Conference PaperPDF Available

Evolutionary Motion Control Optimization in Physical Human-Robot Interaction

Authors:
  • Halodi Robotics

Abstract and Figures

Given that the success of an interaction task depends on the capability of the robot system to handle physical contact with its environment, pure motion control is often insufficient. This is especially true in the context of medical freehand ultrasound where the human body is a deformable surface and an unstructured environment, representing both a safety concern and a challenge for trajectory planning and control. The systematic tuning of practical high degree-of-freedom physical human-robot interaction (pHRI) tasks is not trivial and there are many parameters to be tuned. While traditional tuning is generally performed ad hoc and requires knowledge of the robot and environment dynamics, we propose a simple and effective online tuning framework using differential evolution (DE) to optimize the motion parameters for parallel force/impedance control in a pHRI and medical ultrasound motion application. Through real-world experiments with a KUKA LBR iiwa 7 R800 collaborative robot, the DE framework tuned motion control for optimal and safe trajectories along a human leg phantom. The optimization process was able to successfully reduce the mean absolute error of the motion contact force to 0.537N through the evolution of eight motion control parameters.
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Evolutionary Motion Control Optimization in Physical Human-Robot
Interaction
Nicholas A. Nadeau1,2and Ilian A. Bonev1
Abstract Given that the success of an interaction task
depends on the capability of the robot system to handle physical
contact with its environment, pure motion control is often insuf-
ficient. This is especially true in the context of medical freehand
ultrasound where the human body is a deformable surface and
an unstructured environment, representing both a safety con-
cern and a challenge for trajectory planning and control. The
systematic tuning of practical high degree-of-freedom physical
human-robot interaction (pHRI) tasks is not trivial and there
are many parameters to be tuned. While traditional tuning is
generally performed ad hoc and requires knowledge of the robot
and environment dynamics, we propose a simple and effective
online tuning framework using differential evolution (DE) to
optimize the motion parameters for parallel force/impedance
control in a pHRI and medical ultrasound motion application.
Through real-world experiments with a KUKA LBR iiwa 7
R800 collaborative robot, the DE framework tuned motion
control for optimal and safe trajectories along a human leg
phantom. The optimization process was able to successfully
reduce the mean absolute error of the motion contact force
to 0.537 N through the evolution of eight motion control
parameters.
I. INTRODUCTION
Collaborative industrial robots are increasingly being
used outside of traditional manufacturing where physical
human-robot interaction (pHRI) plays an important role in
the application. Given that the success of an interaction task
depends on the capability of the robot system to handle phys-
ical contact with its environment, pure motion control is often
insufficient. This is especially true in the context of medical
freehand ultrasound where the human body is a deformable
surface and an unstructured environment, representing both
a safety concern and a challenge for trajectory planning and
control.
Within the research domain of robot-assisted freehand
ultrasound, previous studies have focused on ergonomic ben-
efits [1], image quality optimization [2] and reconstruction
[3], pHRI safety [4], and application design [5]. Regardless
of the objective, force control techniques are necessary
to achieve effective and adaptable behaviour of a robotic
system in the unstructured ultrasound environment while also
ensuring safe pHRI. However, while force control does not
require explicit knowledge of the environment, to achieve an
acceptable dynamic behaviour, the control parameters (e.g.,
gain, stiffness, damping) must be tuned.
The performance of a force control strategy is greatly
affected by the tuned parameters. Past studies have explored
This work was funded by the Canada Research Chairs Program.
1´
Ecole de technologie sup´
erieure, Montr´
eal, Qu´
ebec, Canada
2Corresponding author, nicholas.nadeau.1@ens.etsmtl.ca
Fig. 1: The motion task coordinate system. The primary goal
was to maintain a constant normal force (fz) with the probe
while performing a linear motion along a human leg phantom
(xaxis direction).
effective pHRI control and tuning including, iterative tuning
[6], adaptive control [7]–[9], fuzzy learning [10], impact
collision modelling [11], and passivity-based control [12].
