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

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. To 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.