Optimal Design of Constrained Multibody Dynamical Systems

该提案的总体目标是开发一个严格的框架，用于优化具有关节约束、接触和摩擦的多体动力学系统。这将通过开发新的工具来实现，用于优化微分代数方程或具有不等式约束的微分方程所描述的动力系统。这将通过以下方式实现：（a）在容许参数集上的约束下优化具有关节的多体系统;（B）在容许轨迹上的约束下优化具有关节的多体系统。这种约束发生在轨迹规划中，避免静态障碍物，当物理考虑限制运动;（c）优化多体系统的关节，接触和摩擦。 这是最具挑战性的情况，因为接触力是不连续的。(d)识别和开发新算法的有效数值解技术。2本项目的结果将为优化一大类动力系统提供工具，否则这些系统不可能实现。受益于该项目成果的领域包括机器人技术、车辆动力学、航空航天工程、生物医学设备工程和军事应用。拟议的工作将在博士后，研究生，本科生和K-12水平的重要教育组成部分。该项目的成果将纳入研究生课程。将在妇女参与计算机日活动中举行讲座。该项目将支持组织一年一度的优异徽章学院研讨会，以促进K-12学生对科学和工程的兴趣。研究结果将通过期刊论文和会议记录传播。

The overarching goal of this proposal is to develop a rigorous framework for the optimization of multibody dynamical systems with joint constraints, contact, and friction. This will be accomplished by developing new tools for the optimization of dynamical systems described by differential algebraic equations or by differential equations with inequality constraints. This will be accomplished by: (a) optimizing multibody systems with joints under constraints on the admissible parameter set; (b) optimizing multibody systems with joints under constraints on the admissible trajectory. Such constraints occur in trajectory planning where static obstacles are avoided, and when physical considerations limit the motion; (c) optimizing multibody systems with joints, contacts, and friction. This is the most challenging scenario since the contact forces are discontinuous. (d) identifying and developing efficient numerical solution techniques for the new algorithms developed.The results of this project will provide tools for optimizing a large class of dynamical systems which were not otherwise possible to implement. Areas that will benefit from the results of this project include robotics, vehicle dynamics, aerospace engineering, biomedical device engineering, and military applications. The proposed work will have a significant educational component at post-doctoral, graduate, undergraduate, and K-12 levels. The results of the project will be incorporated in a graduate level course. Lectures will be given at the Women in Computer Day events. The project will support the organization of an annual Merit Badge College Workshop to promote interest in science and engineering among K-12 students. The research findings will be disseminated through journal papers and conference proceedings.