Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization

TL;DR

This paper presents a robust control synthesis method for wire-borne underactuated brachiating robots using sum-of-squares optimization, enabling reliable motion despite uncertainties and actuator constraints.

Contribution

It introduces a novel simplified cable dynamics model and applies SOS optimization to design a robust controller with formal guarantees for brachiating robots.

Findings

Robust backward reachable sets are significantly enlarged.

The controller reliably tracks optimal trajectories under uncertainties.

Experimental results validate the effectiveness of the proposed method.

Abstract

Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.