A Hybrid Systems Approach to Tracking Control for a Fully Actuated Walking Bipedal Robot
We model a three-link fully actuated biped as a hybrid system, and propose a prediction-based control algorithm for global tracking of reference trajectories, with nominal robustness to perturbations, in order to track a periodic gait in finite time. Our hybrid model consists of continuous dynamics that describe the bipedal motion in between the impacts where both feet are in contact with the ground, which we consider to be a discrete event. The proposed control strategy consists of a reference system that generates the desired periodic gait, a virtual system that generates a suitable reference trajectory using prediction, and a tracking control law that steers the biped to the virtual trajectory. The proposed algorithms achieves, in finite time, tracking in two steps. We present mathematical properties that define how the hybrid predictive controller is capable of achieving convergence to the reference within the first two steps. Additionally, we validate our results through numerical simulations.