Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

The problem under investigation is how to rapidly design a propellant optimal powered descent trajectory to land a spacecraft on an arbitrarily shaped asteroid, subject to realistic constraints on the trajectory and thrust magnitude, and a gravity model applicable to irregularly shaped asteroids. For a given time of flight, the problem is solved by finding the solutions to a sequence of convex optimization problems. A univariate optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the overall lowest propellant usage. This solution methodology is robust and reliable. It does not require a user-supplied initial guess and no trial and error in selecting problem parameters. The strengths of this method are demonstrated by extensive numerical results by designing the propellant optimal trajectories for landing on the elongated binary asteroid Castalia.