Modeling, Simulation, and Design of Self-Assembling Space Systems: Accurate Collision Detection, Robust Time Integration, and Optimal Control

Abstract

Motivated by issues inherent in modeling and designing self-assembling systems (e.g. multiple collisions, collisions between non-smooth bodies, clumping and jamming behaviors, etc.), the goal of this thesis is to develop robust numerical tools that enable ecient and accurate direct simulation of self assembling systems and the application of optimal control methods to this type of system. The systems will be alternately modeled using linear nite elements, rigid bodies, or chains of rigid bodies. To this end, this work begins with development of a linear programming based collision detection algorithm for general convex polyhedral bodies. The resulting linear program has several features which render it extremely useful in determining the force system at the time of contact in numerical collision integrators. With robust collision detection in hand, three related numerical integration methods for dynamics with collisions are treated; a direct potential-based approach, and exact collision integrator in a discrete variational setting, and a decomposition-based algorithm, again in the discrete variational setting. Finally, several control problems are treated in the Discrete Mechanics and Optimal Control{Constrained (DMOCC) framework in which collisions between non-smooth bodies either need to be avoided or explicitly included in the optimal control problem. A globally stable feedback controller and a family of trajectories for spacecraft docking are also developed and tested with an accurate representation of an optimized CubeSat docking system.