Regardless of the approach, the tuning is generally performed
on an ad hoc basis [13] or requires knowledge of the robot
and environment dynamics [14].
As noted in [6], the systematic tuning of practical high
degree-of-freedom (DOF) robotic tasks is not trivial; there
are many parameters to be tuned simultaneously and heuris-
tically, in addition to the coupling dynamics that must be
considered. Moreover, the authors of [15] point out that
the choice of control parameters depends on the application
and involves a compromise between interaction forces and
position accuracy. Within the context of medical ultrasound,
different human body locations have different stiffnesses [16]
and thus will require different tunings.
Given these challenges, we present an online optimiza-
tion framework for parallel force/impedance control using
differential evolution (DE) [17] in the context of pHRI and
medical ultrasound. While previous research has explored the
integration of DE in robot control, such as simulated control
tuning of a PUMA-560 [18] or PID tuning in a five-bar
mechanism [19], there is a lack of knowledge with regards to
the potential use of evolutionary algorithms in pHRI motion
control. The current study takes inspiration from [20]–[22]
and leverages task repetition to tune motion control for
optimal and safe trajectories along a human leg phantom. In
our approach, DE can enable the robot system to explore the
large parameter domain for candidate tuning solutions using
metaheuristics without any assumptions about the problem
space or environment. Further, a primary advantage of the
framework is the preservation of a simple control structure,
as no additional complexities have been added (i.e., fuzzy
logic, neural networks).
The rest of the paper is organized as follows. First,
Section II explains the problem of controlled motions along
a deformable surface. Second, Section III describes the
proposed optimization method and implementation of DE.
Third, Section IV outlines the experiment and the validation
of the framework. Finally, Section V concludes the paper
and discusses potential future work.
II. PRO BL EM DESCRIPTION
The context of medical freehand ultrasound on a human
leg is the basis of this study with the primary goal of
maintaining a constant normal force with the probe, as
compression effects would distort the resulting images [23].
In the ideal application, robot-assisted ultrasound would
allow for a sonographer to collaborate with the robot
through hand-guidance while the robot performs the repet-
itive force-based motion tasks. Fundamentally, this appli-
cation is a surface following operation on an unstructured
and deformable body, a classical exercise in robotics and
force control (in-depth surveys may be seen in [24] and
[25]). Furthermore, given the pHRI context of this study,
impedance control is an essential component to ensure safe
motion and to compensate for the unstructured environment
[26].
In this paper we combine force and impedance control in
a parallel control model. As shown in [27], parallel control
strategies allow for control in the full-dimensional space
without selection matrices. Parallel control loops override
one another given a prioritization policy. For this task, the
impedance control loop allows for safety and environment
compensation, giving compliance to the tool frame in all
Cartesian axes. At a higher priority level, task-orientated
force control allows for constant force-tracking along the
surface.
Thus, given an initial contact with the surface, the task
can be achieved by assigning the following constraints [15]:
a non-zero linear velocity along the xaxis
zero linear velocity along the yaxis
zero angular velocity about the x,y, and zaxes
a non-zero force along the zaxis
Fig. 2: The high-level steps of differential evolution (DE):
(1) A population of candidate solution vectors is initialized;
(2) Mutations are generated for each candidate; (3) The
mutations are crossed with the original candidates; (4) The
fitness of the crossed candidates is scored; (5) The population
is updated based on the scored fitness. Steps 2-5 are repeated
until a convergence criterion is met.
where the above motion task constraints and coordinate
system are illustrated in Fig. 1.
