Robotics Application of a Method
for Analytically Computing Infinitesimal Phase
Response Curves
Marshaun N. Fitzpatrick 1(B) , Yangyang Wang 2 , Peter J. Thomas 1 ,
Roger D. Quinn 1 , and Nicholas S. Szczecinski 1
1 Case Western Reserve University, Cleveland, OH 44106, USA
marshuan.fitzpatrick@case.edu
2 The University of Iowa, Iowa City, IA 52242, USA
Abstract. This work explores a method for analytically computing the infinitesimal phase response curves (iPRCs) of a synthetic nervous system (SNS) for a
hybrid exoskeleton. Phase changes, in response to perturbations, revealed by the
iPRCs, could assist in tuning the strength and locations of sensory pathways.
We model the SNS exoskeleton controller in a reduced form using a state-space
representation that interfaces neural and motor dynamics. The neural dynamics
are modeled after non-spiking neurons configured as a central pattern generator
(CPG), while the motor dynamics model a power unit for the hip joint of the
exoskeleton. Within the dynamics are piecewise functions and hard boundaries
(i.e. “sliding conditions”), which cause discontinuities in the vector field at their
boundaries. The analytical methods for computing the iPRCs used in this work
apply the adjoint equation method with jump conditions that are able to account for
these discontinuities. To show the accuracy and speed provided by these methods,
we compare the analytical and brute-force solutions.
Keywords: Infinitesimal phase response curve · Synthetic nervous system ·
Hybrid exoskeleton
1 Introduction
Research and development of exoskeleton devices to mimic or assist walking have been
ongoing since the 1960s [1]. The mechanical design and control strategies for these
exoskeletons can vary widely. A collaborative team at Case Western Reserve University and the Cleveland Stokes Veteran’s Affairs (VA) hospital is currently developing
a hybrid exoskeleton [2]. The exoskeleton is considered a hybrid because it combines
functional electrical stimulation (FES) [3] of the user’s muscles with the bracing and
power assistance of an exoskeleton [4]. Such an exoskeleton will enable patients to
regain mobility and act as a form of physical therapy due to the physiological benefits of
FES [5]. Specifically, paraplegic patients benefit from the exoskeleton’s powered joints
that compensate for inadequate muscle activation when using FES.
© Springer Nature Switzerland AG 2020
V. Vouloutsi et al. (Eds.): Living Machines 2020, LNAI 12413, pp. 104–115, 2020.
https://doi.org/10.1007/978-3-030-64313-3_12
for Analytically Computing Infinitesimal Phase
Response Curves
Marshaun N. Fitzpatrick 1(B) , Yangyang Wang 2 , Peter J. Thomas 1 ,
Roger D. Quinn 1 , and Nicholas S. Szczecinski 1
1 Case Western Reserve University, Cleveland, OH 44106, USA
marshuan.fitzpatrick@case.edu
2 The University of Iowa, Iowa City, IA 52242, USA
Abstract. This work explores a method for analytically computing the infinitesimal phase response curves (iPRCs) of a synthetic nervous system (SNS) for a
hybrid exoskeleton. Phase changes, in response to perturbations, revealed by the
iPRCs, could assist in tuning the strength and locations of sensory pathways.
We model the SNS exoskeleton controller in a reduced form using a state-space
representation that interfaces neural and motor dynamics. The neural dynamics
are modeled after non-spiking neurons configured as a central pattern generator
(CPG), while the motor dynamics model a power unit for the hip joint of the
exoskeleton. Within the dynamics are piecewise functions and hard boundaries
(i.e. “sliding conditions”), which cause discontinuities in the vector field at their
boundaries. The analytical methods for computing the iPRCs used in this work
apply the adjoint equation method with jump conditions that are able to account for
these discontinuities. To show the accuracy and speed provided by these methods,
we compare the analytical and brute-force solutions.
Keywords: Infinitesimal phase response curve · Synthetic nervous system ·
Hybrid exoskeleton
1 Introduction
Research and development of exoskeleton devices to mimic or assist walking have been
ongoing since the 1960s [1]. The mechanical design and control strategies for these
exoskeletons can vary widely. A collaborative team at Case Western Reserve University and the Cleveland Stokes Veteran’s Affairs (VA) hospital is currently developing
a hybrid exoskeleton [2]. The exoskeleton is considered a hybrid because it combines
functional electrical stimulation (FES) [3] of the user’s muscles with the bracing and
power assistance of an exoskeleton [4]. Such an exoskeleton will enable patients to
regain mobility and act as a form of physical therapy due to the physiological benefits of
FES [5]. Specifically, paraplegic patients benefit from the exoskeleton’s powered joints
that compensate for inadequate muscle activation when using FES.
© Springer Nature Switzerland AG 2020
V. Vouloutsi et al. (Eds.): Living Machines 2020, LNAI 12413, pp. 104–115, 2020.
https://doi.org/10.1007/978-3-030-64313-3_12