Development of New Nonlinear Control Theory for Underactuated Mechanical Systems with Its Application to Robot Control

研究了任意一个关节为被动关节的n连杆平面旋转机器人的摆动控制问题。本研究的目标是设计和分析一种摆动控制器，使机器人在所有连杆都处于直立位置的情况下，进入直立平衡点的任何小邻域。首先，我们讨论了如何迭代设计由被动关节分隔的两组虚拟复合连杆，用于设计所有主动关节角度的坐标变换。其次，我们设计了一个基于能量的摆动控制器，该控制器使用基于该转换的新Lyapunov函数。第三，分析了机器人在控制器作用下的全局运动，确定了实现摆动控制目标的控制参数条件。所得结果不仅统一了一类被动第一关节欠驱动机器人的研究结果，而且为欠驱动多自由度系统的能量控制提供了新的思路。

This research concerns a swing-up control problem for an n-link revolute planar robot with any one of the joints being a passive joint. The goal of this study is to design and analyze a swing-up controller that can bring the robot into any small neighborhood of the upright equilibrium point with all links in the upright position. First, we address how to iteratively devise two series of virtual composite links separated by the passive joint to be used for designing a coordinate transformation on the angles of all active joints. Second, we devise an energy based swing-up controller that uses a new Lyapunov function based on that transformation. Third, we analyze the global motion of the robot under the controller and establish conditions on control parameters that ensure attainment of the swing-up control objective. The results obtained not only unify some previous results for some underactuated robots with a passive first joint, but also provide insight into the energy-based control of underactuated multi-degree-of-freedom systems.