Vector Trajectory Method for Obstacle Avoidance Constrained Planetary Landing Trajectory Optimization

Considering the requirement of avoiding obstacles in different planetary landing missions, this article presents a generalized method dealing with the obstacle avoidance constrained landing trajectory optimization problem with vectorized strategy, i.e., vector trajectory method (VTM). By introducing a trajectory direction constraint with vectorized description, the character of the obstacle avoidance trajectory can be more specifically depicted. Moreover, by satisfying proper trajectory direction constraint, the landera s particular performances, such as the observation to the target or probability of a safe flight, can be improved. To this end, the VTM and relevant theorem are first developed, revealing the relationship between the two aspects of obstacle avoidance constraint (i.e., distance constraint and trajectory direction constraint). Then, both aspects of constraints are uniformly transformed as the auxiliary angle magnitude constraint with the vectorized strategy, which significantly simplifies the solving procedure of obstacle avoidance constrained trajectory optimization problem. Finally, the proposed VTM is illustrated in detail through the examples with the planetary landing background of atmospheric entry and powered descent landing.