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连杆回转平面机器人的摆动控制问题。本研究的目的是设计并分析一种摆动控制器，该控制器能将机器人带入直立平衡点的任何一个小邻域，且所有的连杆都处于直立位置。首先，我们讨论了如何迭代地设计由被动关节隔开的两系列虚拟组合杆件，用于设计所有主动关节角度的坐标变换。其次，我们设计了一种基于能量的摆动控制器，它使用了一种基于该变换的新的Lyapunov函数。第三，对机器人在控制器下的全局运动进行了分析，建立了保证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些具有被动第一关节的欠驱动机器人的前人结果，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.