Series: Mathematics Colloquium

Date: Thursday, March 25, 2004

Time: 4:00 - 5:00 PM

Place: 101 Osmond Building

Host: Mark Levi

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Philip Holmes, Princeton University

Title: 

  Piecewise-Holonomic Mechanics, Hybrid Dynamical Systems, and
  Escaping Cockroaches

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.