Obstacle avoidance guidance for Mars powered descent using convex optimization and elevation angle

This paper presents a convex optimization framework for obstacle avoidance guidance during the powered descent phase of Mars landing. The proposed approach retains the computational efficiency of convex optimization while enhancing the onboard camera field of view at the terminal phase. First, the relaxed glide-slope constraint and the stepwise constraint are introduced. The trajectory optimization problem is then mathematically formulated, followed by convexification and discretization. Second, a homotopy iteration method is integrated into the sequential convex optimization framework to develop relaxed glide-slope and stepwise obstacle avoidance constraints. Third, leveraging the concept of elevation angle, an axis-weighted position integral is introduced as the objective function, followed by the development of an elevation-angle-based convex optimization algorithm. To assess the algorithm’s effectiveness, three scenarios are evaluated: fixed fuel and terminal time, fixed terminal time, and fixed fuel. Furthermore, an optimal obstacle avoidance framework is formulated based on the maximum elevation angle integral. Simulation results demonstrate that the proposed homotopy iteration-based obstacle avoidance algorithm effectively circumvents obstacles under varying initial conditions while satisfying relaxed glide-slope and stepwise constraints. More importantly, the new convex optimization framework not only enhances obstacle avoidance, but also enables near-vertical landings, thereby improving the terminal camera field of view and reducing the risk of lander tipping upon touchdown. Additionally, simulations confirm that the proposed convex optimization algorithm can achieve effective obstacle avoidance and an enhanced terminal field of view without increasing fuel consumption.