Online generation of quasi-optimal spacecraft rendezvous trajectories

A direct method for rapid generation of combined time-propellant near-optimal trajectories of proximity maneuvers of a chaser spacecraft required to dock a target one, with predetermined thrust history along a master direction, is presented. The predetermined thrust history is generated by applying the Pontryagin maximum principle. The new direct method, already implemented and tested on board real aircraft, is based on three concepts: high-order polynomials as reference functions, preset on-off sequence of a master control, and reduction of the optimization problem to the determination of a small set of parameters. Presetting the master control, the remaining controls act as slaves, guarantying the chaser to move along the desired path. Seeking of the optimum strategy is transformed into a nonlinear programming problem, and then numerically solved through an ad hoc algorithm in accelerated time scale. Examples are reported to prove the rapidness of the approach to generate a sub-optimal docking trajectory.