Optimal Rotation Sequences in Presence of Constraints on Admissible Rotation Axes

In underactuated conditions, satellite attitude actuators can deliver a control torque with two components only. The paper develops a general solution for the problem of attitude maneuver planning for underactuated spacecraft by means of a sequence of N admissible rotations, where a rotation is considered to be admissible if it takes place around an axis which lies on the plane where the actuator system can deliver a control torque. An exact solution for the sequence of two feasible rotations that provides a desired reorientation is derived, where the minimum angular- path sequence can also be identified analytically. The optimal sequence for a higher number of steps is obtained by means of a numerical optimization procedure. The features of the optimal sequences for increasing values of N are investigated in order to obtain a better understanding of their characteristics.