III. DIFF ER EN TI AL EVO LU TI ON FR AM EW OR K
DE, first presented in [17] and reviewed in [28], is a simple
yet powerful evolutionary algorithm for global optimization,
being able to minimize nonlinear and non-differentiable
continuous space functions. Typical direct search optimiza-
tion methods (e.g., Nelder–Mead) use a greedy criterion
to select newly generated parameters. Under this criterion,
the new parameters are only kept if it reduces the fitness
function value, risking convergence to local minima. In
contrast, DE maintains a population of candidate solutions
and creates new solutions through the strategic and stochastic
combination of existing ones, allowing the full (but bounded)
solution space to be continuously explored. This is especially
important with regards to robotics, as the solution space
fitness of a high DOF motion task is assumed to be noisy and
is not guaranteed to be differentiable. An illustrated overview
of DE may be seen in Fig. 2 with the specific implementation
shown in Algorithm 1.
The DE solver for the present study was implemented
using Python v3.6.1 and SciPy v1.0.0 on an external PC
as a client to the robot controller over a local network. As
optimization of the solver itself was outside the scope of
the current study, the solver hyperparameters were set using
the recommendations of both [17] and the SciPy package.
Notably, the population size was set to 5×D, where Dis the
dimension of the input vector. The mutation constant was set
in the range of [0.5,1], whereby dithering randomly changes
this constant every generation, helping to speed convergence.
The recombination constant (crossover probability) was set
to 0.7. The population was initialized using Latin hypercube
sampling (LHS) to maximize coverage of the available
parameter space. Finally, the best1bin evolution strategy
was selected, where for each mutation, two candidates of
the population are randomly chosen, and their difference is
used to mutate the best candidate into a mutant vector. The
crossover process then combines the given candidate with
the mutant, based on a binomial distribution. The resulting
trial vector is to be evaluated by a robot motion session,
generating a fitness score. A detailed overview of this process
is seen in Algorithm 1.
Algorithm 1 The Differential Evolution (DE) solver process.
1: // initialize solver
2: CR 0.7// crossover probability
3: DgetN umP arameters() // number of parameters
4: populationSiz e 5×D
5: population initializeP opul ation(populationSize)
6:
7: // each loop represents a single generation
8: loop
9: // get a random mutation within the given range
10: Frandom(0.5,1)
11: for all candidate population do
12: // ‘best1bin‘ mutation
13: r0population.getRandomC andidate()
14: r1population.getRandomC andidate()
15: r0,1r0r1
16: bc population.getBestCandidate()
17: mutantCandidate bc +F×r0,1
18:
19: // ‘best1bin‘ crossover
20: trialC andidate candidate
21: for ito Ddo
22: cr random(0,1)
23: if cr < CR then
24: trialC andidate[i]mutantCandidate[i]
25: end if
26: end for
27: // one random parameter is always from the mutant
28: irandomInt(0, D)
29: trialC andidate[i]mutantCandidate[i]
30:
31: // perform a session with the trial candidate
32: // this blocks until the motion session is complete
33: result perf ormSession(trialCandidate)
34:
35: // evalute the fitness and update the population
36: fitnesstrial evaluateF itness(result)
37: if fitnesstrial < f itnesscandidate then
38: candidate trialC andidate
39: end if
40: end for
41: end loop
IV. EXP ER IM EN T
The proposed optimization framework was evaluated with
a 7-DOF KUKA LBR iiwa 7 R800 (LBR) collaborative
robot and the experiment setup may be seen in Fig. 3.
The LBR robot was equipped with a rounded probe tool
that was designed to approximate the tool referenced in
Annex A of [16]. In addition, the robot is equipped with
torque sensors at every joint, allowing for calculations of
Cartesian forces acting on the tool. The mass data of the
tool assembly (0.948 kg) was calibrated using the built-in
Fig. 3: The experiment setup. A KUKA LBR iiwa 7 R800
(LBR) collaborative robot (A) was equipped with a rounded
probe tool (B). A mannequin leg with an internal skeletal
structure (C) was used to simulate the ultrasound subject and
water-based lubricant was used on the leg to fully simulate
real ultrasound examination and reduce friction.
calibration procedure of the robot to remove the tool load
from the force measurements.
