# Towards Reuse and Recycling of Lithium-ion Batteries: Tele-robotics for
Disassembly of Electric Vehicle Batteries

Jamie Hathaway 1,2,†, Abdelaziz Shaarawy 1,† , Cansu Akdeniz 1, Ali Aflakian
1,2, Rustam Stolkin 1,2, Alireza Rastegarpanah 1,2,∗,

###### Abstract

Disassembly of electric vehicle batteries is a critical stage in recovery,
recycling and re-use of high-value battery materials, but is complicated by
limited standardisation, design complexity, compounded by uncertainty and
safety issues from varying end-of-life condition. Telerobotics presents an
avenue for semi-autonomous robotic disassembly that addresses these
challenges. However, it is suggested that quality and realism of the user’s
haptic interactions with the environment is important for precise, contact-
rich and safety-critical tasks. To investigate this proposition, we
demonstrate the disassembly of a Nissan Leaf 2011 module stack as a basis for
a comparative study between a traditional asymmetric haptic-“cobot” master-
slave framework and identical master and slave cobots based on task completion
time and success rate metrics. We demonstrate across a range of disassembly
tasks a time reduction of 22%–57% is achieved using identical cobots, yet this
improvement arises chiefly from an expanded workspace and 1:1 positional
mapping, and suffers a 10–30% reduction in first attempt success rate. For
unbolting and grasping, the realism of force feedback was comparatively less
important than directional information encoded in the interaction, however,
1:1 force mapping strengthened environmental tactile cues for vacuum pick-and-
place and contact cutting tasks.

##  1 Keywords:

robotic disassembly, telerobotics, lithium-ion batteries, EV batteries,
haptic, teleoperation

##  2 Introduction

As a result of the increasing demand for electric vehicles (EVs) (Rietmann et
al., 2020), a large number of EV batteries are expected to reach end of life.
Owing to a combination of contained high-value materials such as lithium,
nickel and cobalt (Thies et al., 2018), and a limited lifespan of 10-15 years
(Ai et al., 2019), there is an increasing research interest towards EV battery
disposal. Battery disassembly is a critical step to enable gateway testing and
sorting of end-of-life (EoL) battery components for re-use, and recovery of
high-purity materials for recycling. This remains a predominantly manual
process for trained personnel, requiring a high degree of precision and
attention Tang and Zhou (2004); Tan et al. (2021). However, EV batteries have
numerous associated thermal and chemical hazards due to residual charge held
within the battery and risk of thermal runaway. While previous studies such as
Lander et al. (2023) have emphasised the importance of autonomous disassembly
for reducing disassembly cost, limitations are presented due to the high
degree of variability in EV battery models (Pehlken et al., 2017), as well as
the lack of dexterity alongside the highly dynamic, unstructured work
environments—chiefly due to variety of models and manufacturers and lack of
design standardisation. In consequence, hybrid frameworks for EV battery
disassembly have been proposed in which robot and human work closely and
collaboratively (Tan et al., 2021). However, the fact that robots perform
tasks in the same environment as humans in production poses risks for humans.
EV battery disassembly environments are considered hazardous for a human being
to be present in; thus, direct collaboration with robots in such environments
is critical. This is critical for damaged batteries which are challenging to
disassemble due to further uncertainty in component end-of-life condition,
which further compounds existing safety risks.

Tele-robotics aims to mitigate the hazards of disassembly by enabling a human
operator to carry out disassembly tasks remotely through a local interface
while imparting some of the human operator’s dexterity and fine motor control
to the robot. Haptic devices are commonly employed in telemanipulation studies
due to their ability to deliver force feedback to the operator while carrying
out tasks. Nevertheless, one key challenge in haptic devices can be the
master-slave asymmetry in regards of the kinematics Li et al. (2020); hence,
there exists a range of mapping schemes by which the motion of the master
device can be mapped to that of the slave. Previously, it has been emphasised
the nature of this interface is important for carrying out dangerous/sensitive
tasks (Bernold, 2007). Furthermore, for disassembly in hazardous settings, it
is suggested that the quality and realism of the feedback, and interface
provided to the operator can greatly impact the level of task performance
(Bolarinwa, 2022).

Using tele-robotics for the application of EV battery disassembly is not well
explored, particularly, where damaged batteries present further critical
challenges to the process of disassembly. Each stage of battery disassembly
consists of a range of complex and precise contact-rich tasks which require a
mixture of tactile and visual feedback to successfully complete disassembly.
Given that not all EV battery disassembly tasks can be completed autonomously,
this study demonstrates the application of tele-robotics to a range of battery
disassembly tasks, such as unbolting, sorting and cutting. A series of tools
were custom-designed in order to complete the tasks. We evaluate and compare
the success rate and task execution time between a high-cost platform using
two identical collaborative robots (“cobots”) and a relatively low-cost
platform using a haptic device paired with a single cobot. We examine
causative factors for differences in performance between these two platforms
for each task.

The remainder of the paper is structured accordingly: Section 3 provides a
survey of related studies in disassembly and telerobotics. The experimental
setup for carrying out disassembly tasks is established in Section 4, while
Section 5 introduces the control architecture for bilateral telemanipulation
for both platforms. Section 6 defines the experimental case studies for
different EV battery disassembly tasks, before evaluation of each
telemanipulation platform on the basis of objective performance measures in
Section 7, and finally Section 8 concludes the paper.

##  3 Related Work

Methods of battery disassembly can be broadly categorised into fully-manual,
fully-autonomous, and semi-autonomous approaches. Given the hazards that EV
battery disassembly environments pose against human operators, the literature
has been more oriented towards developing autonomous and semi-autonomous
approaches on the basis of potential improvements in efficiency and safety.
Autonomous approaches aim to increase the efficiency of disassembly by
allowing robots to plan and carry out repetitive tasks in unstructured
environments through the use of visual and tactile feedback. Examples of such
works can be found in Zorn et al. (2022); Zhang et al. (2023); Choux et al.
(2021); Farhan et al. (2021). A common factor in these approaches is the use
of labelling and detection methods to autonomously identify components and
fasteners and construction of plans accordingly. However, this suffers from
dependency on data and prior knowledge, and the risk of misidentification of
battery components. For damaged batteries, existing prior knowledge datasets
may not be suitable, or autonomous disassembly processes may fail; e.g. a
fastener must be dislodged manually, or autonomous grasping fails due to
structural deformation of components, requiring manual alignment. Furthermore,
for sorting and lifting applications, the complexity of planning and collision
avoidance remains an outstanding problem Zhou et al. (2019); Tang et al.
(2022). Other approaches have aimed to reduce complexity of disassembly in
various settings through tool design, such as gripper extensions Borràs et al.
(2018) or flexible grippers Schmitt et al. (2011), to assist with unscrewing,
grasping and other contact-rich manipulation tasks. However, even with such
adaptations, autonomous approaches suffer from difficulties with
generalisation to a range of tasks and across differing battery designs. Other
studies such as Baazouzi et al. (2021) have examined optimisation of the EV
battery disassembly process, emphasising the importance of battery design
considerations for disassembly. As these are currently lacking for EVs, this
introduces a high degree of variability and uncertainty into the disassembly
process.

Recently, human-robot collaboration (HRC) has garnered attention for
disassembly of end-of-life products, integrating both the robot’s high
efficiency in repetitive tasks and the human flexibility with higher
cognition. However, there are few studies on this subject in the literature.
In (Kay et al., 2022), a high-speed rotary cutting wheel was adapted to
perform robotic cutting at various points of the battery module casing. The
proposed framework allowed a robot to efficiently carry out semi-destructive
disassembly processes while allowing human operators to rapidly sort the
battery components and remove connectors. Frameworks have further been
proposed to semi-automate the process of extracting and sorting different
objects from an EV battery pack using a mobile manipulator Rastegarpanah et
al. (2021). This study uses the behaviour tree model, which connects different
robot capabilities, including navigation, object tracking and motion planning,
for cognitive task execution and tracking in a modular format. Another study
looked into human-/multi-robot- collaborations Gil et al. (2007) in a
disassembly scenario, where a technician and a number of robots coexist in the
same environment interacting with each other to complete disassembly tasks.
These presented articles demonstrate that HRC scenarios can offer both safety
and time improvements over manual and autonomous disassembly strategies for EV
LIBs. Nonetheless, issues such as coordination and allocation of tasks between
robot and human and handling camera occlusion Fan et al. (2022) remain
outstanding topics of research. Furthermore, in some cases, it is not possible
for robots to be in the same environment as humans, as the environment is
considered hazardous for humans.

