This paper presents a nonlinear control design for highly underactuated balance robots, which possess more numbers of unactuated degree-of-freedom (DOF) than actuated ones. To address the challenge of simultaneously trajectory tracking of actuated coordinates and balancing of unactuated coordinates, the proposed control converts a robot dynamics into a series of cascaded subsystems and each of them is considered virtually actuated. To achieve the control goal, we sequentially design and update the virtual and actual control inputs to incorporate the balance task such that the unactuated coordinates are balanced to their instantaneous equilibrium. The closed-loop dynamics are shown to be stable and the tracking errors exponentially converge towards a neighborhood near the origin. The simulation results demonstrate the effectiveness of the proposed control design by using a triple-inverted pendulum cart system.

翻译：本文提出了一种针对高度欠驱动平衡机器人的非线性控制设计，这类机器人的非驱动自由度数量多于驱动自由度。为解决驱动坐标轨迹跟踪与非驱动坐标平衡同时控制的难题，所提出的控制方法将机器人动力学转换为一系列级联子系统，并将每个子系统视为虚拟驱动。为实现控制目标，我们依次设计并更新虚拟控制输入和实际控制输入，以融入平衡任务，从而将非驱动坐标平衡至其瞬时平衡点。闭环动力学被证明是稳定的，且跟踪误差指数收敛至原点附近的邻域。通过三阶倒立摆小车系统的仿真结果验证了所提控制方法的有效性。