Passive Vibration-Driven Locomotion

Abstract

We investigate a concept of passive, vibration-driven locomotion, in which a mechanical system achieves horizontal self-propulsion by resonantly harvesting energy from vertical environmental excitations (e.g. ambient vibrations of underwater pipelines), without a direct propulsive actuation. The system consists of a capsule containing an internal pendulum attached to its base mounted on a vertically vibrating substrate. The underlying locomotion mechanism relies on resonant energy transfer from the vertically vibrating substrate to the internal oscillatory element. Under appropriate forcing conditions and in the presence of asymmetric dissipative interactions, this internal oscillator induces a net unidirectional motion of the capsule. The analysis focuses on regimes of progressive motion arising in the vicinity of parametric resonances. Two asymptotic limits are considered: small-amplitude parametric excitation leading to a (2:1) resonant oscillatory motion of the pendulum, and large-amplitude excitation leading to a (1:1) resonant unidirectional rotational motion of the pendulum. Given the asymmetry of the dissipative force acting on the capsule, both resonant regimes result in a progressive motion of the capsule system. To identify optimal locomotion regimes in both cases, we employ tailored asymptotic approaches based on multi-scale expansions and direct averaging analysis. The resulting slow-flow and averaged-flow models reveal the full bifurcation structure of steady-state solutions associated with forward capsule motion for both low- and high- amplitude excitations. Analytical predictions are shown to be in good agreement with direct numerical simulations of the full capsule-pendulum system.