Telemanipulation has been commonly employed in the nuclear industry for
delicate handling of wastes that present a radiation hazard for human
personnel. For example, the use of gloveboxes is examined in Tokatli et al.
(2021) in the context of telerobotics as a means of reducing radiation
exposure risks to human personnel. Another study conducted real world
experiments of a user performing nuclear decommissioning task via a unilateral
teleoperated robotic system Mizuno et al. (2023). The study conducted a
comparison analysis between three teleoperation scenarios: fully manual,
teaching-based, and planning-based, in terms of safety, cognitive demand, and
preparation time. Findings showed that planning-based is the most time
efficient, yet lacks safety. Although these articles presented successful use
cases of teleoperation in hazardous environments, bilateral systems were not
investigated to show the importance of force feedback to the user on
performance. Haptic devices have been extensively used in many studies
developing bilateral teleoperation systems for various applications Giri et
al. (2021). Haptic devices allow the operator to feel external force/torque,
and further haptic cues that can be obtained in complex virtual environments.
One study employed haptic devices as master devices to control dual 7-DOF
serial arm manipulators to perform maintenance and repair tasks in nuclear
power plants Ju and Son (2022). They developed a shared bilateral
teleoperation system including three elementary technologies: egocentric
teleoperation, virtual fixture, and vibration suppression control to assist
the human operator in performing shaft- and clutch-based peg-in-hole tasks.
Furthermore, they conducted human-centric evaluations to measure the
performance in terms of completion time, trajectory length, and human effort.
The results of this study showed that haptic cues improved task performance
significantly. Similar approaches have aimed to examine the effect of virtual
constraints and force feedback guidance on task performance. Such approaches
have been proposed in He and Chen (2008), based on imposition of rotational
constraints on a component when axially aligned with its target. A related
concept is proposed in Abi-Farraj et al. (2016), based on a shared control
approach to remote object manipulation using visual information, and extended
to a real environment in (Abi-Farraj et al., 2018). In this way, the user is
assisted during a grasping task by constraining the gripper orientation to the
surface normal of a virtual sphere, centred on the object centre of mass.
While performance improvements for these tasks have been documented, these
approaches limit the flexibility provided to the operator; such constraints
are often task-specific and susceptible to failure in edge cases, for example,
if the autonomously identified grasp point is not suitable. Alternative
approaches for sorting and separation of objects in an unstructured
environment have been proposed based on haptic guidance cues Abi-Farraj et al.
(2020). In this way, a visual inspection of the object is used to generate
suitable grasp points, and the user is guided towards the suggested grasp
point through tactile cues and vibration without constraining the free
manipulation of the robot.

The majority of considered studies have focused on telerobotics for assembly
tasks, nuclear decommissioning and waste handling applications. However, there
is a paucity of research surrounding the use of telerobotics in an EV
disassembly context. Furthermore, while many studies have explored the effect
of shared autonomy and control system design on task performance, a limited
number of works have investigated the nature of the interface exposed to the
operator and its effects on task performance. Such a comparison has been
explored in Gliesche et al. (2020) between a keyboard-mouse setup, XBOX
controller and a bilateral setup using a haptic device. For a range of patient
care tasks, involving grasping and moving a remote and adjusting a camera
view, a haptic device was found to improve the speed at which operators
carried out tasks, however no subjective differences in mental load were
identified. In Singh et al. (2020), a framework was presented using a pair of
identical cobots, and explores human-centric performance metrics between
methods of rendering guidance and environmental forces to the user on the
performance of a peg-in-hole task. However, the range of tasks remains limited
and the effects of the interface remain unclear for the wider range of tasks
featuring in a disassembly environment.

##  4 Experimental Setup

Figure 1: Overview diagram representing the experimental setup adopted in this
work, alongside a brief breakdown for an EV battery disassembly process, from
the battery pack to the battery cell.

This study focuses on the Nissan Leaf 2011 battery pack as a case study to
demonstrate a range of disassembly tasks using telemanipulation. The Nissan
Leaf 2011 pack comprises 192 cells enclosed within 48 modules, arranged with
two forward vertical stacks of 12 modules and a single rear horizontal stack
of 24 modules. An overview of the main disassembly stages for pack-to-cell
disassembly is given in Table 1; for brevity, this is provided for only the
forward module stacks. The level of autonomy presented in Table 1 was inferred
from understanding of the current manual disassembly process and use of design
features, such as types of fasteners and accessibility of components. In
general, the range of semi-/fully autonomous tasks will vary between battery
designs and manufacturers, however, overall, there is a motivation to increase
the level of autonomy to decrease disassembly costs Lander et al. (2023). We
formulate a basic battery disassembly workstation design consisting of 2
Franka Emika Panda cobots and a Phantom Omni haptic device. The Franka Emika
Panda is a 7 degree of freedom (DoF) robot with a 3kg payload. A combination
of torque control and onboard torque sensing capabilities and low payload
makes this robot suitable for accomplishing precise assembly and disassembly
tasks in a shared human-robot workspace. The Phantom Omni comprises a 6 DoF
handheld articulated arm with independent control of force feedback along 3
axes, with a maximum force capability of 3.3N. All devices were connected in a
ROS network to a desktop with Intel(R) Core(TM) i7-8086K 8-core processor with
4 GHz base clock and 32 GB RAM. An overview of the experimental setup is shown
in Figure 1.

Based on the disassembly sequence in Table 1, we consider a selection of
repetitive tasks identified in related studies Tan et al. (2021) where robots
provide an advantage over manual disassembly. These consist of unbolting, such
as of fasteners connecting a stack of modules; removal and sorting (pick and
place) of disassembled waste components, and cutting to mechanically separate
components where fasteners cannot be removed non-destructively. To deal with
the range of tasks presented in the case of battery disassembly, a range of
commercially available and custom designed tools were employed, shown in
Figure 2. For this study, we design a custom socket wrench tool that can be
employed with a range of fastener sizes. For cutting, a motorised slitting saw
tool was designed specifically for the low-payload cobots presented to
accomplish low-power cutting tasks. For pick and place, the Franka Hand two-
finger gripper was employed for grasping thin, light wastes such as bolts and
plates, while the Robotiq EPick suction gripper is applied for larger, heavier
materials such as battery modules.

Step # | Disassembly task |  Type
---|---|---
1 |  Top case |  Remove service plug retainer |  M
2 |  |  Remove upper case bolts & lift top case |  At
3 |  Battery controller |  Remove mounting bolts |  S-At
4 |  |  Disconnect harness connectors & remove battery controller |  M
5 |  Junction box & harnesses |  Disconnect interlock circuit harness & heater harness connectors |  M
6 |  |  Remove mounting nuts & front stack connecting bus-bar |  S-At
7 |  |  Remove battery member pipe |  S-At
8 |  |  Remove junction box cover |  M
9 |  |  Remove central bus bar bolts and remove central bus bar |  S-At
10 |  |  Remove current sensor bus bar mounting bolt |  S-At
11 |  |  Remove switch bracket mounting bolts |  S-At
12 |  |  Invert switch bracket, disconnect harnesses & remove switch bracket |  M
13 |  |  Remove high voltage (HV) harness bolts & remove HV harnesses |  S-At
14 |  |  Disconnect voltage & temperature sensor harnesses |  M
15 |  |  Remove junction box mounting nuts & junction box |  M
16 |  Heaters |  Disconnect harness connectors from heater and heater relay unit |  M
17 |  |  Remove heater & heater relay mounting nuts |  S-At
18 |  |  Remove heater controller unit & heaters |  M
19 |  _Front module stack(s)_ |  Remove stack mounting nuts |  At
20 |  |  Extract module stack |  At
21 |  |  Remove bus bar cover |  M
22 |  |  Remove bus bar terminal mounting bolts & mounting screws |  S-At
23 |  |  _Remove end plate bolts_ |  At
24 |  |  _Remove end plate_ |  S-At
25 |  |  _Electrical test & sort modules_ |  S-At
26 |  _Module_ |  _Separate module cover_ |  S-At
27 |  |  Glue separation |  At
28 |  |  Separate cell tabs from terminal assembly |  S-At
Table 1: Sequence of disassembly operations for pack-to-cell disassembly of
Nissan Leaf 2011. For brevity, only disassembly of the front module stack is
considered. The type of task can be classified as fully manual (M), requiring
specialised tools or dexterous hand-manipulation, semi-autonomous (S-At),
where a robot can accomplish the task with the assistance of a human operator,
and fully autonomous (At) tasks accomplishable without human intervention. A
contiguous sequence of semi-autonomous processes can be observed for
disassembly and sorting of the module stack; tasks considered in this study
are _emphasised_.

(a) Socket wrench tool

(b) Motorised cutter tool

(c) Two-finger gripper

(d) Vacuum gripper

Figure 2: Tool attachments considered for the tasks of unbolting, cutting and
sorting.

###  4.1 Master-Slave Telemanipulation using a Haptic Device as Master and a
Cobot as Slave

A common framework to accomplish telemanipulation tasks is to use a lower-
cost, handheld platform such as a haptic device in combination with a robot in
a master-slave configuration. In this case, we consider the case of a Phantom
Omni haptic device and a Panda cobot (Figure 3). Due to a mismatch in the DoFs
of the Omni and Panda robot - more generally, any over-actuated robot - there
is a limitation that not all degrees of freedom of the robot can be controlled
independently, reducing the amount of control provided to the user. Typically,
this requires a definition of a mapping function that maps the joint positions
of the haptic device to that of the slave arm. Such a mapping can be achieved
by mirroring the Cartesian pose or twist of the haptic end-effector to that of
the slave robot. This provides a more intuitive framework for the user to
position the robot to accomplish tasks. However, this typically renders the
control vulnerable to singularities and joint limits, due to the solution of
inverse kinematics to compute the required joint-space motion. Furthermore,
the smaller scale of motion afforded by the Omni in both joint and task space
implies a compromise between speed of coarse motion, where the motion of the
haptic device is scaled to achieve larger motions on the robot; or precision
of fine positional alignment, where the motion of the haptic device is mapped
directly to the robot or even reduced. Moreover, due to the limited force
capabilities of the haptic device, the force feedback cannot be mapped from
the robot to the haptic 1:1. Therefore, the feedback can potentially feel
unnatural or deliver insufficient cues for the operator, such as when
exceeding safety limits imposed on force.

Figure 3: Outline of telemanipulation framework consisting of Phantom Omni
haptic device and Franka Emika Panda cobot. FK refers to the forward kinematic
mapping of follower joint configuration $\boldsymbol{q}_{f}$ to end-effector
pose $\boldsymbol{x}_{f}$. Note the transformation matrices relating the base
frames of the haptic and cobot are omitted for simplicity.

