A Motion Planning Framework for Dynamic Monopedal Locomotion on Deformable Terrain

The state-of-the-art in robotic legged locomotion on deformable terrain remains many steps behind the stable, graceful, and agile gaits exhibited by many animals that walk, trot, and run over soft substrates like sand, soil, and snow. A defining trait of legged locomotion on these deformable surfaces is simultaneous intrusion and rotation of the foot, which is neglected in most robotic locomotion planning and control frameworks such as zero moment point control and hybrid zero dynamics. We address this gap, and extend the work of Li et al. (2013) and Xiong et al. (2017), by developing a motion planning framework that fuses resistive force theory with direct collocation trajectory optimization to plan foot trajectories through granular media. We apply our framework to the task of finding period-1 hopping gaits for a monopedal robot. We first formulate a collection of constraints that represent period-1 orbits in state space, and we then use our framework to obtain motions that satisfy these constraints, i.e., monopedal hopping gaits. We find that these gaits scale meaningfully with speed and ground stiffness, suggesting that our approach has the potential to close the gap between robotic and biological legged locomotors.