Passive Vibration-Driven Locomotion

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, such as 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 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. Our analysis focuses on progressive motion regimes arising in the vicinity of parametric resonances, considering two asymptotic limits: small-amplitude parametric excitation leading to a (2:1) resonant oscillatory motion of the pendulum, and large-amplitude excitation resulting in a (1:1) resonant unidirectional rotational motion. Both resonant regimes yield progressive motion due to the asymmetry of the dissipative force. We employ tailored asymptotic approaches based on multi-scale expansions and direct averaging analysis to identify optimal locomotion regimes, revealing the full bifurcation structure of steady-state solutions. Analytical predictions align well with direct numerical simulations of the full capsule-pendulum system.