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: 0604307
• 负责人: Anthony Bloch
• 金额: $ 24.75万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 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=0604307&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.

研究人员计划分析受约束机械系统的动力学和控制。拟议的研究包括研究LR系统的动态和稳定性（具有左右的Lagrangian和Right Variant限制的系统），非独立集成剂的特性，用于控制内部自由度的控制系统的系统的导航和稳定问题，在自由程度上应用，多元化型不合格的远不元素的方法，该系统应用于内部的自由度，并应用于内部自由度。系统，以及在力学和控制中使用过度确定的坐标。研究人员还计划使用几何方法来开发一种系统的方法来在相空间中构造坐标，以考虑到正在研究的系统的固有特性，从而使研究人员可以简单而紧凑的方式写下运动方程。这种方法应有助于理解系统的动力学以及进行尊重机械性能的数值模拟。在各种工业和科学应用中，具有约束的系统的动力学都很重要。此类约束的示例包括滚动和滑动，链式刚性链路，刚体上的转子动力学以及弹性杆和刚体之间的耦合。 在行业，工程和科学中有许多实例出现：机器人技术，轮式车辆的动态以及太空中卫星的运动就是例子。在应用中，通常需要稳定稳定运动（例如以恒定速率的直接运动或圆形运动） - 例如，实现所需的机器人或自动驾驶汽车运动。我们的方法应该有助于实现此类动议，并且通常有助于分析和规定动作或机器人和自动驾驶汽车。我们还将提供一个框架，有助于开发此类系统的计算机模拟。