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.

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