Robust bipedal locomotion on unknown terrain

Abstract

A wide variety of bipedal robots have been constructed with the goal of achieving natural and efficient walking in outdoor environments. Unfortunately, there is still a lack of general schemes enabling the robots to reject terrain disturbances. In this thesis, two approaches are presented to enhance the performance of bipedal robots walking on modest terrain. The first approach searches for a walking gait that is intrinsically easily stabilized. The second approach constructs a robust controller to steer the robot towards the designated walking gait. Mathematically, the problem is modeled as rejecting the uncertainty in the guard function of a hybrid nonlinear system. Two metrics are proposed to quantify the robustness of such systems. The first metric concerns the 'average performance' of a robot walking over a stochastic terrain. The expected LQR cost-to-go for the post-impact states is chosen to measure the difficulty of steering those perturbed states back to the desired trajectory. A nonlinear programming problem is formulated to search for a trajectory which takes the least effort to stabilize. The second metric deals with the 'worst case performance', and defines the L₂ gain for the linearization of the hybrid nonlinear system around a nominal periodic trajectory. In order to reduce the L₂ gain, an iterative optimization scheme is presented. In each iteration, the algorithm solves a semidefinite programming problem to find the quadratic storage function and integrates a periodic differential Riccati equation to compute the linear controller. The simulation results demonstrate that both metrics are correlated to the actual number of steps the robot can traverse on the rough terrain without falling down. By optimizing these two metrics, the robot can walk a much longer distance over the unknown landscape.