###  4.2 Master-Slave Telemanipulation Using Two Identical Cobots

Alternatively, in this work we consider a platform consisting of two identical
Franka Emika Panda cobots operating in a master-slave configuration. With this
approach, the user directly manipulates the master Franka arm, whose motions
are directly mirrored to that of the slave arm. Owing to the identical
configuration of both robots, both joint position and torques can be mapped
between the robots 1:1. This 1:1 mapping results in natural and responsive
feedback being delivered to the user. However, this also poses hazards as the
user will be potentially exposed to the full forces involved in a specific
task. The joint space control of both arms furthermore has advantages in the
problem of singularities and joint limits, which are present in mapping the
Cartesian end-effector pose of the master to the task space pose of the slave
robot. However, the lack of task-space control has potential drawbacks when
accomplishing tasks along specific task directions, such as removing bolts or
cutting, more difficult and less intuitive for the user.

Figure 4: Outline of telemanipulation framework consisting of two identical
Franka Emika Panda cobots.

##  5 Methodology

To achieve a virtual coupling between master and slave devices, we first
consider the dynamic equation of a rigid $N$-link manipulator in joint space

$\mathbf{M}(\boldsymbol{q})\boldsymbol{\ddot{q}}+\mathbf{C}(\boldsymbol{q},\boldsymbol{\dot{q}})+\boldsymbol{g}(\boldsymbol{q})=\boldsymbol{\tau}_{\mathrm{ext}}+\boldsymbol{\tau}$
(1)

where $\mathbf{M}\in\mathbb{R}^{N\times N}$,
$\mathbf{C}(\boldsymbol{q},\boldsymbol{\dot{q}})\in\mathbb{R}^{N\times N}$,
$\boldsymbol{g}(\boldsymbol{q})\in\mathbb{R}^{1\times N}$ are the joint-space
inertia matrix, Coriolis and centrifugal matrix and gravitational torques
respectively, and $\boldsymbol{\tau}_{\mathrm{ext}}\in\mathbb{R}^{1\times N}$,
$\boldsymbol{\tau}\in\mathbb{R}^{1\times N}$ are the vectors of external and
control torques acting on each link respectively. We denote the joint
configurations $\boldsymbol{q}$ and command torques $\boldsymbol{\tau}$ by
subscripts $l,f$ for master and slave respectively.

For the haptic device, 1:1 mapping between each joint cannot be achieved in
practice because of its 6 DoF kinematic chains it has compared to the 7 DoF
Franka arm. Hence, it is required to either map the joint space onto a reduced
subset of the full joint space of the robot, or operate in Cartesian space. In
this work, Cartesian mapping is employed to velocity control the slave Franka
arm with the Phantom Omni master arm in all Cartesian motion axes (XYZ
translation and rotation). As the human operator moves the master arm in its
workspace, delta Cartesian pose $\boldsymbol{\dot{x}_{l}}$, composed of
position and orientation, is computed and then commanded to the slave arm.
However, since reference coordinate systems of both arms are different (as
shown in Figure 5), delta Cartesian pose $\boldsymbol{\dot{x}_{l}}$ undergoes
transformations to correctly map it with respect to Franka arm’s base frame.
The transformation mapping is calculated as

Figure 5: Cartesian mapping for the master-slave telemanipulation setup
between the Phantom Omni haptic device and Franka Panda robot arm.

${{}^{F}}\mathbf{T}_{\Delta}={}^{P}_{F}\mathbf{T}\cdot{{}^{P}}\mathbf{T}_{\Delta}=\left[\begin{array}[]{c
c}{{}^{F}}\mathbf{R}_{\Delta}&{{}^{F}}\boldsymbol{t}_{\Delta}\\\ \hline\cr
0&1\end{array}\right]$ (2)

where ${}^{P}_{F}\mathbf{T}$ is the homogeneous transformation matrix from
Franka arm base frame to Phantom Omni base frame,
${{}^{F}}\mathbf{T}_{\Delta}$, and ${{}^{P}}\mathbf{T}_{\Delta}$ represent the
delta transformation matrices for Franka and Phantom respectively. Position
and orientation components of ${{}^{P}}\mathbf{T}_{\Delta}$ are assigned to
the desired pose $\boldsymbol{x}_{t}$ to compute the pose error
$\boldsymbol{e}_{x}=\boldsymbol{x}_{f}-\boldsymbol{x}_{t}$ for the slave arm.
Thus, the slave arm control law is:

$\boldsymbol{\tau}_{f}=\mathbf{J}^{\mathsf{T}}\left(-\mathbf{K}_{p}\boldsymbol{e}_{x}-\mathbf{K}_{d}\mathbf{J}\boldsymbol{\dot{q}_{f}}\right)+\mathbf{C}(\boldsymbol{q_{f}})+\boldsymbol{g}(\boldsymbol{q_{f}})$
(3)

where $\mathbf{J}\in\mathbb{R}^{7\times 6}$ is the slave manipulator Jacobian
mapping joint to end-effector velocities and $\mathbf{K}_{p}$,
$\mathbf{K}_{d}$ are controller stiffness and damping matrices respectively.
This results in the desired closed-loop dynamic behaviour from (1) (where
$\mathbf{\Lambda}\in\mathbb{R}^{6\times 6}$ is the operational space inertia
matrix):

$\mathbf{\Lambda}\boldsymbol{\ddot{x}_{f}}+\mathbf{K}_{d}\boldsymbol{\dot{x}_{f}}+\mathbf{K}_{p}\boldsymbol{e}_{x}=\boldsymbol{F}_{\mathrm{ext}}$
(4)

Force Feedback is an essential part of a bilateral teleoperation system in
which a force feedback is maintained at control frequency. This helps the user
to have a tactile perception of the slave robot’s environment. In a similar
way to (2), external force vector $\boldsymbol{F}_{\mathrm{ext}}$ experienced
at the Franka end-effector is transformed with respect to the Phantom so the
user is able to perceive it as force $\boldsymbol{F}_{l}$ as follows:

$\boldsymbol{F}_{l}=G\cdot{{}^{P}_{F}}\mathbf{T}^{-1}\cdot\boldsymbol{F}_{\mathrm{ext}}$
(5)

Due to the mismatch in force capabilities between master and slave devices,
the feedback is scaled by a factor $G=0.1$. This factor was determined
experimentally by comparing the maximimum expected force across all tasks from
preliminary data and scaling to the maximum force capabilities of the haptic
device (3.3N). To distort the force feedback to a minimal extent, and to
maintain consistency with the constant 1:1 feedback of the identical cobot
setup, this factor was held constant across all trials.

For the Franka arm, a joint impedance control scheme is used that directly
maps the joint configuration of the master arm to the slave arm (Figure 4).
The control law is defined as follows:

$\boldsymbol{\tau}_{f}=-\mathbf{K}_{p}\boldsymbol{e}_{q}-\mathbf{K}_{d}\boldsymbol{\dot{e}}_{q}+\mathbf{C}(\boldsymbol{q}_{f})+\boldsymbol{g}(\boldsymbol{q}_{f})$
(6)

where $\boldsymbol{e}_{q}=q_{f}-q_{l}$ is the joint space error. This results
in the closed-loop dynamics in joint space for the slave arm

$\mathbf{M}\boldsymbol{\ddot{q}_{f}}+\mathbf{K}_{d}\boldsymbol{\dot{e}}_{q}+\mathbf{K}_{p}\boldsymbol{e}_{q}=\boldsymbol{\tau}_{\mathrm{ext}}$
(7)

To provide force feedback to the user, the master control torques are
calculated as:

$\boldsymbol{\tau}_{l}=\boldsymbol{\tau}_{\mathrm{ext}}-\mathbf{K}_{d,l}\boldsymbol{\dot{q}}_{l}$
(8)

where the force feedback is computed directly as the estimated external torque
applied to the slave arm. Due to the combination of higher forces applied to
the master with the low stiffness of the human operator, an additional damping
term $\mathbf{K}_{d,l}$ is added to the response of the master to reduce
oscillations resulting from the displacement of the master arm caused by the
bilateral master-slave coupling.

##  6 Case Studies

Figure 6: Part of an EV battery disassembly process showing the case studies
experimented on through this work in order: 1) Unbolting fasteners. 2)
Removing fasteners 3) Removing module cover plate. 4) Sorting modules. 5)
Surface contact cutting.

A contiguous sequence of tasks relating to the disassembly and extraction of a
stack of modules from the Nissan Leaf 2011 battery pack were identified as
feasible targets for robotic disassembly, presented in Figure 6. The
considered case study encapsulates a range of contact-rich tasks required to
disassemble and recover the battery modules from an individual stack. The
modules contain the active material within the battery and hence are
considered a safety-critical aspect of the disassembly process due to the
associated handling risks, such as risk of shorting the terminals and risk of
mechanical shock from mishandling. Each task was attempted five times
(trials). For each task, the operator is provided with two fixed camera views
of the module stack, and otherwise does not have a direct view of the scene.
These views are held constant for all tasks with the exception of cutting,
where the operator is instead provided two camera views of a material holder
containing the cutting workpiece. Prior to commencing each task, both master
and slave robots are initialised to a home position in joint space held
constant for all tasks. As the focus of this work is not on human factor
analysis and subjective measures of performance based on end-user evaluations,
but on objective measures of task performance, the operator is assumed to have
familiarity and prior experience with both teleoperation platforms. In
addition, each operator was given 10 minutes of training with each task with
both telemanipulation systems before first attempting each task. Four expert
operators participated in the study. For each trial, a single operator was
selected randomly to perform the task. A more detailed description of each
task is provided as follows.

###  6.1 Unbolting

This task considers the unbolting of a set of 4 fasteners constraining an
individual stack of modules. The operator has access to a motorised universal
socket wrench tool mounted at the robot’s wrist. The operator is responsible
for aligning the socket wrench with the bolt and operating the tool to unscrew
the fastener. The task is considered successful if the bolt is removable by
hand without any further unscrewing action. If the success condition is not
met after the first attempt, or the configured force thresholds (40N) of the
robot are exceeded, the task is considered a failure.

