Highlights • Multi-stage launch vehicle with nonlinear aerodynamics and phase-linkage event is considered. • A mass-projection technique is proposed to eliminate all discontinuous nature. • A sequential penalized convex relaxation method is introduced for convexification. • The robustness, the efficiency, and the capability of onboard replanning are verified numerically.

Abstract Autonomous trajectory planning for multi-stage launch vehicles poses great technical challenges, mainly because of the highly nonlinear flight dynamics and complex multi-phase structure. Here, this problem is solved by a novel, robust, and efficient approach within the framework of convex optimization. Focusing on the multi-phase difficulty, a mass-projection technique that substitutes the original time independent variable with the mass history is introduced to eliminate the problem’s discontinuous nature and phase-linkage event constraints, then a new sequential relaxation-and-penalization method is proposed to address the resulting problem. All non-convex terms involved in the problem are relaxed to formulate a certainly feasible semi-definite problem, the deviation between which and the true problem is penalized by blending the information from the trust region and semi-definite constraint. The combination of the mass-projection technique and the sequential relaxation-and-penalization method is found to be capable of recovering the original problem and providing the optimal solution rapidly and reliably. Three representative simulations are performed to verify the robustness and computational efficiency of the proposed approach, and comparative results show that it achieves a 100$\%$ success rate for all cases, while enabling a 69$\%$ to 98$\%$ saving of computational time compared to typical methods.