Fast, Versatile, and Open-loop Stable Running Behaviors with Proprioceptive-only Sensing using Model-based Optimization

As we build our legged robots smaller and cheaper, stable and agile control without expensive inertial sensors becomes increasingly important. We seek to enable versatile dynamic behaviors on robots with limited modes of state feedback, specifically proprioceptive-only sensing. This work uses model-based trajectory optimization methods to design open-loop stable motion primitives. We specifically design running gaits for a single-legged planar robot, and can generate motion primitives in under 3 seconds, approaching online-capable speeds. A direct-collocation-formulated optimization generated axial force profiles for the direct-drive robot to achieve desired running speed and apex height. When implemented in hardware, these trajectories produced open-loop stable running. Further, the measured running achieved the desired speed within 10% of the speed specified for the optimization in spite of having no control loop actively measuring or controlling running speed. Additionally, we examine the shape of the optimized force profile and observe features that may be applicable to open-loop stable running in general.