###  6.2 Removing the Fasteners

This case study follows from the previous unbolting stage by removing each
fastener from the stack before removal of the cover. For this task, the Franka
hand was used with a configured grasping force of 50N. The operator was
required to remove a set of 8 fasteners by maneuvering the hand towards each
of the fasteners, grasping and removing the bolt from the stack and depositing
into a container. Due to the limitation of the camera views of the object, the
operator must use a mixture of tactile and visual exploration to successfully
remove the fasteners. For each bolt, the failure condition is met if the bolt
is not grasped after the first grasp attempt, or if the grasp is lost outside
of the target container.

###  6.3 Removing the Module Cover Plate

After the removal of the fasteners, the operator must then remove the module
cover plate to access the underlying module stack. Due to the weight and
geometry of the cover plate, it is essential for the operator to find and
manoeuvre towards a good grasp point to ensure safe transportation of the
cover during removal. The configured grasping force was increased to 60N for
all experiments. The failure condition is met if the first grasp is
unsuccessful or the grasp is lost during the transportation of the cover.

###  6.4 Sorting Modules

This case study considers unstacking and sorting of the EV battery modules
using a vacuum suction gripper. The operator must remove a pair of modules
from a stack and deposit them into a container. This task requires visual
positioning of the gripper onto a suitable surface for grasping, while
furthermore maintaining contact to engage the suction cups with the material
without exceeding the force limits of the robot. Similarly to the cover
removal case study, the failure condition is met if the first grasp is
unsuccessful, or if the grasp is lost during transportation.

###  6.5 Contact Cutting

Additional semi-destructive disassembly tasks may be carried out to further
disassemble the individual modules to access the Li-ion cells or to separate
and remove fasteners or connectors that are not amenable to non-destructive
disassembly. We consider the case study of contact cutting of a planar
material along a predefined visually marked desired path using a slitting saw
tool. Due to the limited availability of battery materials and the power
limitations of the spindle, we consider cutting a cardboard sheet as a
benchmark for the more general process of cutting different planar materials.
The operator must use tactile feedback to control the cutting force while also
using visual feedback to achieve precise positioning along the path. The
desired cutting path consists of a window of $\pm$2.5mm measured from the
centroid of the marked path. If the cut deviates from the path greater than
this threshold, or if the cut is incomplete along parts of the desired path,
the failure condition is met.

##  7 Results and Discussion

For each case study, the overall success rate and average task completion time
over all trials are summarised in Table 2. For all tasks, the success rate is
observed to exceed or equal 50% with both platforms, with the lowest success
rate of 50% observed for the task of bolt removal with an identical cobot. For
the majority of the tasks, a success rate of over 75% is achieved,
demonstrating the feasibility of the module stack disassembly process with
both cobot and haptic device tele-robotics platforms. Between each platform,
the success rate is broadly comparable for unbolting and bolt removal, where
the operator success rate is 10-15% higher than the identical cobot case.
However, cover removal is noticeably the most simple task as it is merely
almost a planar trajectory; given that the operator managed to reach a firm
grasp point on the cover plate, which was achieved 100% in all operators’
trials with both platforms. On the other hand, the largest differences are
observed with unstacking and cutting, where in the former case the identical
cobot is outperformed by the haptic device by 30%, whereas in the latter case,
the inverse is true, with a 20% improvement in success rate. Unstacking
findings can be justified due to the design mechanism of the vacuum suction
gripper, where the gripper has to be in a direct contact and, more
importantly, perpendicular orientation with respect to the module surface to
achieve a successful grip. Hence, manipulating the suction gripper’s
position/orientation to achieve this in Cartesian space with the haptic
platform showed higher success rate than in joint space with the identical
cobot platform, where gripping failure cases occurred due to orientation
misalignment. Furthermore, the findings of cutting trials emphasize the
significance of force feedback. Identical cobot platform showed higher success
rate because the force feedback is maintained at a 1:1 scale, whilst in haptic
platform, it is scaled down due to limited force capabilities as (5).
Therefore, the user did not experience the full scaled forces exerted on the
end-effector while cutting.

| Haptic | Franka
---|---|---
| Success rate [%] | Avg. task time [s] | Success rate [%] | Avg. task time [s]
Unbolting (4$\times$) | 95 | 188$\pm$23 | 85 | 124$\pm$13
Nut/bolt removal (8$\times$) | 63 | 713$\pm$89 | 50 | 410$\pm$63
Cover removal | 100 | 101$\pm$15 | 100 | 70$\pm$6
Sorting modules (2$\times$) | 90 | 179$\pm$19 | 60 | 77$\pm$5
Cutting | 60 | 122$\pm$26 | 80 | 95$\pm$18
Table 2: Comparison of performance metrics for disassembly tasks for
telemanipulation with Phantom Omni haptic device and identical cobot (Franka)
platforms.

In Figure 7, a detailed breakdown of task completion times by trial is
presented, indicating the time spent in each stage of the trials. Depending on
the task, these stages subdivide each task consecutively, from start to
completion, into categories: a “Coarse” stage where the operator
telemanipulates the robot through rough visual alignment of the tool, followed
by a “Fine” stage utilising tactile and visual feedback for precise
positioning of the tool towards the interaction point. In the “Action” stage,
the operator interacts with the component to perform a task after successful
alignment of the tool. These actions correspond to unbolting, gripping and
engagement of the cutter for nut/bolt removal, sorting and cutting
respectively. Finally, the “Place” stage is encountered for grasping tasks
after a successful grasp of the target object, during which the operator moves
the grasped object and releases at a target position. The coarse and fine
stages were annotated according to the proximity of the tool to the task-
dependent target; a distance of the tool within 5cm of the target - for
example, bolts and cover grasp points - indicates the fine alignment stage.
The place stage was specified for coarse motions performed after grasping,
which reverts to the coarse phase of motion after release of the grasped
object. The action phase was annotated based on task-specific position and
force thresholds. For example, for the sorting task, the task-relevant action
is engagement and evacuation of the suction cups to grasp the module. From the
4 stages breakdown presented in Figure 7, one can have a clear interpretation
of what stages the operators spent most of the task time at, indicating their
exerted efforts in completing each of the stages with respect to the two
comparable platforms.

(a) Unbolting

(b) Bolt removal

(c) Cover removal

(d) Sorting modules

(e) Cutting

Figure 7: Breakdown by task trial of task completion times between Haptic and
Franka telemanipulation masters. Data are omitted when the failure condition
is met before completion of the task, such as by violation of configured force
limits. Tasks are broadly split into 4 categories: an initial “Coarse” phase
of approximate visual tool alignment, a “Fine” phase of precise visual and
tactile alignment, an “Action” phase consisting of the task-relevant action,
e.g. unbolting, cutting, and “Place” phase where the user deposits grasped
objects.

From an overview of Figure 7, the identical cobot platform achieved shorter
completion times on average across all tasks, compared to the haptic platform.
Additionally, the highest difference in average time between the two platforms
is observed for the bolt removal and sorting tasks, on average requiring
$\sim$1.7–2.3$\times$ longer to complete with the haptic device respectively.
Absolute task completion times were more consistent between trials with the
identical cobot platform for all tasks. To evaluate the difference in task
completion times in a timescale-invariant manner, the standardised mean
difference (SMD) effect size metric was used. Given the mean and standard
deviation $(\bar{t}_{h},\sigma_{{t}_{h}})$, $(\bar{t}_{f},\sigma_{{t}_{f}})$
for each platform respectively, the SMD can be defined as:

$\mathrm{SMD}=\frac{\bar{t}_{h}-\bar{t}_{f}}{\sqrt{\sigma_{t_{h}}^{2}+\sigma_{t_{f}}^{2}}}$
(9)

and provides an evaluation of the effect of each platform on completion time
relative to the amount trial-to-trial variation. Values of
$\left|\mathrm{SMD}\right|\geq 0.8$ implies a significant effect, and the
converse indicates a small or marginal effect.

For the considered module stack disassembly case study, the highest proportion
of time was spent unbolting and removing the retaining fasteners. This is
observed from Figure 7a and 7b, where the ’fine’ stage occupies 60%, 63%, and
47%, 50% of the average task completion time, respectively, in both platforms;
therefore, the fine alignment stage was the primary contributor to the
reduction in overall task completion speed. This indicates that regardless of
the platform used, these two tasks, among the other disassembly tasks, were
the most effort demanding; requiring a combination of precise visual and
tactile alignment of the tool to successfully unbolt/remove the fasteners.
However, the SMD for unbolting and bolt removal respectively were 1.09 and
1.24, which indicates large improvements afforded by the identical cobot
setup.

Figures 8-11 present the position graphs of the Franka slave’s end-effector in
Cartesian space, as well as the external forces experienced during a sampled
trial from each task in the case study with both platforms. The figures also
display the 4 categorised stages (’Coarse’, ’Fine’, ’Action’, ’Place’) color-
shaded in each graph’s background corresponding to each stage, as introduced
in Figure 7, throughout the time span of the presented trial. In Figure 8,
spikes in the force z plot enclosed in the yellow region (’action’ stage)
correspond to the action of unbolting of the fasteners using the wrench tool.
Similarly, Figure 9 represents the bolt removal task in which fasteners are
grasped, lifted up from their holes, and placed in a container; thus, the
position z spikes in the red region (’place’ stage). Interestingly, despite
the differing scale of force feedback between the two platforms, the magnitude
of external force observed over time for the bolt removal task is similar for
both platforms. This suggests that the realism and scaling of the force
feedback is less important for accomplishing precise grasping tasks for
disassembly than the directional guidance provided by the force feedback
during contact.