A mannequin leg with an internal skeletal structure was
used to simulate the ultrasound subject and water-based
lubricant was used on the leg to fully simulate real ultrasound
examination and reduce friction. The desired contact force
for the motion was derived from a review of previous
robot-assisted ultrasound studies. Forces between 15 N,
3.74.6 N, and 520 N were reported in [4], [2], and [29],
respectively. As such, a setpoint force of 5 N was selected.
As discussed in Section II, parallel force/impedance con-
trol was selected as the control strategy and was implemented
as two layers. First, the control architecture exploited the
built-in real-time impedance control of the LBR robot as the
base control strategy (KUKA Sunrise.OS v1.10). The basic
model is a virtual spring-damper system with configurable
values for stiffness and damping, allowing the LBR to
be highly sensitive and compliant (Fig. 4). Second, the
high-priority task-oriented force control was implemented
through the Sunrise.Connectivity DirectServo control loop
interface. This allows for non-deterministic soft real-time
control and fast corrections to the robot path.
Each motion session begins with the DE solver process
providing a candidate Session State (Protocol Buffers v3.5.1)
to the robot controller through a remote procedure call
interface (gRPC v1.9.0). The Session State input vector
defines the parameters that form the optimization problem
Fig. 4: The built-in real-time impedance control of the
KUKA LBR iiwa robot (LBR). The model is a virtual
spring-damper system with configurable values for stiffness
(K) and damping (ζ), allowing the LBR to be highly
sensitive and compliant. The resulting interaction forces are
calculated from the displacement (X) between the desired
position (Pd) and the actual position (Pa) in each Cartesian
axis.
and is given by:
SessionState =
kx
ky
kz
ζx
ζy
ζz
dx
gz
(1)
where kx,y,z and ζx,y,z are the Cartesian stiffnesses
(05000 N/m) and Lehr’s damping ratios (0.11 1), respec-
tively, for the LBR impedance control. dxdefines the xaxis
position displacement per servo iteration (0.110 mm) and
gzdefines the gain of the force-tracking (0.110 1). The
bounds of the impedance control parameters are hard limits
set by the robot while the remaining bounds were selected ex-
perimentally. Furthermore, these parameters remain constant
for the duration of a single session. Finally, the stiffness
and damping of the rotation axes were set to a constant
300 N m/rad and 0.7, respectively, as they were not part
of the optimization process.
Following session initialization, the robot performed a
linear downwards motion until the force condition was
triggered at which point the servo loop was initiated for the
ultrasound motion. A motion session is judged as a success
after 100 mm of travel in the xaxis direction from the initial
contact point (visualized in Fig. 1). A timeout of 3000 servo
iterations was also implemented to avoid endless loops
(successful sessions took an average of 1129 iterations).
Throughout the session, the zaxis force (fz) is logged at
1000 Hz.
Following the completion of a motion session, the robot
controller updated the external client with a Session Result,
consisting of the recorded fzdata and the session success
status. The DE solver used the Mean Absolute Error (MAE)
of the fzdata with respect to the setpoint force as a fitness
score. The first second of data was discarded to avoid edge
effects with respect to the initial contact event (highlighted
in Fig. 6). However, if a timeout occurred, the session
was penalized with a score of infinity. Iteratively, motion
sessions were performed, evaluating candidate control pa-
rameter solutions as generated by the DE solver with the
parameters evolving over time. A detailed description of the
motion optimization process and framework is specified in
Algorithm 2.
Algorithm 2 The motion control session.
