Dynamics, stability and bifurcations of a planar three-link swimmer with passive visco-elastic joint using “ideal fluid” model

Abstract

Articulated swimming robots have a promising potential for various marine applications. A common theoretical model assumes ideal fluid, where the viscosity is negligible and the swimmer–fluid interaction is induced by reactive forces originating from added mass effect. Some previous works used this model to study planar multi-link swimmers under kinematic input prescribing all joint angles. Inspired by biological swimmers in nature that utilize body flexibility, in this work we consider an underactuated three-link swimmer where one joint is periodically actuated while the other joint is passive and viscoelastic. Analysis of the swimmer’s nonlinear dynamics reveals that its motion depends significantly on the amplitude and frequency of the actuated joint angle. Optimal frequency is found where the swimmer’s net displacement per cycle is maximized, under symmetric periodic oscillations of the passive joint. In addition, upon crossing critical values of amplitude or frequency, the system undergoes a bifurcation where the symmetric periodic solution loses stability and asymmetric solutions evolve, for which the swimmer moves along an arc. We analyze these phenomena using numerical simulations and analytical methods of perturbation expansion, harmonic balance, Floquet theory, and Hill’s determinant. The results demonstrate the important role of parametric excitation in stability and bifurcations of motion for flexible underactuated locomotion.