Efficient Computation of Reachable Sets for Critical Space Mission Phases

Abstract

Abstract To achieve true autonomy during critical mission phases in deep space, it is imperative to know which states are attainable from a given starting point using only admissible control inputs. These attainable states form the reachable set. If the latter is computed in real time, this can provide a system for Guidance, Navigation and Control on-board of an autonomous spacecraft with knowledge of all the feasible and infeasible options in order to choose the correct course of action. Though several means exist to compute reachable sets, the most promising ones are based on optimization techniques. We currently explore an approach, in which we approximate a reachable set with an altering polytope. The center of a selected facet of the polytope is the starting point from which a new feasible vertex is placed in normal direction with the largest possible step size. This approximates the set boundary successively. Simultaneously, the underlying equations of motion must be satisfied. We formulate these tasks as an optimal control problem.