Phase space planning and robust control for data-driven locomotion behaviors

We utilize here regression tools to plan dynamic locomotion in the Phase Space of the robot´s center of mass behavior and state feedback controllers to accomplish the desired plans. In real robotic systems, simplified locomotion models and disturbances in the control processes result in deviations from the actual closed loop dynamics with respect to the desired locomotion trajectories. To tackle these challenges, we propose here the use of two control strategies: (1) support vector regression to approximate complex nonlinear center of mass dynamics and plan the feet contact transitions, and (2) sliding mode control to track feet trajectories given the contact timing and location plans. First, support vector regression is utilized to learn a data set obtained through numerical simulation, providing an analytical approximation of the center of mass behavior. To approximate Phase Plane curves, which are characterized by vertical tangents and loop or cyclic behaviors, we use implicit functions for regression as opposed to explicit methods. Based on the proposed regression approximations of the dynamics, we develop contact transition plans and apply robust controllers to converge to the desired feet trajectories. In particular, state feedback controllers might be more convenient than time based controllers in terms of robustness to disturbances. Overall, our methods are capable of learning complex center of mass trajectories and might benefit from the use of robust control techniques. Various case studies are analyzed to validate the effectiveness of the methods including single and multi step planning in a numerical simulation, and swing leg trajectory control on our Hume bipedal robot.