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

• 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

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.

几何方法是几何控制理论中创新控制方法的理论基础。 这些技术允许使用形状变化（而不是化学推进）控制卫星的态度，并且是理解掉落猫总是落在其脚上的能力的基础，即使在倒置方向上也是如此。 计算几何力学旨在利用新型离散的差异几何工具以及拉格朗日式和汉密尔顿力学的离散类似物，以系统地离散机械师的几何方法，同时在离散水平上保留几何结构，从而提供有效的准确准确的方法，可以在很长的时间内获得有效的准确模拟。 该项目的目的是继续开发计算几何力学，并将其应用于几何控制理论，该理论将产生表现出良好长期行为的控制算法的数值实现。这项研究将为准确有效的现代工程系统的实时自动控制系统提供合理的设计原理，例如机器人Arms，SpaceCecraft和Underswater and-nounderwerterwerty和诸如现代工程系统。 这尤其重要，因为具有较长部署时间和低能推进系统的自主空间和水下车辆任务的趋势，因此，必须进行精确的控制算法以最大程度地提高操作寿命和这些任务的范围。 这样的任务将成为分布式空间和水下传感器网络的骨干，这将使我们能够不断监视我们的海洋，环境和气候。