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：本文提出了一种适用于高度欠驱动平衡机器人的非线性控制设计方法，此类机器人具有比驱动自由度更多的未驱动自由度。针对同时实现驱动坐标轨迹跟踪与未驱动坐标平衡控制的难题，所提出的控制方法将机器人动力学转化为一系列级联子系统，并将每个子系统视为虚拟驱动系统。为实现控制目标，我们通过顺序设计与更新虚拟及实际控制输入来融入平衡任务，使未驱动坐标稳定在其瞬时平衡点。闭环动力学系统被证明是稳定的，且跟踪误差以指数形式收敛于原点附近的邻域内。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。