(a) Haptic master

(b) Franka master

Figure 8: Overlay of position and estimated external forces at the end-
effector for the unbolting task (trial 2) using a motorised universal socket
wrench tool. Increases in force ($\sim$10-15N) in the surface normal direction
(Z) indicate establishment of contact with the bolt and tactile exploration to
identify correct alignment of the tool. Execution of unbolting is marked by
rapid force fluctuations around these peaks.

Some tasks involved placing components after disassembly into a waste/recycle
bin, like in the cover removal task, where most of the time was spent on post-
grasp manipulation, i.e. the ’place’ stage. Operators spent on average 39, and
37 seconds placing the objects which averaged 56%, and 35% of the task
completion time with cobot and haptic platform, respectively. Around 30% of
the time was spent in the ’place’ stage for the cobot platform; due to the
lack of Cartesian control, the operator reached joint configurations where
large reconfigurations were required between tasks to access the workspace.
This is evident in Figure 9 around 150s. Comparing trial 4 in Figure 10, for
which a smaller difference in task time was observed (SMD 0.85) suggests that
coarse alignment with the correct grasp point is achieved on a similar
timescale of $\sim$20s. For the haptic, a greater proportion of time is spent
on fine alignment with the correct grasp point, while for the Franka, this
time is predominantly spent on post-grasp manipulation.

(a) Haptic master

(b) Franka master

Figure 9: Overlay of position and estimated external forces at the end-
effector for the bolt removal task (trial 2) using a 2-finger gripper. The
position alignment can be categorised broadly into rapid visual alignment
(indicated by a rapid decrease in Z position), followed by a slower phase of
precise visual & tactile alignment (plateau in Z position). Variations in
force along the X-Y plane are indicative of tactile exploration to find
suitable grasp points for the bolt.

(a) Haptic master

(b) Franka master

Figure 10: Overlay of position and estimated external forces at the end-
effector for the cover removal task (trial 4) using a 2-finger gripper. An
initial coarse alignment stage is marked by a rapid decrease in Z position,
followed by a fine alignment guided by tactile feedback. Grasping and
releasing of the cover is observed as application and release of a $\sim$14N
force in the -Z direction.

For the module sorting task, significant improvements in the task completion
time were observed, with an SMD of 2.31. Similarly to other tasks,
improvements in coarse and fine alignment speed are observed, although the
reduction in completion time is driven by time reductions over all stages of
the task, including the ‘action’ stage. Examining in Figure 11 shows that
after positional alignment, an increase in the force (up to $\sim$25N) occurs
indicating the attempt to reach a successful suction grip at the module
surface. As with the previous tasks, the magnitude of force feedback is
largely consistent between both platforms; however, for the action phase, the
operator exhibited a more slow and conservative approach with the haptic
device, characterised by a slow ramp in the normal (+Z) force. Intuitively,
the operator uses a mix of visual and tactile cues to identify engagement of
the suction cups with the surface. This implies a combination of factors can
be attributed to this behaviour; in the first instance, from similar factors
contributing to faster positional alignment with the Franka, such as 1:1
position mapping, while in the second instance, the operator can identify the
correct force threshold more intuitively, as with direct manipulation of the
slave arm, through 1:1 force mapping. Next, the ‘action’ stage is followed by
the ’place’ stage (red region) where the module is removed from the scene.
Contrasting the cover removal task, a much shorter period of time is spent
both proportionally and in absolute terms on post-grasp manipulation with the
Franka. Comparison of the trial breakdown in Figure 10 and Figure 11 for these
stages implies an effort-related component to the task performance, due to the
higher load exerted by the cover (notable in the Z direction). Furthermore,
the cover exhibits a more dispersed mass distribution in contrast with the
module, where a majority of the weight is concentrated about the grasp point.
Hence, positioning of the cover imposes a greater demand due to higher torque
required to rotate the joints, which is largely abstracted for the Cartesian
controlled haptic-Franka platform. This is corroborated by the more gradual
and tortuous path seen in Figure 10. Therefore, realism of force feedback may
be considered beneficial for the contact-rich stages of the task, but a
telemanipulation framework incorporating 1:1 feedback of external torque
should be aware of detrimental effects on manipulations in free space.

(a) Haptic master

(b) Franka master

Figure 11: Overlay of position and estimated external forces at the end-
effector for the sorting modules task (trial 5) using a vacuum suction
gripper. An initial coarse alignment stage is marked by a rapid decrease in Z
position, followed by a fine alignment guided by tactile feedback. Grasping
and releasing of the module is observed as application and release of a
$\sim$8N force in the -Z direction.

For cutting, a small SMD of 0.41 suggests the effect on task completion time
for the Franka platform is marginal relative to the trial-to-trial variation.
Cutting is a complex task dependent on a wide range of material and tool-
specific parameters, and a wide variation in completion times is observed
between task trials. For the Franka, a greater proportion of time is spent
performing the cutting task proper. This is on average achieved faster with
the haptic device, however, a much greater proportion of time (55%) is
required for initial alignment of the tool with the desired path. The fine
alignment stage in particular is unique for the cutting task in that the
operator must rely purely on visual alignment with the desired path; this
further suggests the reduction in completion time for the presented tasks is
in large part related to the expanded workspace and 1:1 _positional_ mapping
afforded with the Franka, rather than improvements in realism of the tactile
feedback. However, during the cutting task, the realism of feedback is
comparatively more important. This can be examined in Figure 12a, showing the
force profile for the contact cutting task for both platforms. Notably, the
force for the haptic trial steadily increases towards the end of the cutting
operation, which can be attributed to drift of the operator setpoint away from
the path in the transverse (Y) direction and an increase in the depth of cut
(-Z). A similar effect can be observed in the transverse direction for the
Franka, however, these are rapidly corrected during the course of the cutting
task. This force feedback provides important cues to the operator that were
otherwise ignored, or insufficient to prompt a response in the haptic case;
similar force profiles were observed over the majority of the haptic trials.

The increased feedback capability of a setup with identical cobots has some
notable disadvantages. From Figure 12b, it is clear that the cutting path
adopted by the user in the Franka case study is subject to small variations
along the length of the desired path. This is posited to be due to the lack of
task space control, the larger motions achievable with the Franka, and low
stiffness of the human arm. Owing to these factors, the master arm responds
readily to the force feedback created by the executed motions during the
cutting process, causing small deflections from the operator’s desired path.
This can be observed from the comparatively more variable and discontinuous
force profile opposing the feed direction (+X) in Figure 12a. For higher
strength materials, this effect is expected to increase in significance due to
an increase in the feed-rate dependent cutting forces. In the absence of
remediating strategies, this consequently reduces the quality of cut and
increases physical demand on the user. However, remediating strategies such as
scaling the force feedback provided to the user, or applying a Cartesian
impedance behaviour to the master arm to guide the user along the path would
have the effect of distorting the feedback, thus reducing the realism of the
interaction.

(a) Cutting forces for trial 3

(b) Cutting paths, all trials

Figure 12: Comparison of cutting forces between each telerobotics platform for
single trial, and overall paths adopted by each operator for all trials.

For the module stack disassembly case study comprising 4 modules, total
disassembly times averaged 25.8 minutes and 14.7 minutes for the haptic and
Franka platforms respectively, representing a 43% reduction in overall
completion time when using two identical cobots. Considering module cover
separation consisting of 4 linear cutting operations, it is estimated to
require 8 minutes per module to expose the battery cells, reducing by 25% for
the identical cobot case. Overall disassembly times demonstrate that while
disassembly via telemanipulation is feasible, several efficiency improvements
and assistive strategies are required to improve disassembly speed. However,
there is large variation in disassembly time estimates across battery models
and techno-economic analyses in literature. For example, an estimate of 12
seconds for manual unscrewing and 6 seconds for manual removal of free
components across multiple battery designs (Lander et al., 2023) implies large
reductions in efficiency versus manual disassembly. Another technoeconomic
analysis by Alfaro-Algaba and Ramirez (2020) for the Audi e-Tron hybrid
estimates a total disassembly time of 30 minutes for pack-to-module
disassembly. However, in Baazouzi et al. (2021), extraction of the battery
modules from the Smart ForFour was estimated at 10 minutes per module, and 135
minutes for disassembly of individual modules with 2 human personnel. Beyond
module level, disassembly is hampered significantly by expensive cutting
operations required to expose the individual battery cells. Broadly, this is
corroborated across battery designs, chiefly due to the high level of design
compartmentalisation and use of welds, glue and interference fit fasteners
that are difficult to remove non-destructively (Lander et al., 2023; Baazouzi
et al., 2021).

##  8 Conclusion

This study demonstrates the telerobotic disassembly of a stack of modules from
the Nissan Leaf 2011 battery pack. A comparative study between a master-slave
setup consisting of a haptic device paired with a cobot, and two identical
cobots examined the success rate and completion time for accomplishing
unbolting, extraction of bolts, grasping and removal of the cover plate,
sorting of modules with a suction gripper and contact cutting. While overall
success rate was higher with the haptic device, a setup with identical paired
cobots was found to significantly improve task completion times and time
consistency across the entire set of disassembly tasks. This suggests that
quality and realism of force feedback is comparatively less important for
accomplishing precise manipulation tasks, but instead the 1:1 position mapping
between master interface and slave and expanded workspace were main
contributors to the efficiency improvements. While 1:1 mapping of torques
between identical cobots was beneficial for grasping with a vacuum gripper and
cutting, chiefly due to the enhanced realism of the interaction, providing
strengthened tactile cues to the operator, this further had detrimental
effects on operator physical effort and quality of cut.

