Collaborative Research: Dynamics, Geometry, and Control of Constrained Mechanical Systems

协作研究：约束机械系统的动力学、几何和控制

• 批准号: 0604108
• 负责人: Dmitry Zenkov
• 金额: --
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-15 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604108&HistoricalAwards=false
• 关键词: Collaborative; Research; Dynamics; Geometry; Control

The investigators plan to analyze the dynamics and control of constrained mechanical systems. Proposed research includes the study of the dynamics and stability of LR systems (systems with left-invariant Lagrangian and right-invariant constraints), the properties of nonholonomic integrators, navigation and stabilization problems for systems with controls applied to internal degrees of freedom, applications of variational integrators to the method of controlled Lagrangians, dynamics of infinite-dimensional nonholonomic systems, integrable nonholonomic systems, and the use of overdetermined coordinates in mechanics and control. The investigators also plan to use geometric methods to develop a systematic approach to the construction of coordinates in the phase space that take into account intrinsic properties of a system under investigation and thus allows the researcher to write down equations of motion in a simple and compact way. This approach should be helpful both in understanding the dynamics of a system and in doing numerical simulations which respect mechanical properties.The dynamics of systems with constraints is important in various industrial and scientific applications. Examples of such constraints include rolling and sliding, chained rigid links, rotor dynamics on rigid bodies, and coupling between elastic rods and rigid bodies. There are numerous instances in industry, engineering and science where such constraints arise: robotics, the dynamics of wheeled vehicles, and the motion of satellites in space are examples. In applications, stabilization of steady-state motions (such as the straightforward or circular motion at a constant rate) is often desired -- for example in achieving a desired robotic or autonomous vehicle motion. Our methods should be helpful in achieving such motions and in general in analyzing and prescribing the motions or robotic and autonomous vehicles. We will also provide a framework which will be helpful in developing computer simulations of such systems.

研究人员计划分析约束机械系统的动力学和控制。建议的研究包括LR系统的动力学和稳定性的研究（系统与左不变拉格朗日和右不变约束），非完整积分的性质，导航和稳定问题的系统与控制应用于内部自由度，应用变分积分的方法控制拉格朗日，动力学的无限维非完整系统，可积非完整系统，以及超定坐标在力学和控制中的应用。研究人员还计划使用几何方法来开发一种系统的方法来构建相空间中的坐标，该方法考虑到所研究系统的固有特性，从而允许研究人员以简单紧凑的方式写下运动方程。这种方法应该有助于理解一个系统的动力学，并在做数值模拟尊重力学properties. dynamics系统的约束是重要的，在各种工业和科学应用。这种约束的例子包括滚动和滑动、链式刚性连杆、刚性体上的转子动力学以及弹性杆和刚性体之间的耦合。 在工业、工程和科学中有许多这样的限制出现的例子：机器人、轮式车辆的动力学和卫星在太空中的运动就是例子。在应用中，通常需要稳定稳态运动（例如以恒定速率的直线运动或圆周运动）-例如在实现所需的机器人或自主车辆运动时。我们的方法应该有助于实现这样的运动，并在一般情况下，在分析和规定的运动或机器人和自动驾驶车辆。我们还将提供一个框架，这将有助于开发计算机模拟这样的系统。