The Dynamics of Legged Locomotion: Models, Analyses, and Challenges

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General Robotics, Automation, Sensing and Perception Laboratory
Kod*lab
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GRASP
Kodlab
animal locomotion
biomechanics
bursting neurons
central pattern generators
control
systems
hybrid dynamical systems
insect locomotion
Lagrangians
motoneurons
muscles
neural networks
periodic gaits
phase oscillators
piecewise holonomic systems
preflexes
reflexes
robotics
sensory systems
stability
templates
Biomechanics and Biotransport
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Holmes, Philip
Full, Robert J
Guckenheimer, John
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Abstract

Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we explore a corner of this fascinating world. We describe mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain. Newtonian body–limb dynamics are most naturally formulated as piecewise-holonomic rigid body mechanical systems, whose constraints change as legs touch down or lift off. Central pattern generators and proprioceptive sensing require models of spiking neurons and simplified phase oscillator descriptions of ensembles of them. A full neuromechanical model of a running animal requires integration of these elements, along with proprioceptive feedback and models of goal-oriented sensing, planning, and learning. We outline relevant background material from biomechanics and neurobiology, explain key properties of the hybrid dynamical systems that underlie legged locomotion models, and provide numerous examples of such models, from the simplest, completely soluble “peg-leg walker” to complex neuromuscular subsystems that are yet to be assembled into models of behaving animals. This final integration in a tractable and illuminating model is an outstanding challenge.

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2006-05-02
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Copyright SIAM, 2006. Reprinted in SIAM Review, Volume 48, Issue 2, 2006, pages 207-304.
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