Limitations of the present work are that only objective measures of task
performance are considered under the assumption of familiarity with the
necessary tasks and teleoperation platforms (expert operators). However, to
obtain a holistic comparison it is necessary to consider operators of
different experience levels, as well as consideration of subjective
performance measures, such those established in NASA TLX that establish
measures of cognitive load and effort for the sequence of disassembly tasks.
Furthermore, although this study considers a disassembly case study of a
Nissan Leaf 2011 battery pack, a wide range of EV batteries are in circulation
whose designs differ broadly between manufacturers and models. Therefore, this
study could be extended to consider a wider range of battery designs to
achieve a more general overview of expected level of performance for the EV
battery disassembly process.

## 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.

## Author Contributions

Conceptualization, A.R.; methodology, J.H., A.S. and A.R.; software, A.S.,
J.H. and A.A.; investigation, A.S., J.H., A.A. and A.R.; validation, J.H, A.S
and A.R; data curation, J.H. and A.S.; formal analysis, J.H. and A.S.;
visualisation, J.H. and A.S.; writing—original draft, C.A., J.H, A.S and A.R;
writing—review & editing, A.R., C.A. and J.H; resources, A.R. and R.S.;
supervision A.R. and R.S.; funding acquisition, A.R. and R.S.; project
administration, A.R.

## Funding

This research was conducted as part of the project called “Reuse and Recycling
of Lithium-Ion Batteries” (RELiB). This work was supported by the Faraday
Institution [grant number FIRG005].

## Acknowledgments

The authors would like to acknowledge Christopher Gell for his technical
support.

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genes, oncogenes and tumor suppressor genes, detailed mechanistic or causal
information on carcinogenesis is still lacking.

Genes are segments of the DNA chain that contain the information necessary for
the synthesis of functional molecules (gene products) that perform some
function in the cellular environment. The central dogma of molecular biology
postulates that this information flows from DNA genes to RNA (gene
transcription), and from the latter to proteins (translation), through the
mechanism of gene expression. Highly complex processes are involved in the
expression of a specific gene, and gene products are involved in different
ways. For example, a protein resulting from a translation process may
constitute a subunit of the transcription machinery of another gene. For
example, RNA polymerases are enzymes of a protein nature that perform
essential functions of this mechanism, such as recognizing and binding to
specific locations on the DNA molecule to start the transcription process of
the corresponding gene. Similarly, the translation process of the RNA chain
corresponding to a gene is determined by the results of the gene expression of
others. For example, ribosomes are the cytoplasmic organelles where the
translation process takes place, and are largely composed of ribosomal RNA,
which in turn is the result of transcription processes in certain non-coding
genes (those where the transcribed RNA strand is the final gene product and is
not translated). Therefore, the results of transcription and translation
processes of some genes regulate (or deregulate) the form and quantity in
which other gene products are obtained, i.e., the genetic expression of some
genes has a causal effect on the genetic expression of others.

These types of causal relationships between genes are known to exist. However,
it is not known exactly in specific types of cancer what cause-effect
relationships are evident between the genetic dysregulations that trigger
carcinogenesis. The task to be developed in this chapter refers to the
identification of these operative relationships in cancer, with the aim of
detecting genes that play a fundamental role in the regulation of this
disease. In the particular case of the present study, prostate cancer is taken
as a test case, due to its importance as one of the major causes of death in
men worldwide.

####  4.0.2 Data origin

Gene expression data are obtained from The Cancer Genome Atlas Program (TCGA),
obtained from studies of hundreds of normal and tumor tissue samples,
classified by histopathological techniques.ICIMAF In the particular case of
prostate cancer, a total of 551 samples are available, of which 52 correspond
to normal samples and 499 tumor samples. For each sample, a total of 60,483
genes are recorded (the same for all samples). Of these, a subset of 52,870
genes is selected, discarding genes with null or almost null expression in the
study tissue. Expression profiles are measured through the RNA-Seq technique,
and their values are reported in units of Fragments Per Kilobase of
transcription per Million mapped reads (FPKM).ICIMAF

####  4.0.3 Processing

Gene expression has a heavy-tailed distribution, with a large number of
lowfrequency outliers. Therefore, the geometric mean and not the arithmetic
mean is selected as the measure to calculate the average gene
expressionICIMAF. Since RNASeq does not accurately detect low expression
values, a harmless offset of 0.1 FPKM is applied to all dataICIMAF.

Let $e_{gs}$ be the expression level of gene $g$ in sample $s$, the
homeostatic (or reference) gene expression level is estimated as the geometric
mean of $e_{gs}$ over the set of normal samples $N$, ie, ICIMAF

$e_{g}^{(ref)}=\root{}_{\mid N\mid} \of{\prod_{s\in N}e_{gs}}$ (4.1)

where $|N|$ is the number of normal samples.

The logarithmic fold-change ratio with respect to the reference value is
calculated for each sample.

$\hat{e}_{gs}=\log_{2}(\frac{e_{gs}}{e_{g}^{(ref)}})$ (4.2)

As a result, it is obtained that the over- and under-expression are treated
symmetrically. Finally, the measurement obtained is discretized, considering
that a gene $g$ is overexpressed in a sample $s$ if $\hat{e}_{gs}<-1$ (that
is, $e_{gs}<\frac{1}{2}e_{g}^{(ref)}$) and underexpressed if $\hat{e}_{gs}>-1$
(that is, $e_{gs}>2e_{g}^{(ref)}$). Then, a gene $g$ is altered in a sample
$s$ if $|\hat{e}_{gs}|>1$.

Thanks to discretization, the alteration of a specific gene can be taken as a
binary variable, and the study samples as the set of individuals with which it
is associated. Then, the matrix $M$ is constructed so that $m_{gs}=1$ if the
gene is altered in the sample ($|hate_{gs}|>1$) and $m_{gs}=0$ otherwise
($|hate_{gs}|\leq 1$).

This matrix $M$ describes the distribution of genetic alterations in the
samples, and will be the input of the _CChains_ algorithm for the construction
of the associated causal graph of genetic alterations.

####  4.0.4 Artificial cancer state gene

After it is constructed, an additional row is added to the matrix $M$ ,
corresponding to an artificial gene. The variable associated with this gene
will have a value of $1$ in all tumor samples (499 samples) and $0$ in the
remaining ones, so that this gene only appears altered in samples of cells
that have entered carcinogenesis. The objective of this false gene is,
therefore, to symbolize the cellular cancer state within the genetic network
of deregulations. In this way, a path in the graph that ends in the artificial
gene can be interpreted as a chain of genetic alterations that lead to cancer.

####  4.0.5 Construction of the genetic alterations graph

From the processed genetic alteration data, the corresponding causal graph of
genetic alterations is constructed, using the _CChains_ algorithm. In this
graph, an arc $i\rightarrow j$ represents the cause-effect relationship
between the alteration of a gene $i$ and that of another gene $j$, while a
path represents a causal chain of said alterations.

####  4.0.6 Results

The constructed matrix $M$ has a total of 551 columns (one for each tissue
sample in the data) and 52,870 rows (one for each gene recorded in the
samples). This is compressed as proposed in 3.2.1, and an equivalent matrix of
46923 rows is obtained, where the identical variables in the original matrix
start to occupy a single row. The new matrix $M$ is used as input to the
algorithm for the construction of the causal graph $G$.

The characteristics of $G$, after each phase of the algorithm, are the
following:

  * •

Construction of the causal graph:

    * –

46 923 vertices

    * –

69 583 711 arcs

    * –

132 755 undirected edges

  * •

Removal of spurious arcs:

    * –

22 357 509 arcs

    * –

47 undirected edges

Therefore, 47226202 arcs and 132708 undirected edges are eliminated.

  * •

Elimination of redundant arcs:

    * –

10 664 000 arcs

    * –

No undirected edges

Therefore, 11693556 arcs are eliminated, non-directed edges are not
eliminated, and 47 of these are oriented.

  * •

Removal of undirected edges:

    * –

Since the graph does not have undirected edges upon reaching this phase, no
change occurs.

Therefore, a graph $G$ with 46,923 vertices and 10,664,000 arcs is obtained,
without undirected edges. It is also true that it is acyclic, a fact that was
verified by calculating the topological order of $G$ using the Kahn
algorithm.Kahn Furthermore, the undirected graph underlying $G$ consists of a
single connected component, that is, in $G$ there are no isolated vertices.
The distribution of degrees in graph $G$ is quite irregular, and is described
by the following graph:

Figure 4.1: Distribution of degrees in the graph of genetic alterations

We also have that 467 vertices are orphans, and 19460 are childless vertices.
Of these 467, 420 have paths that lead to the artificial vertex of cancer.

A large number of vertices are concentrated around the artificial cancer
vertex. A total of 3872 vertices have this vertex as a child, 12767 are
ancestors at distance 2, and about 13105 at distance 3.

