Adaptive Control of Wire-Borne Underactuated Brachiating Robots Using Control Lyapunov and Barrier Functions

Executing safe brachiation maneuvers with a cable-suspended underactuated robot is a challenging problem due to the complications induced by the cable dynamics. We present and experimentally implement an online adaptive controller for a wire-borne brachiating robot swinging on a vibrating cable. An adaptive function approximation approach is proposed to estimate the unknown dynamics of the flexible cable as an external force applied to the robot. Robust control Lyapunov and barrier functions are designed and incorporated into quadratic programs to synthesize a unified adaptive control framework, which formally guarantees the stability and safety of the brachiating robot in the presence of dynamic uncertainties, actuator constraints, and obstacles in the environment. The stability analysis and derivation of the adaptation law are carried out through a Lyapunov analysis. We demonstrate and validate the proposed control framework using extensive hardware experiments with an underactuated brachiating robot operating on a flexible cable. Simulation results, hardware experiments, and comparisons with a baseline controller show that the proposed quadratic programming-based controller achieves reliable tracking performance and disturbance estimation in the presence of model uncertainties, actuator limits, and safety constraints.