OPTIMAL CONTINUOUS THRUST MANEUVERS FOR SOLVING 3D ORBIT TRANSFER PROBLEMS
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Copyright 2015 California Institute of Technology. We simulate hybrid thrust transfers to rendezvous with space debris in orbit about the Earth. The hybrid thrust transfer consists of a two-impulse maneuver at the terminal boundaries, which is augmented with continuous low-thrust that is sustained for the duration of the flight. This optimal control problem is formulated using the path approximation numerical integration method, Modified Chebyshev Picard Iteration, which converges over a domain of about 1/3 of an orbit. This method differs from traditional two-point boundary value solvers in that it is not a shooting method. We make use of a "warm start" computed by using the two-impulse solution. We find that when continuous thrust is "turned off", the solution to the optimal control formulation reduces to the two-impulse two-point boundary value problem, with zero thrust coast. This study seeks to determine which thrust method is best suited for a specific transfer: Two-impulsive or hybrid? For some transfers we observe a reduced terminal ?V cost for the hybrid thrust relative to the two-impulse, and for others it may be increased. This depends on the relative orbits and the initial phasing of the satellites. Extremal field maps are generated for distinguishing globally optimal from infeasible and sub-optimal orbit maneuver regions. The computations in this paper were done via serial computation, however the structure of the algorithms is ideally suited for parallel algorithms.