Mitigating energy loss in a robot hopping on a physically emulated dissipative substrate

We work with geoscientists studying erosion and desertification to improve the spatial and temporal resolution of their data collection over long transects in difficult realworld environments such as deserts [1]. The Minitaur [2] robot, which can run quickly over uneven terrain and use a single leg to measure relevant ground properties such as stiffness [3], is an attractive scout robot candidate for inclusion in a heterogeneous team in collaboration with a heavily geared, sensor-laden RHex [4]. However, Minitaur is challenged by long-distance locomotion on sand dunes. Previous simulation results [5] suggested that the energetic cost of transport can be mitigated by programming a virtual damping force to slow the intrusion of a Minitaur foot into simulated granular media following a bulk-behavior force law [6]. In this paper, we present a ground emulator that can be used to test such locomotion hypotheses with a physical single-legged hopper jumping on emulated ground programmed to exhibit any compliance and damping characteristics of interest. The new emulator allows us to corroborate the conclusions of our previous simulation with physical hopping experiments. Programming the substrate emulator to exhibit the mechanics of a simplified bulk-behavior model of granular media characterized by linear stiffness and quadratic damping, we achieve a consistent energy savings of 20% in comparison with a nominal controller, with savings of up to 50% under specific conditions.