Optimization of Collision-free Transfer Trajectories for a Lander in a Binary Asteroid System

Aiming at the trajectory optimization problem for the safe surface transfer of a detector in a binary asteroid system, this paper proposes a convex optimization-based method for optimizing low-thrust transfer trajectories with collision avoidance on the surface of binary asteroids. This method avoids collisions between the detector and the surface of the binary asteroid by designing a composite forbidden region constraint in the form of an “ellipsoid + double cone” suitable for surface transfer scenarios. The problem was transformed into a convex problem using convexification techniques. First, the non-convex forbidden region constraints were relaxed into convex constraints using a first-order Taylor expansion. Then, by introducing relaxation variables, the thrust constraints were convexified into second-order cone constraints. Subsequently, the nonlinear dynamics and gravitational acceleration were approximated through sequential solving. Finally, a convex optimization algorithm was employed to obtain a numerical optimal solution, resulting in a fuel-optimal solution for the collision-avoidance surface transfer trajectory of the binary asteroid detector. Numerical simulations for Dimorphos demonstrated that the proposed method can reliably generate safe and fuel-efficient surface transfer trajectories.