Analysis of the inertially symmetric rigid spacecraft time-optimal three-axis reorientation

This paper investigates the classical time‐optimal rest‐to‐rest three‐axis reorientation of the inertially symmetric rigid spacecraft. First‐order necessary optimality conditions are derived from the Pontryagin's maximum principle. Then, control structures (i.e., switching times and control torques) for the time‐optimal solution with five, six, and seven switches are given. For any five‐switch, six‐switch, or seven‐switch time‐optimal solution, a finite number of control structures exist, and relations among the control structures and their associated time‐optimal solutions are analytically derived. By utilizing the control structure, efficient numerical optimization algorithm based on multiple‐interval Radau pseudospectral method is proposed. Numerical results show that, after rounding to integer, five‐switch and six‐switch time‐optimal solutions exist for rotation angles on the interval [1,180] deg, and s es on the interval [1,72] deg. Finally, time‐optimal solutions for typical rotation angles are given to illustrate and validate the new findings.