1: // receive candidate vector from DE solver
2: LBR SessionState
3:
4: // initialize session
5: numServoIterations 0
6: maxServoIterations 3000
7: fz,d ← −5// Newtons, desired force
8: xd100 // millimeters, desired travel distance
9: ¯
P0getC urrentC artesianP osition()
10:
11: // initialize internal impedance control layer
12: LBRkx,ky,kzSessionStatekx,ky,kz
13: LBRkrx,r y,rz 300 // Nm/rad
14: LBRζxyzSessionStateζxyz
15: LBRζrx,r y,rz 0.7// Lehr’s damping ratio
16:
17: isServoRunning T rue
18: while isServoRunning do
19: numServoIterations numServoIterations + 1
20: if numServoIterations > maxS ervoI terations or
xix0>xdthen
21: isServoRunning F alse
22: else
23: // force control layer
24: ¯
FigetF orceV ector()
25: fzfz,d ¯
Fz,i
26: zfz
kz
27: zz×SessionS tategz
28:
29: // calculate next servo position
30: ¯
PigetC urrentC artesianP osition()
31: ¯
Px,i+1 ¯
Px,i +SessionS tatedx
32: ¯
Py,i+1 ¯
Py,0
33: ¯
Pz,i+1 ¯
Pz,i + ∆z
34: ¯
Prx,ry,r z,i+1 ¯
Prx,ry,r z,0
35: setDestination(¯
Pi+1)
36: end if
37: end while
A. Results
A total of 795 sessions were performed, representing
nearly 20 generations of candidate solutions, with 709 suc-
cessful sessions (89.2 %). The optimization process was
terminated due to the fitness score leveling off, as clearly
seen in Fig. 5. The mean servo loop period was 3.12 ms
(320.49 Hz), on par with the responsive ultrasound force
control reported in [2].
Comparisons of motion behaviour throughout the process
is shown in Figs. 6 and 7. The poor performing sessions
noticeably suffer from strong oscillations or completely miss
the desired contact force, as compared to stable and accurate
optimized motion. It should be noted that the optimization
of the initial contact event was outside the scope of this
study, as this transient event would require its own set
of motion control parameters, thus resulting in the force
overshoots seen outside the shaded area in Fig. 6. In an actual
robot-assisted application, the initial contact would most
likely be achieved through the sonographer hand-guiding the
robot.
Over the evolution of the candidate parameters, corre-
lations were found between three key parameters (ζz,gz,
and kz), the fitness score, and the session index. The raw
parameter evolution may be seen in Fig. 8a and Fig. 8b.
These correlations give insight into the evolutionary process
of the DE solver as it generates candidate solutions. It is also
interesting to note how even at later indexes the DE solver
still explores the full parameter domain and does not simply
converge to local parameter minima.
Finally, the evolution of the best candidates is visualized
in Fig. 9 and the optimal parameters are summarized in
Table I. While hundreds of motion sessions were performed,
the MAE fitness reached 0.607 N after only 28 sessions
and the optimal value of 0.537 N after 689 sessions. Close
examination of the evolution in Fig. 9 shows relatively
wide parameter exploration in sessions prior to session
28 and relative stabilization afterwards. The trend towards
high z-direction rigidity (Fig. 8) suggests the application
favours stronger position control, but the results in Table I
demonstrate that the optimal parameters were not simply
at maximum. Moreover, Fig. 7 clearly demonstrates that a
simple fixed z-depth motion would not be a valid approach
to this application.
V. DISCUSSION
The systematic tuning of practical high DOF robotic tasks
is not trivial and there are many parameters to be tuned, espe-
cially in the context of pHRI force control. While traditional
tuning is generally performed ad hoc and requires knowledge
of the robot and environment dynamics, we propose a simple
and effective online framework using DE to optimize the
motion parameters for parallel force/impedance control in a
medical ultrasound motion application.
Through real-world experiments with a KUKA LBR iiwa
7 R800 collaborative robot, probe tool, and a mannequin
leg with an internal skeletal structure, the DE framework
was able to successfully reduce the MAE of the motion
0 100 200 300 400 500 600 700
Session Index
2
4
Fitness Score
100101102
Session Index
1
2
Best Fitness Score
Fig. 5: Raw fitness scores and linear regression (top) and
best fitness scores (bottom) vs. session index.
−15
−10
−5
0
5
Force [N]
0 1 2 3 4 5
Time [s]
−15
−10
−5
0
5
Force [N]
0 1 2 3 4 5
Time [s]
(a) First few sessions.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Time [s]
−12
−10
−8
−6
−4
−2
0
Force [N]
(b) Best session.
