Accurate control of a humanoid robot's global position (i.e., its three-dimensional position in the world) is critical to the reliable execution of high-risk tasks such as avoiding collision with pedestrians in a crowded environment. This paper introduces a time-based nonlinear control method that achieves accurate global-position tracking (GPT) for multi-domain bipedal walking. Deriving a tracking controller for bipedal robots is challenging due to the highly complex robot dynamics that are time-varying and hybrid, especially for multi-domain walking that involves multiple phases/domains of full actuation, over actuation, and underactuation. To tackle this challenge, we introduce a continuous-phase GPT control law for multi-domain walking, which provably ensures the exponential convergence of the entire error state within the full and over actuation domains and that of the directly regulated error state within the underactuation domain. We then construct sufficient multiple-Lyapunov stability conditions for the hybrid multi-domain tracking error system under the proposed GPT control law. We illustrate the proposed controller design through both three-domain walking with all motors activated and two-domain gait with inactive ankle motors. Simulations of a ROBOTIS OP3 bipedal humanoid robot demonstrate the satisfactory accuracy and convergence rate of the proposed control approach under two different cases of multi-domain walking as well as various walking speeds and desired paths.

翻译：准确控制仿人机器人的全局位置（即其在世界坐标系中的三维位置）对于可靠执行高风险任务（如在拥挤环境中避免与行人碰撞）至关重要。本文提出了一种基于时间的非线性控制方法，可实现多域双足步行的精确全局位置跟踪。由于双足机器人具有高度复杂的时变与混合动力学特性，尤其是在涉及全驱动、过驱动和欠驱动等多个相位/域的多域步行中，推导其跟踪控制器极具挑战性。为解决这一难题，我们提出了一种用于多域步行的连续相位全局位置跟踪控制律，该控制律可证明地确保全驱动域和过驱动域内整个误差状态的指数收敛，以及欠驱动域内直接调节误差状态的指数收敛。随后，我们基于所提出的全局位置跟踪控制律，构建了混合多域跟踪误差系统的充分多重李雅普诺夫稳定性条件。我们通过两种情形说明所提出的控制器设计：所有电机均激活的三域步行，以及踝关节电机未激活的两域步态。对ROBOTIS OP3双足仿人机器人的仿真实验表明，所提出的控制方法在两种不同的多域步行情况以及多种步行速度和期望路径下均具有令人满意的精度和收敛速度。