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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.
Apgar et al. (Tue,) studied this question.