Life at Low Coasting Number

Abstract: In 1974 Purcell authored a paper “Life at Low Reynolds Number” to describe the counterintuitive world of microscopic organisms in which viscous dissipation so dominates inertia that “coasting” is impossible, and that the geometry of a path in an internal movement space dominates self-propulsion. It is typically assumed that a key difference between self-propulsion in the microworld and in the world inhabited by macroscopic organisms (like those studied in my lab) is that inertial effects are negligible in the former, but not the latter. However, our experimental studies and theoretical models of organisms like lizards, snakes and centipedes moving in frictionally dissipative environments (like rough ground and granular media) have revealed that macroscopic locomotion bears similarities to microscopic locomotors. In both environments, a parameter we refer to as the Coasting number (which we define as the ratio of coasting time to a cyclic timescale and in frictional systems is the ratio of inertial to frictional forces) is small (<0.1). As such, we can use microscopic organism modeling tools like Resistive Force Theory to gain insight into aspects of self-propulsion in granular and frictional systems. Most generally, the concept of geometric phase in locomotion introduced by Wilczek & Shapere in the 1980s as a framework for locomotion at low Reynolds number allows us to generate hypotheses for optimal movement in macroscopic systems. Coupling this to our approach of modeling living systems with robots (which we refer to as robophysics) gives us insights into control principles for effective locomotion. And surprisingly, our robophysical models show impressive mobility outside the lab, leading to my recent cofounding of a company, Ground Control Robotics, with the goal to develop robot swarms to discover and control weeds and in specialty crop fields.