To illustrate the above, see the corresponding Fig.4.1 a subgraph of radius 2,
around the fictitious cancer vertex, in which only vertices of _contrast_
greater than 5% (at least 5% of their adjacencies are the cancer vertex or one
of its ancestors) are considered. The vertices correspond to the genes in the
4.1 and 4.2 tables, in order of numbering. The genes are accompanied by their
Ensembl IDs, which are the stable identifiers by which they can be located in
the Ensembl database.Ensembl

Figure 4.2: Subgraph of the simplified graph, induced by the vertices with
contrast greater than 5%

Número | Gen | Ensembl ID
---|---|---
0 | MIR1299 | ENSG00000275377
1 | - | ENSG00000223180
2 | - | ENSG00000221211
3 | RNA5SP199 | ENSG00000200275
4 | RNU6-32P | ENSG00000206675
5 | - | ENSG00000280673
6 | AC087393.1 | ENSG00000263729
7 | RNU6-1107P | ENSG00000201687
8 | - | ENSG00000263913
9 | Y_RNA | ENSG00000252894
10 | HP | ENSG00000257017
11 | RPL35P6 | ENSG00000244018
12 | SETD6P1 | ENSG00000236877
13 | AC006463.1 | ENSG00000225795
14 | AC023421.1 | ENSG00000266968
15 | AC024257.2 | ENSG00000258273
16 | LINC02244 | ENSG00000259590
17 | AC104985.1 | ENSG00000267746
18 | TRAJ45 | ENSG00000211844
19 | AC092653.1 | ENSG00000273245
20 | Y_RNA | ENSG00000206817

Table 4.1: Vertices with contrast greater than 5%

Número | Gen | Ensembl ID
---|---|---
21 | LINC00533 | ENSG00000235570
22 | AC006249.1 | ENSG00000274578
23 | Y_RNA | ENSG00000207480
24 | RNA5SP452 | ENSG00000199874
25 | - | ENSG00000273631
26 | Y_RNA | ENSG00000199979
27 | RNU6-514P | ENSG00000206935
28 | Y_RNA | ENSG00000200118
29 | - | ENSG00000277347
30 | RNU6-906P | ENSG00000207431
31 | ATG3 | ENSG00000144848
32 | RNU6-575P | ENSG00000223258
33 | AP005136.1 | ENSG00000238575
34 | AP000350.5 | ENSG00000272973
35 | AC003072.1 | ENSG00000250318
36 | RNU6-858P | ENSG00000199306
37 | TRDJ2 | ENSG00000211827
38 | - | ENSG00000216067
39 | AL360157.1 | ENSG00000260574
40 | FAM136BP | ENSG00000232654
41 | CancerGene | -

Table 4.2: Vertices with contrast greater than 5%

The subgraph induced by these vertices, prior to the application of the
spurious and redundant arcs elimination algorithms, had the structure
described in the Fig.4.3. As can be seen, in addition to the above
relationships, there were spurious arcs (39 $39\rightarrow 9$, $39\rightarrow
21$ and $39\rightarrow 28$. The vertex $42$ is added to the subgraph.
corresponding to AC008871.1 (ENSG00000250383) is added to the subgraph, since
it is the common parent of to $9$, $21$, and $28$, responsible for the
appearance of these arcs, eliminated in the corresponding phase. On the other
hand, $42$ is also the parent of vertex $0$, but the connection $39\rightarrow
0$ is not lost, since it is not spurious. Note that there were also present
the arcs $39\rightarrow 41$ and $31\rightarrow 41$ were also present,
representing transitive relationships, and were therefore eliminated. On the
other hand, the phenomenon of _loss of transitivity_ explained in the section
2.6, in the causal chains $1\rightarrow 32\rightarrow 41$, $22\rightarrow
17\rightarrow 41$ and $7\rightarrow 13\rightarrow 41$ (the arcs $1\rightarrow
41$, $22\rightarrow 41$ and $7\rightarrow 41$ do not exist).

Figure 4.3: Subgraph of the base network, induced by vertices with contrast
greater than 5% in the simplified network

To measure the importance of each gene in the deregulation network, a PageRank
algorithm is used. PageRank is a family of algorithms created and developed by
the Google company to classify web pages by importance and optimize their
search engines. It is based on the initial idea that the “importance” of a
page depends in turn on that of all the pages that have links to it, and
measures this value with a measure homonymous to the algorithm. Thus, the
PageRank of a page defines its importance on the network. In the analysis
proposed in this study, this notion is used in reverse: the importance of a
vertex in the graph depends on the importance of all its child vertices, ie,
the PageRank of a vertex under this new definition is the PageRank of the
vertex in the transposed graph, using the usual definition. The idea with this
is to qualify the deregulatory potential of each gene based on the
deregulatory potential of all the genes altered by it. The PageRank of the
vertices of the transposed graph is then calculated and ordered by it, from
highest to lowest, to obtain a ranking by importance. The first 15 vertices of
the ranking correspond to table 4.3, which shows the main data of each vertex,
that is, index of the vertex in the resulting graph, number of genes
corresponding to said vertex (due to the compression process), number of arcs
from the vertex to others (out-degree), number of arcs from other vertices to
this (in-degree) and PageRank calculated on it.

Vértice | Cantidad de genes | Out-degree | In-degree | Ranking
---|---|---|---|---
106 | 904 | 296 | 0 | 0.0280089084549199
203 | 387 | 231 | 0 | 0.0169252646143832
53 | 266 | 194 | 0 | 0.0138095007882416
232 | 405 | 4631 | 2 | 0.00951893530407698
54 | 200 | 4037 | 2 | 0.0070904279384024
894 | 67 | 3647 | 2 | 0.00593953728884232
107 | 135 | 186 | 0 | 0.00483720906329685
59 | 108 | 126 | 0 | 0.00346518187070434
1518 | 102 | 112 | 0 | 0.00314751044972811
477 | 70 | 144 | 0 | 0.00291192330216641
126 | 22 | 219 | 0 | 0.0026924875847944
1476 | 58 | 119 | 0 | 0.0024063629481943
1810 | 78 | 172 | 0 | 0.00227731537509089
669 | 52 | 114 | 0 | 0.00221713079450858
2504 | 16 | 13469 | 0 | 0.00218459734706735

Table 4.3: First 15 vertices of the ranking by PageRank

The PageRank algorithm evaluates the significance of each vertex in the
network considering the entire network. However, to analyze the significance
of each vertex with respect to cancer, the algorithm is evaluated only on the
subgraph of $G$ which comprises only the vertices that have paths to the
cancer vertex, and the connections between these. The first 15 genes
correspond to the table 4.4:

Vértice | Cantidad de genes | Out-degree | In-degree | Ranking
---|---|---|---|---
106 | 904 | 296 | 0 | 0.0386629717239762
203 | 387 | 231 | 0 | 0.0228670690866003
53 | 266 | 194 | 0 | 0.0191475773473782
232 | 405 | 4631 | 2 | 0.0141473304810091
54 | 200 | 4037 | 2 | 0.0107754221143982
894 | 67 | 3647 | 2 | 0.00868884719466811
107 | 135 | 186 | 0 | 0.00713393130155398
1476 | 58 | 119 | 0 | 0.00393586413393418
238 | 38 | 94 | 0 | 0.00373306252059571
1518 | 102 | 112 | 0 | 0.00354108602504106
59 | 108 | 126 | 0 | 0.00351365491373061
1810 | 78 | 172 | 0 | 0.00321007251876712
477 | 70 | 144 | 0 | 0.00310394431725929
126 | 22 | 219 | 0 | 0.00296362179658831
1270 | 47 | 118 | 0 | 0.00293891200199811

Table 4.4: First 15 vertices of the ranking by PageRank, in the graph induced
by vertices with paths to the artificial vertex of cancer

Next, it is of interest to examine the genes that emerge from a principal
component analysis (PCA) on the same data used in this study. It is worth
recapitulating several notable results of the above PCA: 1) normal and tumor
samples are evidently separated on the first principal component, 2) it is
possible to establish a hierarchy or ranking of genes according to their
contribution to the first principal component, and 3) a small number of genes
($32$) from this hierarchy suffices to satisfactorily rank the samples. The
hierarchy of genes by PageRank is similar to the one calculated by PCA (2),
with the important difference that the PageRank in graded in the 4.3 table
depends on an asymmetric measure of connection between variables/vertices
(Loevinger coefficient) whereas the ranking provided by PCA is built on
symmetric matrices of correlations or covariances. In fact, a gene at the top
of the PageRank hierarchy of a directed network will not necessarily appear
prioritized in the ranking of genes in the corresponding transposed network or
the underlying undirected network. Another significant difference is that the
PCA analysis directly employs the fold-change (4.2) as a continuous measure,
not discretizing it in the manner proposed in the 4.0.3 section.

The vertices corresponding to result 3) of this PCA analysis occupy a
relatively low place in the calculated PageRank, as can be seen in the tables
4.5 and 4.6.

Gen | Ensembl ID | Vértice | In-degree | Ranking | Posición en el rank
---|---|---|---|---|---
DLX1 | ENSG00000144355 | 20565 | 3186 | 8.33393955008047e-06 | 31609
PCA3 | ENSG00000225937 | 8137 | 4442 | 8.33393955008047e-06 | 31909
AP006748.1 | ENSG00000223400 | 40665 | 3353 | 8.33393955008047e-06 | 31769
AL359314.1 | ENSG00000274326 | 34974 | 2773 | 8.33393955008047e-06 | 27860
RPL7P16 | ENSG00000242899 | 39644 | 2529 | 8.33393955008047e-06 | 32778
HOXC6 | ENSG00000197757 | 46096 | 3504 | 8.33393955008047e-06 | 32868
ARLNC1 | ENSG00000260896 | 20221 | 2829 | 8.33393955008047e-06 | 32134
PCAT14 | ENSG00000280623 | 15811 | 3196 | 8.33393955008047e-06 | 28480
AP001610.3 | ENSG00000232806 | 555 | 2873 | 8.33393955008047e-06 | 30696
AMACR | ENSG00000242110 | 17232 | 1917 | 8.33393955008047e-06 | 30085
COMP | ENSG00000105664 | 24764 | 2050 | 8.33393955008047e-06 | 33009
SIM2 | ENSG00000159263 | 866 | 4038 | 8.33393955008047e-06 | 31729
AC092535.5 | ENSG00000273179 | 2734 | 2625 | 8.33393955008047e-06 | 34137
TDRD1 | ENSG00000095627 | 4970 | 1529 | 8.33393955008047e-06 | 28812
AP002498.1 | ENSG00000254988 | 1093 | 2148 | 8.33393955008047e-06 | 34382
OR51E2 | ENSG00000167332 | 489 | 2228 | 8.33393955008047e-06 | 35117
HPN | ENSG00000105707 | 4241 | 2463 | 8.33393955008047e-06 | 32708
TRGC1 | ENSG00000211689 | 15036 | 3849 | 8.33393955008047e-06 | 30160
SLC45A2 | ENSG00000164175 | 4870 | 1580 | 8.33393955008047e-06 | 30533
AC139783.1 | ENSG00000250767 | 18423 | 1979 | 8.33393955008047e-06 | 30036

