Weight-adaptive augmented Lagrange multiplier sequential convex programming for nonlinear trajectory optimization - Dong, Cheng-Long; Xie, Lei; He, Rui-Zhi; Zhou, Xiang; Zhang, Hong-Bo (Aerospace science and technology, 2024)
•An improved sequential convex programming method is proposed with the idea of Augmented Lagrange multiplier method.•Analyze the reason why it is difficult to determine the weight in general sequential convex programming method.•The iteration formulation of the Lagrange multiplier is designed using theoretical analysis.•Two simulation scenarios are tested and compared with general sequence convex programming, highlighting the advantages of the proposed method. Sequential convex programming has become a prominent research focus in aerospace trajectory optimization due to its high computational efficiency. One critical challenge in sequential convex programming is the infeasibility of subproblems, which significantly impacts its stability. To address this issue, certain constraints must be relaxed using relaxation variables, which are then incorporated into the objective function as a penalty term. However, the choice of penalty weight greatly influences the optimality and convergence of sequential convex programming. Therefore, this paper proposes a weight-adaptive augmented Lagrange multiplier sequential convex programming algorithm to tackle the challenge. First, this paper analyzes the difficulty of determining an appropriate penalty weight from the perspective of its penalty effect. Based on this analysis, an augmented penalty term is introduced, and the update rule for the augmented Lagrange multiplier is formulated using the Karush-Kuhn-Tucker conditions. Subsequently, a method with adaptive weight adjustment is designed based on the change in the penalty term to further improve the algorithm's solving speed. Finally, the proposed method is validated through numerical simulations in a Mars-powered landing problem and a small glide vehicle reentry problem. The results show that the proposed method is 20.59 % and 25.16 % faster compared to the general sequential convex programming algorithm, respectively. Furthermore, the proposed method is demonstrated to be robust to the initial choice of penalty weight.