Geometric Foundations of Motion and Control
Geometric Foundations of Motion and Control
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运动与控制的几何基础
DOI：
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发表时间：
2003
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通讯作者：
J. Marsden
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作者：
J. Marsden
运动和控制的一些有趣方面，例如生物和机器人运动以及航天器姿态控制中发现的那些，涉及几何概念。当动物或机器人以周期性方式移动其关节时，它可以旋转或向前移动。这一观察引出了这样一个普遍观点：当系统中的一个变量以周期性方式移动时，就会导致整个物体的运动。该属性可用于控制目的；例如，卫星的位置和姿态通常由卫星部件（例如旋转转子）的周期性运动控制。用于描述这种现象的几何工具之一是连接，这一概念广泛应用于广义相对论和理论物理学的其他部分。该工具是几何力学一般学科的一部分，有助于研究系统及其分岔的稳定性或不稳定性，即随着某些参数的变化而导致的系统动力学性质的变化。例如，目前正处于快速发展时期的几何力学已被用于设计姿态动力学中的稳定反馈控制系统。该理论还针对具有滚动约束的系统（例如简单滚动轮中的系统）进行了开发。本文解释了如何使用其中一些几何力学工具来研究运动控制和运动生成。
Some interesting aspects of motion and control such as those found in biological and robotic locomotion, and attitude control of spacecraft, involve geometric concepts. When an animal or a robot moves its joints in a periodic fashion, it can rotate or move forward. This observation leads to the general idea that when one variable in a system moves in a periodic fashion, motion of the whole object can result. This property can be used for control purposes; the position and attitude of a satellite, for example, are often controlled by periodic motions of parts of the satellite, such as spinning rotors. One of the geometric tools that has been used to describe this phenomenon is that of connections, a notion that is extensively used in general relativity and other parts of theoretical physics. This tool, part of the general subject of geometric mechanics, has been helpful in the study of the stability or instability of a system and in its bifurcations, that is, changes in the nature of the systems dynamics, as some parameter changes. Geometric mechanics, currently in a period of rapid evolution, has been used, for example, to design stabilizing feedback control systems in attitude dynamics. The theory is also being developed for systems with rolling constraints such as those found in a simple rolling wheel. This article explains how some of these tools of geometric mechanics are used in the study of motion control and locomotion generation.