humboldt Research Fellowship.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Lee and Harris. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Minimally Actuated Walking: Identifying Core Challenges to Economical Legged Locomotion Reveals Novel Solutions

#### *Ryan T Schroeder 1\* and John EA Bertram 2*

*1 Biomedical Engineering Graduate Program, University of Calgary, Calgary, AB, Canada, 2 Cumming School of Medicine, University of Calgary, Calgary, AB, Canada*

Terrestrial organisms adept at locomotion employ strut-like legs for economical and robust movement across the substrate. Although it is relatively easy to observe and analyze details of the solutions these organic systems have arrived at, it is not as easy to identify the problems these movement strategies have solved. As such, it is useful to investigate fundamental challenges that effective legged locomotion overcomes in order to understand why the mechanisms employed by biological systems provide viable solutions to these challenges. Such insight can inform the design and development of legged robots that may eventually match or exceed animal performance. In the context of human walking, we apply control optimization as a design strategy for simple bipedal walking machines with minimal actuation. This approach is used to discuss key facilitators of energetically efficient locomotion in simple bipedal walkers. Furthermore, we extrapolate the approach to a novel application—a theoretical exoskeleton attached to the trunk of a human walker—to demonstrate how coordinated efforts between bipedal actuation and a machine oscillator can potentially alleviate a meaningful portion of energetic exertion associated with leg function during human walking.

#### *Edited by:*

*Monica A. Daley, Royal Veterinary College, United Kingdom*

#### *Reviewed by:*

*Madhusudhan Venkadesan, Yale University, United States Christian Michael Hubicki, Georgia Institute of Technology, United States*

*\*Correspondence:*

*Ryan T Schroeder<EMAIL_ADDRESS>
#### *Specialty section:*

*This article was submitted to Bionics and Biomimetics, a section of the journal Frontiers in Robotics and AI*

> *Received: 22 December 2017 Accepted: 24 April 2018 Published: 22 May 2018*

#### *Citation:*

*Schroeder RT and Bertram JEA (2018) Minimally Actuated Walking: Identifying Core Challenges to Economical Legged Locomotion Reveals Novel Solutions. Front. Robot. AI 5:58. doi: 10.3389/frobt.2018.00058*

Keywords: bipedal locomotion, energetics, control optimization, dynamics modelling, work minimization

## 1. Introduction

The movement patterns of humans and other animals have been described in remarkable detail (Bregler et al., 2004; Winter, 2009). However, why any given movement pattern is used, and not some other, is currently not thoroughly understood. Some of the machinery of biological systems (aspects of their morphology and internal organization) is inherited (involving inevitable evolutionary inertia). As a result, it becomes a challenge to distinguish true adaptive design modifications that improve locomotory capability from adaptations that simply accommodate functionally neutral, or even detrimental, anachronistic features. This makes it very difficult to interpret the actions used in locomotion, regardless of the technical detail in which it is analyzed. It would be beneficial to put the actions observed in locomotion in the context of what they accomplish, and determine the advantages and limitations a particular strategy provides to the motor control system.