Self propulsion via slipping: frictional resistive force theory for multi-legged locomotors

Abstract

Locomotion is typically studied in continuous media where bodies and legs experience forces generated by the flowing medium, or on solid substrates dominated by friction. In the former, slipping through the medium is unavoidable and necessary for propulsion. In the latter, slip is often assumed undesirable and/or minimal. We discover in laboratory experiments that the land locomotion of a multisegmented/legged robophysical model proceeds via slipping and can be viewed as terrestrial "swimming". Robophysical experiments varying leg and body wave reveal that inertial effects are minimal. Numerical simulations and theoretical analysis demonstrate that the periodic leg-substrate contact allows analysis via an effective Resistive Force Theory akin to that in flowable media such that the system experiences an effective viscous drag and acquired drag anisotropy. Analysis of body and leg dominated propulsion reveals how body undulation can buffer the robot against vertical heterogeneities (randomly distributed leg scale vertical obstacles) in otherwise flat frictional terrain. Locomotion performance of the 40 legged 10 cm long desert centipede S. polymorpha) moving at relatively high speeds (∼ 0.5 body lengths/sec) over a range of body and leg waves is well described by the theory. Our results could facilitate control of multilegged robots in complex terradynamic scenarios.