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Dynamics of Legged Locomotion: Models, Analyses, and Challenges

SIAM Review, 2006

P. Holmes*, R. J. Full†, D. E. Koditschek‡, and J. Guckenheimer**
*: Princeton University
†: University of California
‡: University of Pennsylvania
**: Cornell University

Full PDF | Penn ScholarlyCommons

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.
BibTeX Entry
@article{
	location = {http://www.scientificcommons.org/16162024},
	title = {The Dynamics of Legged Locomotion: Models, Analyses, and Challenges},
	author = {Holmes, Philip and Full, Robert J and Koditschek, Daniel E and Guckenheimer, John},
	year = {2006},
	keywords = {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},
        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.},
	publisher = {ScholarlyCommons@Penn},
	url = {http://repository.upenn.edu/ese_papers/200},
	institution = {ScholarlyCommons@Penn [http://repository.upenn.edu/cgi/oai2.cgi] (United States)},
}

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