Optimizing wearable assistive devices with neuromuscular models and
optimal control
Manish Sreenivasa, Matthew Millard, Paul Manns and Katja Mombaur
Abstract— The coupling of human movement dynamics with
the function and design of wearable assistive devices is vital to
better understand the interaction between the two. Advanced
neuromuscular models and optimal control formulations pro-
vide the possibility to study and improve this interaction. In
addition, optimal control can also be used to generate predictive
simulations that generate novel movements for the human
model under varying optimization criterion.
I. INTRODUCTION
In this paper we provide an overview of the methods
involved in the modeling of the human-exoskeleton system,
as well as the solution process to determine optimal neural
inputs and exoskeleton design parameters.
II. MATERIALS AND METHODS
We model the human body as an articulated multi-body
system, with each joint having 1 to 3 rotational degrees of
freedom (DoFs). The model shown in Fig. 1a consists of a
total of 33 rotational DoFs with an additional 6 DoFs for
the non-actuated root joint. Each rotational DoF is actuated
by a pair of agonist-antagonist “torque muscles” [1], which
represent the combined torques being generated by muscle
forces in that direction, Fig. 1b.
A. Subject-specificity
Depending on the application, the kinematic and dynamic
parameters of the human model may be further specified
towards individual characteristics. For example, for healthy
participants it may be sufficient to adjust joint centers using
graphical interfaces such as PUPPETEER [3], and segment
masses and inertia from regression equations [2]. For patho-
logical cases, it may be necessary to develop patient specific
models from functional analysis of motion capture data [4]
as well as segmentation from MRI images [5].
B. Neuromuscular Dynamics
The concept of agonist-antagonist torque muscles [1]
along with excitation-activation dynamics [6] provides a
good balance between model complexity and the ability to
This work was supported by the European Union’s Horizon 2020 research
and innovation programme under grant agreement No. 687662 (SPEXOR
project).
Authors
are
with
the
Optimization
in
Robotics
&
Biomechan-
ics group, Interdisciplinary Center for Scientific Computing, Heidel-
berg University, Berlinerstr. 45, 69120 Heidelberg, Germany (e-mail:
manish.sreenivasa@iwr.uni-heidelberg.de).
This is the author’s version of the abstract that has been published
on SpringerLink. The final publication is available on: https://link.
springer.com/chapter/10.1007/978-3-319-46669-9_103
Fig. 1.
(a) 3D Human model (b) Illustration of agonist-antagonist torque
muscles that actuate each rotational DoF (c) Smooth approximation of
torque muscle dynamics using 2D 5th order Bezier curves.
simulate physiologically realistic (aggregated) muscle and
neural behavior. Here, muscle torques are computed as:
τt = τp(q, ˙q) + τa(q, ˙q)
(1)
τa(q, ˙q) = fa(q)fv( ˙q)τmaxa
(2)
where, the torque at time t, τt is the summation of the
torque due to passive musculotendon components, τp, and
active muscle contraction, τa. Passive and active torques
are functions of joint angle q and joint rotational velocity
˙q. Muscle activation a is computed from the excitation-
activation dynamics as per [6]:
˙a
=
(e −a)
 e
tca
+ 1 −e
tcd

, e ≥a
(3)
˙a
=
e −a
tcd
, e < a
(4)
where, e denotes the neural excitation, and tca = 0.011,
tcd = 0.068 the activation and deactivation time constants.
We approximate the active-torque-angle and torque-velocity
curves as 2D 5th order Bezier curves, Fig. 1c. A smooth
function behavior was an important prerequisite to the sub-
sequent treatment in the optimal control problem.
arXiv:1804.02959v1  [cs.RO]  9 Apr 2018
C. Rigid-Body Dynamics
Dynamics computation of the multi-body system is done
using the open-source C++ library RBDL - Rigid Body
Dynamics Library [3]. RBDL builds on the concept of
Spatial Algebra [8] and provides efficient implementations
of state-of-the-art multi-body dynamics algorithms.
D. Parametrized Exoskeleton Models
Exoskeletons such as actuated lower-body devices or
those to support spinal loads (Fig. 3) are parametrized
with respect to size, weight, spring-damper dynamics and
actuator capabilities. In addition to the dynamics of the
exoskeleton, we also model the interaction between the
human and the exoskeleton with rigid or compliant contacts.
