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Real-Time Optimization

Task Objective

Our objective is to develop fast and robust global optimization algorithms that solve formation flying guidance, control, estimation, and decision making problems, which include formation flying fuel optimal reconfiguration path planning, fast distributed estimators for formation flying, robust formation keeping control, distributed resource allocation among spacecraft, and mode commanding. .

Task Description

We adapt global optimization methods based on convex optimization. There are polynomial time methods, such as interior point methods (IPMs), that are guaranteed to compute the global optimal solutions of COPs without an expert in the loop tweaking. Therefore we formulate many formation flying guidance, control, estimation, and decision-making problems as convex optimization problems, particularly as semi-definite programming (SDP) or second-order-cone-programming (SOCP) problems. This approach enables us to find the globally optimal, the "best", solutions for these formation flying problems. Furthermore, the deterministic convergence properties of the IPMs make them suitable for onboard autonomous use, which lead to formulation of many onboard guidance and control problems as COPs, particularly as SOCPs. Once this formulation is done, we can solve them quickly and reliably. Unfortunately not all formation flying problems can be cast as COP. Indeed some of the interesting guidance problems in formation flying are inherently non-convex, such as formation reconfiguration guidance problem. For those problems, we are developing successive convexification methods. Our current focus areas: 1. Formulation of formation flying guidance, control, estimation, and decision making problems as optimization problems, preferably as COPs whenever possible. 2. Developing fast and reliable IPMs for design and ground operations. 3. Developing customized IPMs for onboard real-time operations. 4. Developing a successive convexification for global optimization of nonconvex problems. 5. Developing multiparametric programming, table lookup, methods for real-time onboard solution of SOCPs. 6. Developing distributed IPMs for sparse formations, where centralized processing is not an option or is prohibitive. Task Products: G-OPT: Ground software implementing a primal-dual IPM to solve SOCPs.

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