A Lyapunov-based approach for the control of biomimetic robotic systems with periodic forcing inputs

Bio-mimetic Robotics often deploys locomotion mechanisms(swimming, crawling, flying etc...) which rely on repetitivepatterns for the actuation schemes. This directly translates intoperiodic forcing inputs for the dynamics of the mechanical system.Closed loop control is achieved by modulating shape-parameters(e.g. duty cycle) which directly affect the mean values of theforcing inputs. In this work, guided by an intuition inspired bylinear systems theory, first a linear feedback law is derived thatstabilizes a linearization of the average system, i.e. the systemsubject only to the average values of the forcing inputs, and thenit is shown how this very feedback law can also guaranteeboundedness of solutions of the original system. Boundedness isproved my means of a Lyapunov energy function easily derived inthe linearized case. Unlike classical results found in literaturein the areas of averaging and perturbation theory, this workinstead of focussing on the existence of periodic limit cycles,simply restricts its attention on the boundedness of solutions,which directly translates into the possibility of deploying inputfunctions which are continuous but not continuouslydifferentiable.