This parametrization follows from related recent work in the
ORB research group, on design of lower limb exoskeletons
using optimal control [12].
Fig. 2.
Neuromuscular dynamics at the ankle joint during walking. Top
panels plot the neural excitations, middle panels the muscle activations,
and bottom panels the muscle torques. Vertical lines indicate the change of
model stages due to stepping during walking.
III. RESULTS
The optimal control problem (OCP) corresponding to
model dynamics described above is solved using the direct
multiple shooting method [9] implemented in the software
package MUSCOD-II [10]. The OCP consists of several
model stages with corresponding constraints based on the
changing dynamics of the multi-body model and the interac-
tion with the environment (e.g. foot contacts during stepping,
hand contacts during lifting etc).
The controls to be identified correspond to the neural
excitations, e. These controls were discretized as piecewise
linear functions with additional continuity conditions be-
tween model stages. Fig. 2 plots the excitations, activations
and computed muscle torques for the agonist-antagonist
pair at the ankle joint. Details of the OCP formulation
corresponding to human movement models similar to the
one developed here, can be found elsewhere [3], [11].
Fig. 3.
Ongoing work is focused on developing more complex models of
spinal joints and exoskeletons.
IV. DISCUSSION
The modeling and optimal control framework summarized
here, provides a powerful basis to approximate the human
body dynamics as well as to generate novel movements. On-
going work is focused on developing more complex models
of joint kinematics (e.g. a complex spine) and exoskeletons,
Fig. 3. We are also developing methods to identify subject-
specific torque muscle parameters, as well as exoskeleton
parameters by treating them as variables of the OCP. Another
focus is to compute the relative movements and contact
forces between the exoskeleton and the user, in order to make
the human-machine interface as comfortable as possible.
REFERENCES
[1] D. Anderson, M. Madigan, and M. Nussbaum, Maximum voluntary
joint torque as a function of joint angle and angular velocity: model
development and application to the lower limb, Journal of Biomechan-
ics, vol. 40, no. 14, pp. 31053113, 2007
[2] P. De Leva, Adjustments to Zatsiorsky-Seluyanovs segment inertia
parameters, Journal of Biomechanics, vol. 29, no. 9, pp. 12231230,
1996.
[3] M. L. Felis, ”RBDL: an efficient rigid-body dynamics library using
recursive algorithms”, Autonomous Robots, 2016, pp. 1-17.
[4] S. S. U. Gamage and J. Lasenby, New least squares solutions for
estimating the average centre of rotation and the axis of rotation,
Journal of Biomechanics, vol. 35, no. 1, pp. 8793, 2002.
[5] M. Sreenivasa, C. Chamorro, D. Alvarado, O. Rettig, and S. Wolf,
Patient-specific bone geometry and segment inertia from mri images
for model-based analysis of pathological gait, Journal of Biomechan-
ics.
[6] D.Thelen,F.Anderson,andS.Delp,Generatingdynamicsimulations
of
movement using computed muscle control, Journal of Biomechanics,
vol. 36, no. 3, pp. 321328, 2003.
[7] J. M. Winters and L. Stark, Estimated mechanical properties of
synergistic muscles involved in movements of a variety of human
joints, Journal of Biomechanics, vol. 21, no. 12, pp. 102741, 1988.
[8] R. Featherstone, Rigid Body Dynamics Algorithms. Springer, New
York, 2008.
[9] H. G. Bock and K. J. Pitt, A multiple shooting algorithm for direct
solution of optimal control problems, in 9th IFAC World Congress
Budapest, 1984.
[10] D. Leineweber, I. Bauer, H. Bock, and J. Schloder, An efficient
multiple shooting based reduced SQP strategy for large-scale dynamic
process optimization. Part 1: Theoretical aspects, Computers & Chem-
ical Engineering, vol. 27, no. 2, pp. 157166, 2003.
[11] K. Mombaur, Using optimization to create self-stable human-like
running, Robotica, vol. 27, no. 03, pp. 321330, 2009.
[12] K. H. Koch and K. Mombaur, Exoopt - a framework for patient
centered design optimization of lower limb exoskeletons, in IEEE Int.
Conf. Rehabilitation Robotics, 2015.