Sliding Mode Control and Subspace Stabilization Methodology for the Orbital Stabilization of Periodic Trajectories

TL;DR

This paper introduces a combined sliding-mode control and subspace stabilization approach for orbital stabilization of periodic trajectories in underactuated systems, enhancing robustness and computational efficiency, validated on the Butterfly robot.

Contribution

It proposes a novel methodology integrating sliding-mode control with subspace stabilization for orbital stabilization, avoiding complex LQR computations and improving disturbance robustness.

Findings

Successful experimental validation on Butterfly robot.

Enhanced robustness to matched disturbances.

Reduced computational complexity compared to traditional methods.

Abstract

This paper presents a combined sliding-mode control and subspace stabilization methodology for orbital stabilization of periodic trajectories in underactuated mechanical systems with one degree of underactuation. The approach starts with partial feedback linearization and stabilization. Then, transverse linearization along the reference orbit is computed, resulting in a periodic linear time-varying system with a stable subspace. Sliding-mode control drives trajectories toward this subspace. The proposed design avoids solving computationally intensive periodic LQR problems and improves robustness to matched disturbances. The methodology is validated through experiments on the Butterfly robot.