Initial Three-Dimensional Trajectory Design for Solar Sails Using Bezier Shaping Approach

An approach for the fast generation of a minimum-time, three-dimensional trajectory for a spacecraft propelled by a solar sail with reflection control devices (RCDs) is presented using the authors' previously proposed Bezier curve-based shaping approach. In this approach, the time variation of the position components of the spacecraft are assumed in advance to follow Bezier curve functions. By optimizing a finite set of unknown coefficients defining the shape of the Bezier curves used to approximate the generic state variables, the boundary constraints and equations of motion are satisfied simultaneously under a time-optimized performance index. Unlike the thrust vector of a conventional electric thruster, that of an RCD-equipped solar sail is constrained. To consider the thrust characteristics of such solar sails, the propulsive acceleration inequality constraints were numerically investigated for an asteroid rendezvous. The simulation results demonstrate that the presented approach is able to design the transfer trajectory of a spacecraft propelled by an RCD-equipped solar sail in about 1% of the time required by the conventional Gauss pseudospectral method with comparable accuracy by considering the actual characteristics of the thrust vector. This allows for quick feasibility assessments of different solar sail spacecraft mission profiles during the preliminary mission design stage.