The 31st Chinese Control Conference July 25 27, 2012, Hefei, China. Biological Control Mechanisms for Oscillation and Locomotion
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1 The 31st Chinese Control Conference July 25 27, 2012, Hefei, China Biological Control Mechanisms for Oscillation and Locomotion TIwasaki T. UCLA
2 Motivation: Animal locomotion
3 Locomotion Control System Brain CPG Body Environment High-level commands (e.g. start/stop) Command for rhythmic muscle contraction ti CPG is directly responsible for locomotion
4 Systems View Point Membrane Potential Stretch Receptor Tension CPG Biological Oscillator Tension Muscle Mechanical Rectifier Motoneuron Length Membrane Potential Impulses Find Principles Behind: Adaptive pattern formation Coupled oscillator/rectifier Distributed local feedback Velocity Vl Velocity Body Fluid Force Example: Leech swimming
5 Robotics Applications Bio-inspired Robots New Functionalities from Animal Locomotion: Crawling/ Walking Robot Micro Efficiencyi Aerial Robustness Vehicle Adaptability Agility Stealth Autonomous Underwater Vehicle
6 Medical Applications Understanding of CPG mechanisms will help to address issues such as: Prosthesis Neurological Disorder Locomotor Rehab. Spinal Cord Injury
7 Technical Challenges Understand biological mechanisms and translate into engineering i principles i of: Optimality Conformity Adaptivity Complexity
8 Optimality What is the most efficient gait?
9 Conformity How to exploit inherent dynamics? (natural oscillation) Human walking exploits resonance of leg pendulum Undulatory swimming exploits natural oscillation of body-fluid dynamics? How do we define and characterize natural oscillation for locomotion?
10 Adaptivity How to adapt the gait to environment? Ref.Gen. Regulator CPG Body Body Environment Ground Ice Environment Ground Ice Engineering i Biology
11 Complexity How to generate various gait patterns? Tritonia Lamprey Leech Locust
12 Central Pattern Generator (CPG)
13 Various Gait Patterns exist Atlantic Ray (undulator) Cownose Ray (oscillator)
14 CPG sets Gait Patterns Oscillation Profile
15 General Pattern lpattern Formation on Phase Problem Plane
16 More Generally Global l Pattern Formation via Local Dynamic Interactions in Multi-agent Complex Systems Gene regulatory networks Neuronal circuits (Brain/CPG) Bird flocking, fish schooling Climate dynamics Power grids Traffic
17 Problem Statement Remarks:
18 Definition: Orbital Stability Dynamical System Periodic Orbit x Orbital Stability
19 A Complication
20 Possible Approaches General methods (linearization, averaging, g Floquet, ) Guckenheimer and Holmes 1997 Hoppensteadt and Izhikevich 1997 Izhikevich i h 2007 Farkas 2010 Weakly Coupled Oscillators (Phase model) Kuramoto 1984 Ermentrout and Kopell 1984 Winfree 2001 Contraction Theory Lohmiller and Slotine 1998 Multivariable Harmonic Balance Mees 1981, Iwasaki 2008, Chen et al. 2008
21 Our Approach Coordinate transformations Isolate the rigid body mode Linearization LP dynamics for phase & amplitude Weak coupling + Averaging LTI dynamics
22 Coordinate Transformation Weakly Coupled Oscillators Limit Cycle Coordinate Transformation
23 Linearization + Averaging Rigid Body Mode
24 Theorem LMI Problem
25 Structured Design
26 Multi Pattern Design
27 Conclusion Biological oscillations in animal locomotion provide a research platform for robotics neural information processing complex systems Coupled harmonic oscillators can be designed by LMIs through weak coupling + averaging coordinate transformation Floquet multiplier
28 Acknowledgments Colleagues: Otto Friesen (UVA) Zhiyong Chen (USTC > Univ.Newcastle) Students and post docs: X. Liu, S. Kohannim, A. Wu (UCLA) J. Blair, T. Bliss, J. Chen (UVA) Y. Futakata, J. Tian, M. Zheng (UVA) Funding agencies: National Science Foundation (USA) National Institutes of Health (USA) Office of Naval Research (USA)
29 Thank you!
30 References Modeling of leech swimming Tian, Iwasaki, and Friesen, Journal of Comparative Physiology A, Zheng, Friesen and Iwasaki, Journal of Computational Neuroscience, Tian, Iwasaki, and Friesen, Journal of Comparative Physiology A, Chen, Friesen, Iwasaki, Journal of Experimental Biology, 2011 Chen, Tian, Iwasaki, Friesen, Journal of Experimental Biology, 2011 Chen, Friesen, Iwasaki, Journal of Experimental Biology, 2012 Optimal gait of locomotion Humphrey, Chen, Iwasaki, Friesen, J. of Royal Society Interface,, Blair and Iwasaki, IEEE Transactions on Automatic Control, CPG analysis and synthesis Iwasaki, Automatica, Chen, Zheng, Friesen, and Iwasaki, J. Computational Neuroscience, Chen and Iwasaki, IEEE Transactions on Automatic Control, Chen and Iwasaki, Systems & Control Letters, Feedback control by CPG Iwasaki and Zheng, Biological Cybernetics, Futakata and Iwasaki, Journal of Mathematical Biology, Futakata t and Iwasaki, IEEE Transactions on Automatic ti Control, 2011.
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