Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation combined with very short ground phases wherein ground interactions must be modulated to regulate global state. In this work, we explore the use of hybrid nonlinear model predictive control paired with a low-level feedback controller in a multi-rate hierarchy to achieve dynamically stable motions on a 3D hopping robot. In order to demonstrate richer behaviors on the manifold of rotations, both the planning and feedback layers must be designed in a geometrically consistent fashion; therefore, we develop the necessary tools to employ Lie group integrators and appropriate feedback controllers. We experimentally demonstrate stable 3D hopping, as well as trajectory tracking and flipping in simulation.

翻译：实现稳定跳跃一直是动态腿式运动领域的标志性挑战。受控跳跃尤为困难，因为其包含长时间欠驱动阶段与极短的地面接触阶段——后者必须通过调节地面相互作用来调控整体状态。本研究探索将混合非线性模型预测控制与多速率层级中的低层反馈控制器相结合，在三维跳跃机器人上实现动态稳定运动。为在旋转流形上展现更丰富的运动行为，规划层与反馈层均需采用几何一致性设计；因此，我们开发了必要的工具以应用李群积分器及相应的反馈控制器。通过仿真实验，我们成功演示了稳定的三维跳跃、轨迹跟踪以及空翻动作。