This paper presents a hierarchical control framework that enables robust quadrupedal locomotion on a dynamic rigid surface (DRS) with general and unknown vertical motions. The key novelty of the framework lies in its higher layer, which is a discrete-time, provably stabilizing footstep controller. The basis of the footstep controller is a new hybrid, time-varying, linear inverted pendulum (HT-LIP) model that is low-dimensional and accurately captures the essential robot dynamics during DRS locomotion. A new set of sufficient stability conditions are then derived to directly guide the controller design for ensuring the asymptotic stability of the HT-LIP model under general, unknown, vertical DRS motions. Further, the footstep controller is cast as a computationally efficient quadratic program that incorporates the proposed HT-LIP model and stability conditions. The middle layer takes the desired footstep locations generated by the higher layer as input to produce kinematically feasible full-body reference trajectories, which are then accurately tracked by a lower-layer torque controller. Hardware experiments on a Unitree Go1 quadrupedal robot confirm the robustness of the proposed framework under various unknown, aperiodic, vertical DRS motions and uncertainties (e.g., slippery and uneven surfaces, solid and liquid loads, and sudden pushes).

翻译：本文提出了一种分层控制框架，使得四足机器人能够在具有一般性和未知垂直运动的动态刚性表面上实现鲁棒运动。该框架的关键创新在于其上层，即一个离散时间、可证明稳定的落脚点控制器。该落脚点控制器的基础是一种新型混合时变线性倒立摆模型，该模型维度低，且能准确捕捉动态刚性表面运动过程中机器人的核心动力学特性。随后推导出一组新的充分稳定性条件，以直接指导控制器设计，确保HT-LIP模型在一般性、未知的垂直动态刚性表面运动下的渐近稳定性。此外，落脚点控制器被设计为一种计算高效的二次规划，其中融合了所提出的HT-LIP模型和稳定性条件。中间层以上层生成的期望落脚点位置为输入，生成运动学可行的全身参考轨迹，并由下层力矩控制器精确跟踪。在宇树Go1四足机器人上的硬件实验验证了所提框架在多种未知、非周期性垂直动态刚性表面运动及不确定性（如湿滑不平地面、固体与液体负载、突然推力）下的鲁棒性。