Orbital Stabilization and Time Synchronization of Unstable Periodic Motions in Underactuated Robots

Abstract-- This paper presents a control methodology for achieving orbital stabilization with simultaneous time synchronization of periodic trajectories in underactuated robotic systems. The proposed approach extends the classical transverse linearization framework to explicitly incorporate time-desynchronization dynamics. T o stabilize the resulting extended transverse dynamics, we employ a combination of time-varying LQR and sliding-mode control. The theoretical results are validated experimentally through the implementation of both centralized and decentralized control strategies on a group of six Butterfly robots. I. INTRODUCTION The problem of trajectory tracking for underactuated robots has been addressed in a series of publications [1]-[7].