Robotics Application of a Method for Analytically Computing Infinitesimal
115
9. Martin, J.P., Guo, P., Mu, L., Harley, C.M., Ritzmann, R.E.: Central-complex control of
movement in the freely walking cockroach. Curr. Biol. 25, 2795–2803 (2015)
10. Chiel, H.J., Beer, R.D.: The brain has a body: adaptive behavior emerges from interactions
of nervous system, body and environment (1997)
11. Hunt, A., Schmidt, M., Fischer, M., Quinn, R.: A biologically based neural sys-tem coordinates
the joints and legs of a tetrapod. Bioinspiration Biomimet-ics 10, 055004 (2015)
12. Li, W., Szczecinski, N.S., Quinn, R.D.: A neural network with central pattern generators entrained by sensory feedback controls walking of a bipedal mod-el. Bioinspiration
Biomimetics 12, 065002 (2017)
13. Szczecinski, N.S., et al.: Introducing MantisBot: hexapod robot controlled by a high-fidelity,
real-time neural simulation. In: IEEE International Conference on Intelligent Robots and
Systems, pp. 3875–3881. Institute of Electrical and Electronics Engineers Inc. (2015)
14. Szczecinski, N.S., Hunt, A.J., Quinn, R.D.: Design process and tools for dy-namic neuromechanical models and robot controllers. Biol. Cybern. 111, 105–127 (2017)
15. Klein, T., Lewis, M.A.: A neurorobotic model of bipedal locomotion based on principles
of human neuromuscular architecture. In: Proceedings - IEEE In-ternational Conference on
Robotics and Automation, pp. 1450–1455. Institute of Electrical and Electronics Engineers
Inc. (2012)
16. Wang, Y., Gill, J.P., Chiel, H.J., Thomas, P.J.: Shape versus timing: linear responses of a limit
cycle with hard boundaries under instantaneous and static perturbation. https://arxiv.org/abs/
1906.04387. Accessed 29 Apr 2020
17. Park, Y., Shaw, K.M., Chiel, H.J., Thomas, P.J.: The infinitesimal phase response curves of
oscillators in piecewise smooth dynamical systems. Eur. J. Appl. Math. 29, 905–940 (2018)
18. Winter, D.A.: Biomechanics and Motor Control of Human Movement. Wiley (2009)
19. Izhikevich, E., Ermentrout, B.: Phase model. Scholarpedia 3, 1487 (2008)
20. Lyttle, D.N., Gill, J.P., Shaw, K.M., Thomas, P.J., Chiel, H.J.: Robustness, flexibility, and
sensitivity in a multifunctional motor control model. Biol. Cybern. 111, 25–47 (2017)
21. Gabbiani, F., Cox, S.J.: Mathematics for Neuroscientists. 2nd edn. Elsevier Inc. (2017)
22. Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid
systems. IEEE Trans. Autom. Control 43, 475–482 (1998)
115
9. Martin, J.P., Guo, P., Mu, L., Harley, C.M., Ritzmann, R.E.: Central-complex control of
movement in the freely walking cockroach. Curr. Biol. 25, 2795–2803 (2015)
10. Chiel, H.J., Beer, R.D.: The brain has a body: adaptive behavior emerges from interactions
of nervous system, body and environment (1997)
11. Hunt, A., Schmidt, M., Fischer, M., Quinn, R.: A biologically based neural sys-tem coordinates
the joints and legs of a tetrapod. Bioinspiration Biomimet-ics 10, 055004 (2015)
12. Li, W., Szczecinski, N.S., Quinn, R.D.: A neural network with central pattern generators entrained by sensory feedback controls walking of a bipedal mod-el. Bioinspiration
Biomimetics 12, 065002 (2017)
13. Szczecinski, N.S., et al.: Introducing MantisBot: hexapod robot controlled by a high-fidelity,
real-time neural simulation. In: IEEE International Conference on Intelligent Robots and
Systems, pp. 3875–3881. Institute of Electrical and Electronics Engineers Inc. (2015)
14. Szczecinski, N.S., Hunt, A.J., Quinn, R.D.: Design process and tools for dy-namic neuromechanical models and robot controllers. Biol. Cybern. 111, 105–127 (2017)
15. Klein, T., Lewis, M.A.: A neurorobotic model of bipedal locomotion based on principles
of human neuromuscular architecture. In: Proceedings - IEEE In-ternational Conference on
Robotics and Automation, pp. 1450–1455. Institute of Electrical and Electronics Engineers
Inc. (2012)
16. Wang, Y., Gill, J.P., Chiel, H.J., Thomas, P.J.: Shape versus timing: linear responses of a limit
cycle with hard boundaries under instantaneous and static perturbation. https://arxiv.org/abs/
1906.04387. Accessed 29 Apr 2020
17. Park, Y., Shaw, K.M., Chiel, H.J., Thomas, P.J.: The infinitesimal phase response curves of
oscillators in piecewise smooth dynamical systems. Eur. J. Appl. Math. 29, 905–940 (2018)
18. Winter, D.A.: Biomechanics and Motor Control of Human Movement. Wiley (2009)
19. Izhikevich, E., Ermentrout, B.: Phase model. Scholarpedia 3, 1487 (2008)
20. Lyttle, D.N., Gill, J.P., Shaw, K.M., Thomas, P.J., Chiel, H.J.: Robustness, flexibility, and
sensitivity in a multifunctional motor control model. Biol. Cybern. 111, 25–47 (2017)
21. Gabbiani, F., Cox, S.J.: Mathematics for Neuroscientists. 2nd edn. Elsevier Inc. (2017)
22. Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid
systems. IEEE Trans. Autom. Control 43, 475–482 (1998)