Homotopic Approach for High-Fidelity Convex Low-Thrust Trajectory Optimization

The low-thrust minimum-fuel trajectory optimization problem is solved in a high-fidelity model using convex optimization. The problem is convexified and discretized with the first-order-hold method. A homotopic approach is developed to improve convergence, accuracy, and computational effort. The homotopy is embedded into the optimization process where the homotopic parameter is dynamically adjusted based on the constraint violation. This method is combined with a high-fidelity model where the complexity of the dynamics and constraints is successively increased. In particular, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-body dynamics, solar radiation pressure, variable specific impulse and maximum thrust are considered. The effectiveness of the proposed method is assessed in several fuel-optimal transfers and compared with related works and a state-of-the-art nonlinear programming solver.