Shape-based approach for solar sail trajectory optimization

The analysis of the optimal control law that steers a solar sail-based spacecraft from a given initial condition toward a final target state is typically carried out using either indirect or direct approaches. Both these methods are usually time-consuming and require good initial guesses of costates or state vector. This paper presents a procedure requiring minimum user-computer interaction to compute an approximate three-dimensional optimal trajectory using a shape-based approach. To that end, novel shaping functions are introduced to describe the time evolution of the spacecraft state vector. The optimization problem is solved using a genetic algorithm, in which a set of shape coefficients and the initial and final spacecraft position are computed while enforcing suitable constraints on the magnitude and direction of the propulsive acceleration vector. Numerical simulations of transfers from Earth to potentially hazardous asteroids show that this method provides good estimates of solar sail trajectories, which can be used as guesses for more refined direct optimization approaches.