Fuel optimal low thrust rendezvous with outer planets via gravity assist

Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations. In this paper the two techniques are combined and treated comprehensively, both on modeling and numerical techniques. Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions, various transversality conditions and stationary conditions are derived by Pontryagin’s Maximum Principle (PMP). Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP). Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO), is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method. Two scenarios in the end show the merits of the present approach.