Orbital Stabilization and Time Synchronization of Unstable Periodic Motions in Underactuated Robots
Maksim Surov, Maksim Grigorov, Sergei V. Gusev, Oleg Yu. Sumenkov
AI summary
Problem
Standard orbital stabilization only guarantees convergence to a periodic trajectory up to an arbitrary phase shift, making it inadequate for synchronized multi-robot tasks where exact time alignment is required.
Approach
The method augments transverse linearization with a desynchronization variable and stabilizes the resulting dynamics using a hybrid time-varying LQR and bounded sliding-mode controller.
Key results
- Extended transverse linearization framework incorporating time desynchronization dynamics
- Hybrid LQR and sliding-mode control law ensuring bounded synchronization corrections
- Experimental validation of asymptotic trajectory tracking on a single Butterfly robot
- Decentralized synchronization of a six-robot network using neighbor- and average-based time references
Why it matters
Enables robust, time-synchronized coordination for cooperative underactuated robotic systems, bridging the gap between theoretical orbital control and practical multi-robot applications.
Abstract
This paper presents a control methodology for achieving orbital stabilization with simultaneous time syn- chronization of periodic trajectories in underactuated robotic systems. The proposed approach extends the classical trans- verse 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.