Low-Thrust Trajectory Optimization via Covector Mapping Principle: Bridging Direct and Indirect Methods for Spacecraft Autonomous Guidance

Low-thrust spacecraft trajectory optimization is an established problem in applied mathematics and space mission design. The current state-of-the-art methods for solving it primarily fall into two categories: indirect and direct methods. This work investigates the Covector Mapping Principle in order to bridge these two approaches, allowing the transformation of NLP Lagrange multipliers into costates. Pseudospectral direct collocation and indirect shooting methods are implemented, and costate mapping is verified with excellent accuracy for different problem formulations. By combining these two methodologies, we mitigate their respective limitations and pave the way for a robust, flexible, and computationally efficient hybrid guidance algorithm for onboard spacecraft applications. Benchmarks against traditional indirect methods are performed to demonstrate that the proposed hybrid approach improves convergence and robustness. The algorithm is tested and simulated in different deep-space mission scenarios, highlighting its potential for onboard implementation in autonomous spacecraft. The hybrid algorithm is deployed on relevant hardware for processor-in-the-loop experiments to evaluate its performance under realistic constraints and limitations imposed by the onboard computational resources.