Obstacles constrained Mars powered descent trajectory optimization via navigation function

The scientifically interesting areas on Mars always spread of all kinds of obstacles (e.g., mountains and craters), and landing in scientifically interesting areas have the potential to obtain more scientific data in one Mars mission. In this paper, the issue of landing in the scientifically interesting areas on Mars with safety guaranteed and minimum fuel consumption is studied. Firstly, the elevation data of the target landing terrain are assumed. Then, the threat of the obstacles to the lander is treated as the virtual thrust acting on the lander through navigation function. By introducing the virtual thrust, the total thrust is separated into two parts in this paper. One part is used to avoid the obstacles and the resultant force is optimized. By this means, the obtained optimal trajectory is fuel-saving and has the obstacle avoidance ability. Finally, several sets of simulations are performed in the target landing terrain. The optimal and the obstacles constrained optimal trajectories are obtained at the same conditions. The results show that the obtained obstacles constrained optimal trajectories avoid the obstacles effectively, and take only 2.3kg more fuel consumption than the optimal trajectories for the lander of 1905kg. However, the collision probability of optimal trajectories is generally about 45.5% in the target landing terrain. In addition, the results show that the optimal trajectories with the glide slope constraint have no feasible solution in this situation. This indicates that the glide slope constraint reduces the solution space, especially for the terrain with large obstacles. The comparison of the results indicates that the obstacles constrained trajectory optimization method in this paper is fuel-saving and has the potential to achieve safe landing in the areas with obstacles.