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 novel 3D hopping robot. In order to demonstrate richer behaviors on the manifold of rotations, both the planning and feedback layers must be done in a geometrically consistent fashion; therefore, we develop the necessary tools to employ Lie group integrators and an appropriate feedback controller. We experimentally demonstrate stable 3D hopping on a novel robot, 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。控制跳跃尤为困难，原因在于长时间欠驱动状态与极短的地面接触阶段并存——在此阶段必须调节地面相互作用以控制整体状态。本研究探索采用混合非线性模型预测控制，结合多速率层级中的低层反馈控制器，在一款新型三维跳跃机器人上实现动态稳定运动。为在旋转流形上展示更丰富的行为，规划层与反馈层均需保持几何一致性；因此，我们开发了应用李群积分器及相应反馈控制器所需的关键工具。实验证明，该新型机器人实现了稳定三维跳跃，并在仿真中验证了轨迹跟踪与翻转能力。