Feedback Stabilization and Control of Constrained MechanicalSystems

该项目为研究与约束机械系统相关的反馈镇定和控制问题提供了理论框架。对于不受约束的机械系统，如果施加外部约束，达到一定性能目标的控制器可能是不合适的。这项工作受到与机器人和空间系统相关的重要工程问题的强烈推动。当实体之间进行接触时，就会产生约束。在机器人技术中，当末端效应器和有效载荷对象之间存在接触时，就会发生这种情况。例如，轮廓跟随、去毛刺、紧固和拾取放置等操作都属于此类。对于空间系统，卫星对接机动中会出现约束。受约束的机器人问题一直是最近在柔顺和阻抗控制方面进行研究的动机，但总是没有明确考虑保持对约束的满足所需的接触力。本研究大量运用数学方法对动力系统进行非线性分析。将进行计算机模拟实验，以验证所开发的理论，并提出新的理论问题以供研究。要模拟和研究的例子包括一个被约束在光滑椭圆线上运动的粒子。这一理论也可以在仪表式x-y工作台上进行实验验证。

This project develops the theoretical framework for the study of feedback stabilization and control problems associated with constrained mechanical systems. A controller which achieves certain performance objectives for an unconstrained mechanical system may be unsuited if external constraints are imposed. The work is strongly motivated by important engineering problems associated with robots and space systems. The constraint arises when contact is made between bodies. In robotics, this occurs when there is contact between end effectors and payload objects. For example, such operations as contour following, deburring, fastening, and pick and place fall within this class. For space systems, constraints arise in satellite docking maneuvers. Constrained robot problems have been the motivation for much recent research in compliance and impedance control, but always without explicit consideration of contact forces required to maintain satisfaction of the constraints. The research makes substantial use of mathematical methods for nonlinear analysis of dynamic systems. Computer simulation experiments will be performed to verify the theory developed and to suggest new theoretical issues for study. The example to be simulated and investigated comprises a particle constrained to move on a smooth elliptic wire. The theory may also be tested experimentally on an instrumented x-y table.