Fig. 6: Comparisons of the probe contact force, fzthrough-
out the differential evolution optimization process. The
shaded region highlights the motion data used to score the
candidate fitness.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Time [s]
105
106
107
108
109
110
111
112
Z Position [mm]
Best Session
Worst Session
Fig. 7: Probe z-position of the best and worst sessions of the
differential evolution optimization process.
0.5
1.0
Lehr'S Damping
Ratio
Zeta Z
0
10
Gain
Gz
0 100 200 300 400 500 600 700
Session Index
0
5000
Stiffness [N/m]
Kz
(a)
0.5
1.0
Lehr'S Damping
Ratio
Zeta Z
0
10
Gain
Gz
12345
Fitness Score
0
5000
Stiffness [N/m]
Kz
(b)
Fig. 8: Evolution of key parameters with the optimization
process (a) and the fitness score (b). Linear regressions are
represented by the red lines.
1 2 6 13 28 181 392 587 622 625 689
Session Index
Dx
Gz
Kx
Ky
Kz
Zeta X
Zeta Y
Zeta Z
0.0
0.2
0.4
0.6
0.8
1.0
Normalized Value
Fig. 9: Evolution of the motion control parameters in the
best candidates. The columns represent the parameters of
best candidate up to a given session. Each parameter row is
normalized over its evolution.
TABLE I: Parameters and fitness of the best differential
evolution (DE) candidate. The fitness is calculated as the
mean absolute error (MAE) between the desired contact force
and the recorded force through a motion session.
Parameter Value
dx8.865 mm
gz9.736
kx3703.233 N/m
ky2777.930 N/m
kz4885.149 N/m
ζx0.132
ζy0.407
ζz0.327
MAE 0.537 N
task to 0.537 N through the optimization and evolution of
eight motion control parameters. Although real-world fitness
function evaluations are a relatively expensive process, the
total optimization time was just 55 min for 20 generations,
well under the 50 generation benchmark set in [18].
This simplicity of the framework has three key benefits.
First, inferring the motion parameters from the application
is not trivial, especially since the human leg has varying
stiffness [16]. Second, it can easily be used to extend and
improve existing control schemes through a simple com-
munication network between the DE solver and the robot.
Third, it allows for the optimization process to be well
understood by the user, unlike black-box methods such as
neural networks. As this approach is model-based, the motion
parameters may be easily updated with respect to changing
environments (e.g., change in leg orientation), whereas a
black-box model would have difficulty adapting.
Consequently, while the mannequin leg may not perfectly
represent a human subject, this framework can be adopted as
a starting point for more advanced control paradigms, such as
reinforcement learning. Future motion control architectures
for pHRI and intelligent systems will likely rely on forms
of continuous learning, highlighting the importance of an
optimization framework that allows the robot system to
explore, evolve, and evaluate the solution space for more
effective motion behaviour.
As stability analysis was outside the scope of the current
study, it provides a foundation for future work. Other po-
tential extensions of this study include the optimization of
the DE solver, the exploration of new motion parameters
and control architectures, and the development of smooth
transitions between initial contact and surface following
motion control.
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... The main challenge of evolutionary optimization is the slow convergence due to the many trials the system must run, especially when working with hardware-in-the-loop optimization [16], [17]. Furthermore, an unconstrained optimization may employ parameters that could lead to instability, especially when dealing with humans. ...
... Lahr et al. [13] optimized an admittance controller for industrial robots along one DOF in an experimental setup, optimizing in an experimental design taking into account several nonlinearities. Nadeau and Bonev [16] used an evolutionary algorithm to optimize the impedance controller during a human-machine task with multiple DOFs using an industrial robot. In contrast, Lahr et al. [17] optimized an admittance controller for an industrial robot with three-DOF for an assembly task using dimensionality reduction for faster convergence. ...
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