Minimum-Time Continuous Trajectory Optimization For Electric Sails with Sequential Convex Programming

The electric sail is a propellant-less propulsion system that utilizes the force exerted by the solar wind on the high-voltage tethers. This paper introduces a sequential convex programming (SCP) approach to solving the minimum-time continuous trajectory problem for the electric sail. The primary contribution is the transformation of the original non-convex optimal control problem into a convex program. Specifically, change of variables and a path constraint are introduced. Given that the final time is free, the path and terminal state constraints are convexified. The successive linearization technique transforms the nonlinear problem into a sequence of second-order cone programming problems, which are then solved iteratively by a successive solution algorithm. Numerical simulations of interplanetary transfers demonstrate the SCP approach's effectiveness and robustness, outperforming traditional direct methods.