Ascent Trajectory Optimization Using Second-Order Birkhoff Pseudospectral Methods

This paper proposes a novel convex optimization framework for two-stage launch vehicle (TSLV) ascent trajectory planning from liftoff to orbit insertion, featuring two groundbreaking advancements over existing convex optimization methodologies: (1) an innovative second-order Birkhoff pseudospectral (BPS) method is developed that reduces the number of dynamic equality constraints by 50% compared to traditional PS methods, meanwhile, an augmented variable transcription technique is used to formulate inequality constraints; therefore, the sparsity ratio of the inequality matrix is reduced to less than 1%; (2) a new iterative solution strategy initialized by a few guesses is proposed to efficiently obtain the optimal solution. The framework is rigorously supported by theoretical convergence guarantees and validated through comprehensive numerical experiments. The numerical results demonstrate around a 50% reduction in computational time compared to the differential PS baseline method. With the significantly reduced computational cost, the proposed method exhibits strong potential for real-time onboard implementation in the future.