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. .
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
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
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.
G-OPT: Ground software implementing a primal-dual IPM to solve SOCPs.