STUDY ON NONHOLONOMIC MANIPULATORS

在本项目中，我们基于一种新的概念，设计并制作了一种仅由两个电机驱动的可控n关节机械手。建立并验证了其定位和轨迹控制的非线性控制理论。在这项研究之前，世界上从来没有开发过只用两个电机控制任意自由度的机械手的想法。从非线性控制理论的观点来看，它是一个具有非完整约束的新系统。与传统的非完整系统研究集中于对各种现有机构的分析不同，我们利用最近发展起来的非完整系统的非线性控制理论，发明了一种从未有过的新机构。由于非完整机械手的两个执行器位于底部，因此适合于可重构模块化机器人系统的设计，并研究了是否可以用一台电机控制两个以上关节的机械手。我们具体讨论了一种平面两关节机械手，其中1个关节是致动的，2个关节是自由转动的。将这样的系统描述为具有关于加速度的不可积动态约束的系统是一个独特的特征。它通常被称为具有漂移的非线性系统，其控制的一般理论尚未建立。在本研究中，我们从非线性动力学的角度对系统进行了分析，发现简单的周期控制可能会表现出混沌行为。其中，我们讨论了对周期轨迹的镇定，并建立了两个关节的同时定位。

In this project, we designed and prototyped a contorollable n-joint manipulator actuated by only two motors based on a new concept. We also established and verified its nonlineat control thepry for positioning and trajectory control. The idea of controlling a manipulator of an arbitrary number of degrees of freedom with only two motors, had never been developed nor studied in the world before this research. From nonlinear control theory point-of-view, it is a new system that has nonholonomic constraines. In contrast to the fact that nonholonomic systems research had conventionally focused on analysis of various existing mechanisms, we have invented a new mechanism that had never existed, with the knowledge of nonlinear control thepry recently developed for nonholonomic systems. Since hte nonholonomic manipulator locates its two actuators at the base, it is a suitable design of reconfigurable modular robot systems.We also studied whether we can control a manipulator with more than two joints with only one motor. We specifically discussed a planar two-joint manipulator of which 1^<st> joint is actuated and the 2^<nd> is free to rotate. It is a unique feature that such a system is described as a system with nonintegrable dynamic constraines with respect to acceleration. It is often called a nonlinear system with drift, for which a general theory of control has not yet established. In this research, we analyzed the system from the scope of nonlinear dynamics, and showed that a simple periodic control may exhibits chaotic behavior. Them, we discussed stabilization to periodic trajectories and established simultaneous poritioning of the both joints.