Quaternion Solution to the Problem of Optimal Control for Spacecraft’S Spatial Reorientation With Use of a Combined Quality Criterion Taking Into Account Energy Costs

Objective: This research focuses on economically controlling spacecraft motion to minimize energy costs during reorientation. It constructs an optimal control method that considers both control forces and rotational kinetic energy, aiming for efficient spatial reorientation. Methods: Utilizing the quaternion method and Pontryagin's maximum principle, the study devises a restricted control for optimal spacecraft turns. Analytical solutions are derived from differential equation relating orientation quaternion and angular velocity, with numerical simulations used for verification. Results: The study presents a solution to the optimal control synthesis problem for spacecraft reorientation, optimizing for minimal energy costs. Key properties of optimal solutions are formulated analytically, aiding in determining optimal control algorithm parameters. Mathematical modeling illustrates the process and practical feasibility of the designed method for attitude control. Conclusion: This research provides a comprehensive solution to spacecraft orientation optimal control, particularly beneficial for spacecraft equipped with electric-jet engines. The explicit control law improves efficiency and economizes spacecraft motion during orbit flight, contributing to smoother, continuous functions of time for both control functions and phase variables. The study's relevance lies in addressing the cost-effectiveness of spacecraft motion control, with potential for further research on optimal control with additional restrictions.