Homotopy Method for Fuel-Optimal Trajectory Design in Flyby Mission

A new homotopy method is proposed to solve the fuel-optimal transfer trajectory with flyby of other celestial bodies in the deep space exploration, overcoming the difficulty due to the interior point constraints and discontinuous structure of the Bang-Bang control. The homotopic parameter is embedded in both the performance index and interior point constraint equations. By starting from a related and easier energy-optimal problem without inner constraints, and solving a series of iterative subproblems with homotopic parameter increased, the solution of the original problem is obtained when the parameter reaches one. With the approach, the difficulty of the optimization variables increased caused by the flyby inner constraints can be resolved, and the low-thrust fuel-optimal transfers can be completed effectively. At last, two examples about the Jupiter rendezvous with the Mars flyby and the Mars rendezvous with an asteroid flyby are given to substantiate the effectiveness and optimality of the homotopy method.