Dynamics, Geometry, and Control of Discrete Mechanical Systems

离散机械系统的动力学、几何和控制

• 批准号: 0908995
• 负责人: Dmitry Zenkov
• 金额: $ 23万
• 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: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908995&HistoricalAwards=false
• 关键词: Dynamics; Geometry; Control; Discrete; Mechanical

The objective of this project is to study discretizations of mechanical systems with constraints. This study is motivated by the facts that such discretizations may be used for numerical simulations of mechanical systems and that problems of studying periodic motions in mechanics and control are intrinsically discrete. The proposed research is aimed at two areas:(i) Structurally-stable and structure-preserving discretizations of systems with velocity constraints. The dynamics of systems with velocity constraints is remarkably diverse. The goal is the development of discrete dynamical systems that adequately represent the continuous-time constrained dynamics.(ii) The use of such discretizations in stabilization of periodic orbits of mechanical systems. It is anticipated that such control techniques will be especially useful in cases when the period is long and/or intrinsic structure of controlled systems should be preserved during numerical simulations.The dynamics of systems with constraints is important in various industrial and scientific applications. Such constraints include rolling and sliding constraints, chained rigid links, and various constraints found in thermodynamics and electromechanical systems. 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 periodic motions may be desirable--for example in achieving a desired robotic or autonomous vehicle motion. Our methods should be helpful in analyzing and prescribing motions of constrained systems, such as robotic and autonomous vehicles.

本计画的目标是研究具限制条件的机械系统之离散化。这项研究的动机是这样的事实，这种离散化可用于机械系统的数值模拟，并在力学和控制研究周期性运动的问题本质上是离散的。所提出的研究是针对两个领域：（i）结构稳定和结构保持离散化系统的速度约束。具有速度约束的系统的动力学是非常多样的。我们的目标是离散动力系统的发展，充分代表连续时间约束动力学。(ii)这种离散化在机械系统周期轨道稳定中的应用。可以预见，这种控制技术将是特别有用的情况下，当周期长和/或内在结构的控制系统应保持在数值simulation.The动态系统的约束是重要的，在各种工业和科学应用。这些约束包括滚动和滑动约束、链式刚性链接以及热力学和机电系统中的各种约束。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，周期性运动的稳定性可能是期望的-例如在实现期望的机器人或自主车辆运动时。我们的方法应该有助于分析和规定运动的约束系统，如机器人和自动驾驶汽车。