Table 4.5: PageRank of the vertices corresponding to the genes of the PCA
analysis

Gen | Ensembl ID | Vértice | In-degree | Ranking | Posición en el rank
---|---|---|---|---|---
HOXC4 | ENSG00000198353 | 24217 | 1996 | 8.33393955008047e-06 | 33013
TRGV9 | ENSG00000211695 | 41519 | 2364 | 8.33393955008047e-06 | 27660
TP63 | ENSG00000073282 | 3558 | 1365 | 8.33393955008047e-06 | 30581
CRTAC1 | ENSG00000095713 | 28554 | 3556 | 8.33393955008047e-06 | 31561
KRT5 | ENSG00000186081 | 29782 | 2317 | 8.33393955008047e-06 | 29638
GPX2 | ENSG00000176153 | 8765 | 1718 | 8.33393955008047e-06 | 37926
WFDC2 | ENSG00000101443 | 22645 | 2113 | 8.33393955008047e-06 | 33020
GSTM1 | ENSG00000134184 | 23068 | 1656 | 8.33393955008047e-06 | 32503
SERPINA5 | ENSG00000188488 | 23401 | 2742 | 8.33393955008047e-06 | 29863
SLC39A2 | ENSG00000165794 | 30024 | 2764 | 8.33393955008047e-06 | 31823
ACTC1 | ENSG00000159251 | 10114 | 3533 | 8.33393955008047e-06 | 31678
SEMG2 | ENSG00000124157 | 41127 | 3543 | 8.33393955008047e-06 | 29250
SEMG1 | ENSG00000124233 | 36756 | 5766 | 8.33393955008047e-06 | 31509

Table 4.6: PageRank of the vertices corresponding to the genes in the analysis
by PCA

Each of these vertices corresponds only to the analogous gene (they do not
compress other genes), and all are childless vertices (out-degree=0). The
difference in the results of the two studies may be due to the symmetrical
nature of the former. The importance of these genes in the prostate cancer
dysregulation network may not be due to their dysregulatory potential in the
network, i.e., as important causes of dysregulation. It may be due, instead,
to a high probability of being dysregulated when the tissue has begun the
process of carcinogenesis, perhaps due to a common cause. Strong support for
the above hypothesis is that in the PageRank calculated on the untransposed
network, these genes occupy high positions in the resulting ranking (tables
4.7 and 4.8). This ranking, as opposed to the previous one, measures the
importance of each vertex by that of its parent vertices, that is, the
potential of each gene to be deregulated based on the same measure of the
genes that deregulate it.

Gen | Ensembl ID | Vértice | In-degree | Ranking | Posición en el rank
---|---|---|---|---|---
DLX1 | ENSG00000144355 | 20565 | 3186 | 0.000164793805964374 | 151
PCA3 | ENSG00000225937 | 8137 | 4442 | 0.000254304840322668 | 35
AP006748.1 | ENSG00000223400 | 40665 | 3353 | 0.000162914728880933 | 158
AL359314.1 | ENSG00000274326 | 34974 | 2773 | 0.000165346803992387 | 148
RPL7P16 | ENSG00000242899 | 39644 | 2529 | 0.000268863327673889 | 32
HOXC6 | ENSG00000197757 | 46096 | 3504 | 0.000193321361183645 | 82
ARLNC1 | ENSG00000260896 | 20221 | 2829 | 0.000150749974167285 | 189
PCAT14 | ENSG00000280623 | 15811 | 3196 | 0.000150343735332684 | 193
AP001610.3 | ENSG00000232806 | 555 | 2873 | 0.000125864681798513 | 318
AMACR | ENSG00000242110 | 17232 | 1917 | 0.000135374156142189 | 254
COMP | ENSG00000105664 | 24764 | 2050 | 0.000213930674223797 | 61
SIM2 | ENSG00000159263 | 866 | 4038 | 0.00027256701492603 | 31
AC092535.5 | ENSG00000273179 | 2734 | 2625 | 0.000110463834864383 | 459
TDRD1 | ENSG00000095627 | 4970 | 1529 | 7.34848942035608e-05 | 1151
AP002498.1 | ENSG00000254988 | 1093 | 2148 | 9.96802582240097e-05 | 583
OR51E2 | ENSG00000167332 | 489 | 2228 | 0.00014917499465663 | 194
HPN | ENSG00000105707 | 4241 | 2463 | 0.000163927728714361 | 154
TRGC1 | ENSG00000211689 | 15036 | 3849 | 0.000224990760449499 | 48
SLC45A2 | ENSG00000164175 | 4870 | 1580 | 6.26704655930819e-05 | 1577
AC139783.1 | ENSG00000250767 | 18423 | 1979 | 8.33662001639185e-05 | 871

Table 4.7: PageRank of the vertices corresponding to genes from PCA analysis

Gen | Ensembl ID | Vértice | In-degree | Ranking | Posición en el rank
---|---|---|---|---|---
HOXC4 | ENSG00000198353 | 24217 | 1996 | 0.000156169111412572 | 173
TRGV9 | ENSG00000211695 | 41519 | 2364 | 0.000106160510958864 | 507
TP63 | ENSG00000073282 | 3558 | 1365 | 4.41089879412608e-05 | 2857
CRTAC1 | ENSG00000095713 | 28554 | 3556 | 0.000217476069832593 | 57
KRT5 | ENSG00000186081 | 29782 | 2317 | 7.00959440693382e-05 | 1289
GPX2 | ENSG00000176153 | 8765 | 1718 | 7.9655960496375e-05 | 964
WFDC2 | ENSG00000101443 | 22645 | 2113 | 7.20540863212926e-05 | 1207
GSTM1 | ENSG00000134184 | 23068 | 1656 | 7.01189032374503e-05 | 1286
SERPINA5 | ENSG00000188488 | 23401 | 2742 | 0.000156867918023487 | 171
SLC39A2 | ENSG00000165794 | 30024 | 2764 | 0.000232173817725135 | 43
ACTC1 | ENSG00000159251 | 10114 | 3533 | 0.000162686091206463 | 159
SEMG2 | ENSG00000124157 | 41127 | 3543 | 0.000289345829676181 | 24
SEMG1 | ENSG00000124233 | 36756 | 5766 | 0.000423225689758056 | 8

Table 4.8: PageRank of the vertices (without transposition of the graph)
corresponding to genes from PCA analysis

In the present work, an analysis of some of the theoretical currents that
study causality was carried out, and some of the main concepts and strategies
of current methods of causal discovery were examined. A scheme for the
discovery of causal sufficiency relationships was presented, similar to the
probabilistic theory, with several original ideas. The proposed algorithm
shows a different approach for the discovery of causal relationships, which,
with due analysis and development, can represent an alternative to current
methods, mainly in cases of causal modeling on Big Data.

A program was designed for scientific use, in the C++ programming language,
which includes the ideas of the algorithm and is currently in use. As a
particular application, a network of genetic deregulations associated with
cancer is found and modeled, in the specific case of prostate adenocarcinoma.
This network can be the starting point for intervention studies, allowing a
better understanding of carcinogenesis. The methods of the proposed algorithm
still need to be analyzed in detail, to obtain have a general notion of their
behavior in different areas.

On this basis, the following investigations are recommended:

  * •

Find and implement a solution to the ordering problems of the spurious and
redundant arc elimination methods, respectively, for cases where they fail.

  * •

Find all the transitive causal chains of the graph, particularly those that
reach the vertex of the cancer. Furthermore, find the causal chains where all
arcs $i\rightarrow j$ of the associated path have $H_{ij}=1$.

  * •

Develop gene rankings by other metrics.

  * •

Find minimal gene panels for cancer diagnosis, ie, minimally necessary sets of
genes to alter for carcinogenesis to occur.

  * •

Computational improvements to the program.

Use dictionaries or ordered tree structures instead of lists. Sort the
vertices and their adjacencies by frequency of the associated variable.
Implement algorithms designed ad hoc to take advantage of this order. Consider
parallelization in the phases of the algorithm where possible.

  * •

Study of the convergence of the algorithm with respect to the number of
individuals. From a set of data, referring to a set $I$ of individuals and $V$
of associated variables, make a succession of sets of individuals $I_{i}$
where each one is a superset of the previous one and a subset of $I$.
Construct the succession of graphs $G_{i}$ resulting from executing the
algorithm on the set $V$ of variables, for each set $I_{i}$. Check if the
distribution of arcs of the graphs $G_{i}$ converges to the distribution in
the final graph.

  * •

Detailed study of transitivity. Particularly, the possibility of a redundant
arc being maintained by being the shared hypotenuse of two transitive
triangles. If this is the case, analyze possible solutions to eliminate the
redundant arc.

  * •

Incorporate methods based on Hausman’s principle of causal independence to
guide double arcs, adapting it appropriately for causal networks where
transitivity does not necessarily occur.

  * •

Check the causal sufficiency of the causal relationships discovered by the
algorithm, under the proposals of Cartwright or Skyrme, or use Baumgartner’s
scheme to find minimal probabilistic INUS conditions.

  * •

Comparison, on the same data sets, of the results of the algorithm with those
of other causal discovery algorithms, such as the PC algorithm.

  * •

Comparison of the graphs constructed by the algorithm with co-expression
networks modeled on the same data sets.

  * •

Study of the behavior of interventions on the causal graphs constructed, using
Pearl’s do-calculus.

  * •

Construction of a graph that represents the causal relationships of
prevention. Design of a scheme to eliminate spurious and redundant arcs for
the prevention graph.

  * •

Consider modifications to the algorithm for sets of non-binary variables.

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