Feedback Motion Planning and Control of Brachiating Robots Traversing Flexible Cables

This paper presents an optimal feedback control design for a two-link, underactuated brachiating robot traversing a flexible cable. Building on previous work that presented a dynamic model and optimal trajectory generation scheme, a parameterized time-varying linear quadratic regulator (LQR) is developed to track a generated optimal trajectory for the robot on a flexible cable. A simplified dynamic system, in which the brachiating robot is attached to a rigid bar, is linearized about the optimal trajectory and the dynamics of the flexible cable are treated as a disturbance to the system. An LQR approach is then employed to solve for a set of time-varying optimal feedback gains. Through simulation and comparison with a partial feedback linearization controller, it is shown that the LQR controller is able to reliably achieve the desired brachiating motion in the presence of dynamic uncertainty, external perturbations, and off-nominal initial conditions.