Title: Piecewise-holonomic mechanics, hybrid dynamical systems, and escaping cockroaches
Speaker: Philip Holmes, Princeton University
Date: Wednesday, December 17, 2003, 1:00 pm
Location: Hill Center, Room 260, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
I will discuss joint work with John Schmitt, Raffaele Ghigliazza and Justin Seipel, in which nonlinear mechanics and hybrid dynamical systems meet biology. Motivated by Robert Full's experimental studies of insects at UC Berkeley, we propose a mechanical model for the dynamics of legged locomotion in the horizontal plane. Our three-degree-of freedom rigid body model with massless, compliant legs in intermittent contact with the ground allows for passive and prescribed (active muscle) force and torque generation. Starting with energetically conservative bipedal models (each leg corresponding to the front/rear/opposite-middle tripod used in rapid running by many insect species), we move on to include active muscles and to develop hexapedal models with more realistic leg geometries. We show that the (piecewise holonomic) mechanics due to intermittent foot contacts can confer strong asymptotic stability, and discuss the relevance of our idealised models to experiments and simulations on insect running and turning. We show that their gait and force characteristics match observations reasonably well, and consider their implications for the neural control of locomotion.
Some of this work appears in:
J. Schmitt and P. Holmes, (2000) Biological Cybernetics 83 (6), 501-515 {\rm{and}} 517-527. Mechanical models for insect locomotion: {D}ynamics and stability in the horizontal plane I: Theory; II: Application.
J. Schmitt and P. Holmes (2001) Physica D 156, 139-168. Mechanical models for insect locomotion: {S}tability and parameter studies.
J. Schmitt, M. Garcia, R. Razo, P. Holmes and R.J. Full (2002) Biological Cybernetics 86 (5), 343-353. Dynamics and stability of legged locomotion in the horizontal plane: A test case using insects.
J. Schmitt and P. Holmes (2003) Biological Cybernetics 89 (1), 43-55. Mechanical models for insect locomotion: {A}ctive muscles and energy losses.
Seminar sponsored by DIMACS/BIOMAPS Seminar Series on Quantitative Biology and Epidemiology.