114
M. N. Fitzpatrick et al.
The ability of the analytical methods to account for piecewise and sliding conditions
is also of great value. As shown in our methods and [14], the SNS can depend on piecewise equations to function correctly. Importantly, such piecewise equations enable the
output of a neuron to be completely “shut off,” such as when a neuron stops firing action
potentials. This effect cannot be produced by traditional recurrent neural networks with
continuous synaptic activation functions [21]. As the system in this work is scaled up and
developed for use as a controller for an assistive exoskeleton for walking gait rehabilitation, the discontinuous mechanics of walking will introduce more sliding conditions
[22], such as making and breaking contact with the ground, which must be accounted
for. We believe we can continue to scale this method up to more accurately and quickly
predict how a dynamical system’s periodic orbit may be altered by perturbations in a
phase-dependent way.
For future work we intend to continue development towards a larger and more realistic
network for controlling our exoskeleton, that would include additional joints, as well
as expanded sensory pathways and descending commands. We also plan to explore
additional methods in [16] for analytically finding the infinitesimal shape response curves
(iSRCs) for our systems. The iSRC would show how the values of each state change
throughout its period when system parameters are perturbed from their baseline values
for the duration of the limit cycle. Understanding how these lasting perturbations alter
the periodic trajectory of the system will assist tuning of parameter values. Essentially,
by perturbing one or more parameters for the full period of the limit cycle, their effects on
the state values can be determined at each instance of the period. With this information,
the proper parameter values needed for the trajectory to exhibit key features (i.e. level
body height during the stance phase) can be found. We expect this analytical method
to again be faster and computationally less expensive than solving the iSRC via brute
force, allowing tuning to be done more quickly and efficiently.
References
1. Yan, T., Cempini, M., Oddo, C.M., Vitiello, N.: Review of assistive strategies in powered
lower-limb orthoses and exoskeletons. Robot. Auton. Syst. 64, 120–136 (2015)
2. Chang, S.R., et al.: A muscle-driven approach to restore stepping with an exoskeleton for
individuals with para-plegia. J. NeuroEng. Rehabil. 14, 48 (2017)
3. Lee, B.Y., Ostrander, L.E.: The spinal cord injured patient. Demos (2002)
4. del-Ama, A.J., Koutsou, A.D., Moreno, J.C., de-los-Reyes, A., Gil-Agudo, Á., Pons, J.L.:
Review of hybrid exoskeletons to restore gait following spinal cord injury. J, Rehabil. Res.
Dev. 49, 497–514 (2012)
5. Kobetic, R., et al.: Implanted Functional Electrical Stimulation System for Mobility in
Paraplegia: A Follow-Up Case Report (1999)
6. Buschmann, T., Ewald, A., von Twickel, A., Büschges, A.: Controlling legs for locomotion—
insights from robotics and neurobiology. Bioinspiration Bio-mimetics 10, 041001 (2015)
7. Szczecinski, N.S., Hunt, A.J., Quinn, R.D.: A functional subnetwork approach to designing
synthetic nervous systems that control legged robot locomotion. Front. Neurorobot. 11, 37
(2017)
8. Rossignol, S., Dubuc, R., Gossard, J.P.: Dynamic sensorimotor interactions in locomotion
(2006)
M. N. Fitzpatrick et al.
The ability of the analytical methods to account for piecewise and sliding conditions
is also of great value. As shown in our methods and [14], the SNS can depend on piecewise equations to function correctly. Importantly, such piecewise equations enable the
output of a neuron to be completely “shut off,” such as when a neuron stops firing action
potentials. This effect cannot be produced by traditional recurrent neural networks with
continuous synaptic activation functions [21]. As the system in this work is scaled up and
developed for use as a controller for an assistive exoskeleton for walking gait rehabilitation, the discontinuous mechanics of walking will introduce more sliding conditions
[22], such as making and breaking contact with the ground, which must be accounted
for. We believe we can continue to scale this method up to more accurately and quickly
predict how a dynamical system’s periodic orbit may be altered by perturbations in a
phase-dependent way.
For future work we intend to continue development towards a larger and more realistic
network for controlling our exoskeleton, that would include additional joints, as well
as expanded sensory pathways and descending commands. We also plan to explore
additional methods in [16] for analytically finding the infinitesimal shape response curves
(iSRCs) for our systems. The iSRC would show how the values of each state change
throughout its period when system parameters are perturbed from their baseline values
for the duration of the limit cycle. Understanding how these lasting perturbations alter
the periodic trajectory of the system will assist tuning of parameter values. Essentially,
by perturbing one or more parameters for the full period of the limit cycle, their effects on
the state values can be determined at each instance of the period. With this information,
the proper parameter values needed for the trajectory to exhibit key features (i.e. level
body height during the stance phase) can be found. We expect this analytical method
to again be faster and computationally less expensive than solving the iSRC via brute
force, allowing tuning to be done more quickly and efficiently.
References
1. Yan, T., Cempini, M., Oddo, C.M., Vitiello, N.: Review of assistive strategies in powered
lower-limb orthoses and exoskeletons. Robot. Auton. Syst. 64, 120–136 (2015)
2. Chang, S.R., et al.: A muscle-driven approach to restore stepping with an exoskeleton for
individuals with para-plegia. J. NeuroEng. Rehabil. 14, 48 (2017)
3. Lee, B.Y., Ostrander, L.E.: The spinal cord injured patient. Demos (2002)
4. del-Ama, A.J., Koutsou, A.D., Moreno, J.C., de-los-Reyes, A., Gil-Agudo, Á., Pons, J.L.:
Review of hybrid exoskeletons to restore gait following spinal cord injury. J, Rehabil. Res.
Dev. 49, 497–514 (2012)
5. Kobetic, R., et al.: Implanted Functional Electrical Stimulation System for Mobility in
Paraplegia: A Follow-Up Case Report (1999)
6. Buschmann, T., Ewald, A., von Twickel, A., Büschges, A.: Controlling legs for locomotion—
insights from robotics and neurobiology. Bioinspiration Bio-mimetics 10, 041001 (2015)
7. Szczecinski, N.S., Hunt, A.J., Quinn, R.D.: A functional subnetwork approach to designing
synthetic nervous systems that control legged robot locomotion. Front. Neurorobot. 11, 37
(2017)
8. Rossignol, S., Dubuc, R., Gossard, J.P.: Dynamic sensorimotor interactions in locomotion
(2006)