Computational Geometric Mechanics and its Applications to Geometric Control Theory

计算几何力学及其在几何控制理论中的应用

基本信息

批准号：
0726263
负责人：
Melvin Leok
金额：
$ 7.27万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2007
资助国家：
美国
起止时间：
2007-02-15 至 2009-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0726263&HistoricalAwards=false
关键词：
Computational Geometric Mechanics its Applications

项目摘要

The geometric approach to mechanics serves as the theoretical underpinning of innovative control methodologies in geometric control theory. These techniques allow the attitude of satellites to be controlled using changes in shape, as opposed to chemical propulsion, and are the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation. Computational geometric mechanics aims to leverage novel discrete differential geometric tools and discrete analogues of Lagrangian and Hamiltonian mechanics to systematically discretize the geometric approach to mechanics, while preserving geometric structure at a discrete level, thereby providing an efficient method of obtaining qualitatively accurate simulations over long times. The goal of this project is to continue the development of computational geometric mechanics and to apply it to geometric control theory, which will yield numerical implementations of control algorithms that exhibit good long-time behavior.This research will provide rational design principles for the construction of accurate and efficient real-time automatic control of modern engineering systems, such as robotic arms, spacecraft, and underwater vehicles. This is particularly important, due to the trend towards autonomous space and underwater vehicle missions with long deployment times and low energy propulsion systems, wherein accurate control algorithms are necessary to maximize the operational lifespan and range of these missions. Such missions will serve as the backbone of distributed space and underwater sensor networks that will enable us to continually monitor our oceans, environment, and climate.

力学的几何方法是几何控制理论中创新控制方法的理论基础。这些技术允许通过形状的变化来控制卫星的姿态，而不是化学推进，并且是理解坠落的猫始终用脚着地的能力的基础，即使是以倒置方向释放时也是如此。计算几何力学旨在利用新颖的离散微分几何工具以及拉格朗日和哈密顿力学的离散类似物来系统地离散力学的几何方法，同时在离散水平上保留几何结构，从而提供一种长期获得定性精确模拟的有效方法。该项目的目标是继续发展计算几何力学并将其应用于几何控制理论，这将产生具有良好长期行为的控制算法的数值实现。这项研究将为构建对机械臂、航天器、水下航行器等现代工程系统进行准确、高效的实时自动控制。这一点尤其重要，因为自主空间和水下航行器任务的趋势是部署时间长和低能量推进系统，其中需要精确的控制算法来最大限度地延长这些任务的使用寿命和范围。此类任务将成为分布式空间和水下传感器网络的支柱，使我们能够持续监测我们的海洋、环境和气候。