SLIP-Inspired Hopping on Yielding Terrain

Legged robots offer the possibility of superior performance relative to wheeled or treaded vehicles on yielding substrates. However, the tools for planning and controlling legged locomotion on these substrates are significantly less advanced than their rigid-ground counterparts, due largely to nontrivial coupling between ground reaction forces and foot kinematics and irrecoverable energy loss through permanent terrain deformation. We recently addressed these challenges using direct-collocation trajectory optimization, informed by resistive force theory (RFT), discovering hopping gaits for a monopod that closely resemble the spring-loaded inverted pendulum (SLIP) motions characteristic of running animals. Inspired by these results, and within the same RFT framework, we develop and implement an augmented SLIP template parameterized by leg and ankle impedance. We optimize these parameters to maximize energetic efficiency, forward speed, and robustness during steady-state hopping on yielding terrain. These results lay the groundwork for a two-pronged approach that will use control and foot design to explore the tradeoffs between efficient, agile, and robust legged locomotion on soft ground.