Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid substrates. In this study we focus on the ramifications of plastic terrain deformation on the hop-to-hop energy dynamics of a spring-legged monopedal hopping robot animated by a switched-compliance energy injection controller. From this deliberately simple robot-terrain template, we derive a hop-to-hop energy return map, and we use physical experiments and simulations to validate the hop-to-hop energy map for a real robot hopping on a real deformable substrate. The dynamical properties (fixed points, eigenvalues, basins of attraction) of this map provide insights into efficient, responsive, and robust locomotion on deformable terrain. Specifically, we identify constant-fixed-point surfaces in a controller parameter space that suggest it is possible to tune control parameters for efficiency or responsiveness while targeting a desired gait energy level. We also identify conditions under which fixed points of the energy map are globally stable, and we further characterize the basins of attraction of fixed points when these conditions are not satisfied. We conclude by discussing the implications of this hop-to-hop energy map for planning, control, and estimation for efficient, agile, and robust legged locomotion on deformable terrain.

翻译：腿式机器人的运动能力受到应用场景与现有规划控制工具之间不匹配的制约：在那些腿部性能可能优于轮子或履带的应用中，地形多为可变形基底，而现有的大多数规划控制工具却假设地面平坦且刚性。本研究聚焦于塑性地形变形对单腿弹簧弹跳机器人逐跳能量动力学的影响，该机器人由一种切换刚度的能量注入控制器驱动。基于这一经过精心简化的机器人-地形模板，我们推导出了逐跳能量返回映射，并通过物理实验与仿真验证了真实机器人在真实可变形基底上弹跳时的逐跳能量映射。该映射的动力学特性（不动点、特征值、吸引域）为在可变形地形上实现高效、响应迅速且鲁棒的 locomotion 提供了深刻见解。具体而言，我们在控制器参数空间中识别出了恒定不动点曲面，这表明有可能在针对期望步态能量水平的同时，为追求效率或响应性而调整控制参数。我们还确定了能量映射的不动点具有全局稳定性的条件，并进一步刻画了当这些条件不满足时不动点的吸引域。最后，我们讨论了这一逐跳能量映射对于在可变形地形上实现高效、敏捷、鲁棒的腿式 locomotion 的规划、控制与估计的意义。