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Objectives and Significance
Objectives and Significance
Rhythmic body motions observed in animal locomotion are known to be controlled by neuronal circuits called central pattern generators (CPGs). It appears that CPGs are energy efficient controllers that cooperate with biomechanical and environmental constraints through sensory feedback. In particular, the CPGs tend to induce rhythmic motion of the body at a natural frequency, i.e., the CPGs are entrained to a mechanical resonance by sensory feedback. The objective of this research is to uncover the mechanism of entrainment resulting from the dynamic interaction of the CPG and mechanical system.
Results
Results
We developed multiple models for the simplest CPG called the half-center model, or the reciprocal inhibition oscillator (RIO). The reciprocal inhibition is the fundamental mechanism underlying anti-phasic neural oscillations that drive a pair of antagonistic muscles required for bidirectional torque generation through contractions only (without active extension). We examined through numerical experiments whether the CPG models can be entrained to the natural oscillation of a simple pendulum. The figure below shows an example of the natural entrainment, where v1 and v2 are the membrane potentials of the two neurons and theta is the pendulum angle. The result indicates that the RIO, when placed within the feedback loop, is able to identify the natural frequency of the pendulum based on the angular displacement information and drive the closed-loop system into the natural oscillation. This comparative study identified the neuronal properties essential for the entrainment. We then analyzed the simplest model that captures the essential dynamics via the method of harmonic balance. It is shown that robust entrainment results from a strong, positive-feedback coupling of a lightly damped mechanical system and the RIO consisting of neurons with the complete adaptation (zero static gain) property.
The mechanisms underlying the resonance entrainment are then examined through analytical study. We found two basic mechanisms, positive derivative feedback and negative integral feedback, both of which has the negative damping effect to destabilize the resting position. The trajectories divergent near the origin are stabilized by the boundedness of the neural threshold nonlinearity, resulting in a stable limit cycle. This analysis has been extended for multi-DOF mechanical systems and we found methods for entraining to a selected mode of natural oscillation by placing an RIO control for each DOF (e.g. joint) or one of the joints for underactuation.
The theory was first verified by simulation for a three-link flexible arm by entrainment to three modes of natural oscillations with mode switching between them. Experimental validation was then provided for a flapping wing made of silicon, which is driven by a motor through a spring mechanism emulating an antagonistic muscle pair. The difference between the commanded position u and the resulting deflection y carries the information on the flexible wing dynamics, allowing for the RIO to achieve natural entrainment.
Transition from 1st to 2nd mode
Transition from 2nd to 3rd mode
References
References
T. Iwasaki and M. Zheng, Biological Cybernetics, vol.94, pp.245-261, 2006.
Formal analysis of resonance entrainment by central pattern generator
Y. Futakata and T. Iwasaki, Journal of Mathematical Biology, vol.57, no.2, pp.183-207, 2008.
Entrainment to Natural Oscillations via Uncoupled Central Pattern Generators
Y. Futakata and T. Iwasaki, IEEE Transactions on Automatic Control, vol.56, no.5, pp.1075-1089, 2011, accepted version
Resonance entrainment of tensegrity structures via CPG control
T. Bliss, T. Iwasaki, and H. Bart-Smith, Automatica, vol.48, pp.2791-2800, 2012.
Experimental Validation of Robust Resonance Entrainment for CPG-Controlled Tensegrity Structures
T. Bliss, J. Werly, T. Iwasaki, and H. Bart-Smith, IEEE Transactions on Control Systems Technology, vol.21, no.3, pp.666-678, 2012.
Exciting multi-DOF systems by feedback resonance
D. Efimov, A. Fradkov, and T. Iwasaki, Automatica, vol.49, pp.1782-1789, 2013.
J. Zhao and T. Iwaasaki, IEEE Transactions on Automatic Control, 2019 (To appear), accepted version
Central pattern generator control of a tensegrity based swimmer
Tom Bliss, Ph.D Dissertation, University of Virginia, September 2011
Natural mode entrainment by CPG-based decentralized feedback controllers
Yoshiaki Futakata, Ph.D Dissertation, University of Virginia, August 2009
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