Repeated jumping of a single-legged robot on soft ground

Achieving high-performance locomotion on yielding substrates such as sand and snow presents substantial challenges for robotic design and control, and to our understanding of the physics of soft ground. To advance these areas, we study the locomotion of a single-leg hopping robot on model ground. The robot consists of two masses, the body and the leg, between which an internal force is applied; the ground consists of particles contained in a fluidized bed, which allows control of the packing density and, consequently, the ground intrusion properties. Unlike rigid or purely compliant substrates, soft ground exhibits hysteresis in the form of tracks created during the stance phase. Consequently, we consider three different cases: 1) jumping in place; 2) gaits in which the leg always encounters undisturbed ground; and 3) gaits where tracks partially overlap. For 1) and 3), we characterize the temporal development of the ground reaction force for repeated leg intrusions, and show that steady states are reached after around five intrusions. Using this knowledge to inform a feed-forward control model, we compare the performance of inter-jump and intra-jump control schemes to achieve fixed height jumps for the three track overlap cases.