Collaborative Research: Dynamics, Stabilization and Control of Nonholonomic Systems

建议：DMS-0306017PI：Dmitry V.Zenkov[dvzenkov@unity.ncsu.edu]机构：北卡罗来纳州立大学标题：合作研究：非完整系统的动力学、稳定和控制摘要研究人员探索非完整系统的动力学，即受速度约束的机械系统。提出的研究内容包括：研究非完整动力学中动量守恒定律的存在性和性质，稳定性分析中的能量-动量方法，具有非自由群作用的系统动力学的定性分析，非线性反馈镇定，以及完整和非完整跟踪问题的基于能量的方法。非完整力学中的动量守恒定律是微妙的，因为经典的Noether定理一般不适用。这导致了研究人员研究的丰富的动力学。还分析了可积性和离散对称性在非完整系统中的作用。研究人员研究了能量动量方法对物理系统的稳定性、镇定和控制的各种扩展。在非完整环境下，利用动量方程的可积性，而一般使用控制拉格朗日方法。具有速度约束(如滚动和滑动约束)的系统的动力学在工业中有许多应用；机器人和轮式车辆的动力学就是例子。在应用中，经常需要稳定的稳态运动(如汽车以恒速直线运动)。研究人员使用动力学和控制的几何理论中的各种工具来研究这种运动，更重要的是，在控制力的存在下对所需的运动进行编程。这项研究的最终目的是根据被调查系统的自然机械特征设计节能控制器。单轮车辆的动力学因其特殊的机动性而引起人们的特别兴趣。对更复杂的系统也进行了研究。

Proposal: DMS-0306017PI: Dmitry V. Zenkov [dvzenkov@unity.ncsu.edu]Institution: North Carolina State UniversityTitle: Collaborative Research: Dynamics, Stabilization and Control of Nonholonomic SystemsABSTRACTThe investigators explore the dynamics of nonholonomic systems, that is, mechanical systems subject to velocity constraints. Proposed research includes studying the existence and properties of momentum conservation laws in nonholonomic dynamics, energy-momentum methods in stability analysis, the qualitative analysis of dynamics of systems with non-free group actions, nonlinear feedback stabilization, and the energy-based approach to tracking problems, both holonomic and nonholonomic. Momentum conservation laws in nonholonomic mechanics are subtle as the classical Noether theorem does not in general apply. This leads to rich dynamics which the investigators study. The role of integrability and discrete symmetries in nonholonomic systems is also analyzed. The investigators study various extensions of the energy-momentum method to both stability, stabilization and control of physical systems. In the nonholonomic setting integrability of the momentum equation is utilized, while in general use is made of the method of controlled Lagrangians.The dynamics of systems with velocity constraints (such as rolling and sliding constraints) has numerous applications in industry; robotics and the dynamics of wheeled vehicles are examples. In applications, stabilization of steady-state motions (such as the straightforward motion of a car at a constant speed) is often desired. The investigators use various tools from the geometric theory of dynamics and control for studying such motions and, more importantly, for programming desired motions in the presence of control forces. The study is ultimately aimed at the design of energy-efficient controllers based on the natural mechanical features of the systems under investigation. The dynamics of single-wheeled vehicles is of special interest because of their exceptional, maneuverability. More complex systems are studied as well.