Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential for deploying humanoid robots in dynamic real-world environments such as moving trains, ships, and airplanes. This paper introduces a real-time, provably stabilizing control approach for underactuated humanoid walking on periodically swaying rigid surface. The first key contribution is the analytical extension of the classical angular momentum-based linear inverted pendulum model from static to swaying grounds. This extension results in a time-varying, nonhomogeneous robot model, which is fundamentally different from the existing pendulum models. We synthesize a discrete footstep control law for the model and derive a new set of sufficient stability conditions that verify the controller's stabilizing effect. Another key contribution is the development of a hierarchical control framework that incorporates the proposed footstep control law as its higher-layer planner to ensure the stability of underactuated walking. The closed-loop stability of the complete hybrid, full-order robot dynamics under this control framework is provably analyzed based on nonlinear control theory. Finally, experiments conducted on a Digit humanoid robot, both in simulations and with hardware, demonstrate the framework's effectiveness in addressing underactuated bipedal locomotion on swaying ground, even in the presence of uncertain surface motions and unknown external pushes.

翻译：在动态刚性表面（即在惯性参考系中加速的刚性表面）上的运动对控制器设计提出了复杂挑战，这对于在动态现实环境（如移动的火车、船舶和飞机）中部署人形机器人至关重要。本文提出了一种用于欠驱动人形机器人在周期性摇摆刚性表面上行走的实时、可证明稳定的控制方法。第一个关键贡献是将经典的基于角动量的线性倒立摆模型从静态地面解析扩展至摇摆地面。该扩展产生了一个时变、非齐次的机器人模型，这与现有的摆模型有根本区别。我们为该模型合成了一种离散足步控制律，并推导出一组新的充分稳定性条件，以验证控制器的稳定效果。另一个关键贡献是开发了一个分层控制框架，该框架将所提出的足步控制律作为其高层规划器，以确保欠驱动行走的稳定性。基于非线性控制理论，对该控制框架下完整的混合、全阶机器人动力学的闭环稳定性进行了可证明的分析。最后，在Digit人形机器人上进行的仿真和硬件实验表明，即使在存在不确定表面运动和未知外部推力的情况下，该框架也能有效解决在摇摆地面上的欠驱动双足运动问题。