A Homotopic Approach for Robust Low-Thrust Trajectory Design Through Convex Optimization

The space industry has recently witnessed a significant decrease of the overall costs of space missions, thanks to the miniaturization of satellites and their components. CubeSats have granted institutions and small companies access to space. However, space operations are still entirely performed from ground, limiting the potentiality of such spacecraft. Enhancing the autonomy of satellites, for example enabling on-board guidance, represents thus an interesting research challenge. The low control authority and little on-board resources of CubeSats require a new trajectory design paradigm. Optimization methods can be compared in terms of computational effort, optimality (the quality of the solution found), and feasibility (the capability of converging to a feasible solution). State-of-the-art approaches lack of computational efficiency, as powerful computers can be used to design the fuel-optimal trajectory of a spacecraft offline. Convex optimization represents instead a sustainable approach when real-time applications are considered due to the limited resources required to solve convex programs. This technique has been recently applied to different space-related problems, including powered descent and landing, entry and low-thrust trajectory optimization. This paper presents a sequential convex programming algorithm based on a Legendre-Gauss-Lobatto discretization scheme with nonlinear control interpolation to solve the minimum-fuel space trajectory optimization problem. Moreover, an adaptive second-order trust region radius change mechanism is developed to reduce the overall computational time. Finally, the sequential convex programming is combined with the homotopic approach to increase robustness of the method. The effectiveness of the approach is shown by means of numerical simulations with poor initial guesses.