Philip Holmes
Department of Mechanical and Aerospace Engineering
Program in Applied and Computational Mathematics
Princeton University
Models of Insect Locomotion: Why Cockroaches Get Away
I will discuss joint work with John Schmitt in which we study the dynamics and stability of legged locomotion in the horizontal plane. Inspired by experimental studies of insects due to R.J. Full, et al., we develop two and three-degree-of freedom rigid body models with both rigid 'peg-legs' and pairs of elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed 'muscle' forces, leg displacements and combined strategies. The resulting (piecewise-holonomic) mechanical systems exhibit periodic gaits whose neutral and asymptotic stability characteristics are due to intermittent food contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and relative body orientation. We discuss the relevance of our idealized models to recent experiments and simulations on insect running and turning, and argue that our models may help understand the scaling of gait characteristics over a wide range of animal types and sizes.