Homotopic approach applied to skip-entry trajectory optimization

The skip reentry trajectory of Apollo type vehicle for lunar return is optimized under the performance of minimum total heat load with a second-order state constraint on heat flux. The indirect shooting method is based on the multi-points boundary value problem, which may be difficult to initialize because of the small domain of convergence. In addition, the priori knowledge about the structure of constraints is required. To overcome these difficulties, a novel homotopy Approach was presented, which combined homotopic method with the technique that automatically determines the structure of the constraints and initializes the associated shooting parameters. The optimal control problem can be solved by starting the homotopy path from an easier unconstrained problem, and then introducing it into the constraint problem progressively. At last, a numerical example was introduced, and it shows that the state constraints solved with the homotopic approach can be satisfied effectively for optimal reentry of lunar return vehicle.