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 repetitive patterns for the actuation schemes. This directly translates into periodic 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 the forcing inputs. In this work, guided by an intuition inspired by linear systems theory, first a linear feedback law is derived that stabilizes a linearization of the average system, i.e. the system subject only to the average values of the forcing inputs, and then it is shown how this very feedback law can also guarantee boundedness of solutions of the original system. Boundedness is proved my means of a Lyapunov energy function easily derived in the linearized case. Unlike classical results found in literature in the areas of averaging and perturbation theory, this work instead 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 input functions which are continuous but not continuously differentiable.Copyright c ©2005 IFAC.