Technology for the Solution of Hybrid Optimal Control Problems in Astronautics

149 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.Many interesting problems in spacecraft mission design are hybrid optimal control problems (HOCP) however there are only a small number of successful solutions of such problems in the literature because the problems are so challenging. The difficulty stems partly from the size of the problems and the fact that every solution method requires the solution of a very large number of individual optimal control problems. Since present technology for solving even one optimal control problem can be problematic and time consuming, improved technologies are needed for the solution of HOCP's. The principal contributions of this work are the development of new methods and the refinement of existing methods for the efficient and robust solution of optimal trajectory problems in astrodynamics. This enables the very large number of solutions required by HOCP solvers to be quickly and reliably obtained and is accomplished in several ways. First, genetic algorithm (GA) based methods are specialized to solve several types of orbit transfer problems. The resulting solutions are less exact than a conventional direct or indirect method would yield but are shown to in fact be quite good. Then a "shape-based" method is developed for rapidly approximating spacecraft trajectories that use low-thrust propulsion. Two new shapes are developed for the solution of time-free and time-fixed rendezvous problems respectively. The shape-based trajectories are compared to "exact" solutions and shown to be effective in determining near-optimal orbit transfers, interception, rendezvous, and escape or capture trajectories. The GA and shape-based methods offer the possibility of finding a large number of (near) optimal trajectories required by HOCP solvers robustly and rapidly. These near-optimal trajectory solvers are then used in the development of efficient strategies for constructing HOCP solvers using a combined outer-loop problem solver and inner-loop problem solver approach. The advantages and disadvantages of various methods available as either outer-loop or inner-loop problem solvers are described and illustrated by example. A capstone problem, a low-thrust multiple asteroid tour problem, is solved with two algorithms, (i) using a B&B outer-loop problem solver with a GA inner-loop problem solver (B&B+GA) and (ii) using a GA outer-loop problem solver with a GA inner-loop problem solver (GA+GA) where both the GA inner-loop problem solvers implement the shape-based method. The solution to the capstone problem shows that the GA+GA solution method is an improvement on current HOCP solution methods and is capable of solving very large hybrid optimal control problems.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD