Lossless Control-Convex Formulation for Solar-Sail Trajectory Optimization via Sequential Convex Programming

Sequential convex programming (SCP) has been gaining popularity for space trajectory optimization. However, application of SCP for solar-sail trajectory optimization has suffered from the nonlinear coupling between the magnitude and direction of solar radiation pressure acceleration, which renders the optimal control problem highly nonconvex in the control variables. To address this issue, this paper proposes a formulation that transforms the solar-sail optimal control problem into a problem that is convex with respect to control (called control-convex). This convexification is achieved by introducing a slack variable and applying a change of variable. This paper mathematically shows the lossless property of the proposed control-convex formulation by using Pontryagin’s minimum principle, and develops an SCP-based trajectory optimization algorithm for solar sails. We then apply the developed trajectory optimization algorithm to two interplanetary-transfer scenarios, demonstrating its effectiveness in solving complex sail optimal control problems efficiently and robustly, with better optimality compared to a conventional formulation.