Discrete Element Method Study of Hopping on Granular Media to Develop Analytical Model for Hopping Robot Design

Small-scale planetary exploration missions have been attracting significant attention in recent years. To maxi- mize the scientific return from these missions, compact rovers are required. Hopping is a promising locomotion strategy for achieving both high traversability and compactness. However, hopping on soft granular terrain such as regolith is challenging due to significant energy dissipation into the medium. The dy- namics of sand flow during hopping are not yet well understood, especially for diagonal trajectories. This study investigates sand behavior during diagonal hopping using the Discrete Element Method (DEM) simulations. We focused on how the added- mass effect and the effective friction coefficient vary with the hopping angle. Our results revealed a fundamental trade-off: shallower hopping angles decrease the inertial resistance from added mass, yet simultaneously increase effective friction, which enhances propulsive force. In addition, we applied the observed friction behavior to hopping simulations and confirmed its effectiveness. A reduced-order simulation incorporating this variable friction behavior reproduced the experimental hopping efficiency (0.31 in simulation versus 0.35 in experiment) more accurately than the fixed-friction model. These insights provide a physical basis for the development of more efficient hopping mechanisms for future planetary rovers.