Abstract-We apply fast online trajectory optimization for multi-step motion planning to Cassie, a bipedal robot designed to exploit natural spring-mass locomotion dynamics using lightweight, compliant legs. Our motion planning formulation simultaneously optimizes over center of mass motion, footholds, and center of pressure for a simplified model that combines transverse linear inverted pendulum and vertical spring dynamics. A vertex-based representation of the support area combined with this simplified dynamic model that allows closed form integration leads to a fast nonlinear programming problem formulation. This optimization problem is continuously solved online in a model predictive control approach. The output of the reduced-order planner is fed into a quadratic programming based operational space controller for execution on the full-order system. We present simulation results showing the performance and robustness to disturbances of the planning and control framework. Preliminary results on the physical robot show functionality of the operational space control system, with integration of the trajectory planner a work in progress.

Recent work has demonstrated the success of reinforcement learning (RL) for training bipedal locomotion policies for real robots. This prior work, however, has focused on learning joint-coordination controllers based on an objective of following joint trajectories produced by already available controllers. As such, it is difficult to train these approaches to achieve higher-level goals of legged locomotion, such as simply specifying the desired end-effector foot movement or ground reaction forces. In this work, we propose an approach for integrating knowledge of the robot system into RL to allow for learning at the level of task space actions in terms of feet setpoints. In particular, we integrate learning a task space policy with a model-based inverse dynamics controller, which translates task space actions into joint-level controls. With this natural action space for learning locomotion, the approach is more sample efficient and produces desired task space dynamics compared to learning purely joint space actions. We demonstrate the approach in simulation and also show that the learned policies are able to transfer to the real bipedal robot Cassie. This result encourages further research towards incorporating bipedal control techniques into the structure of the learning process to enable dynamic behaviors.

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