Quasi-closed-form solution to the time-optimal rigid spacecraft reorientation problem

The problem of slewing a rigid body from an arbitrary initial orientation to a desired target orientation in minimum time is addressed. The nature of the time-optimal solution is observed via an open-loop solution using the switch time-optimization algorithm developed by Meier and Bryson. Conclusions as to the number and timing of control switches are drawn and substantiated analytically. The solution of the kinematic differential equations for Euler parameters is examined for systems in which the applied torque is much greater than the nonlinear terms in Euler’s equations. An approximate solution to these equations is used to construct the state transition matrix as a function of a given control sequence and control intervals. This allows a rapid solution for the required switch times for all admissible control sequences. Uncoupled switching functions can be generated given the approximate switch times for the optimal sequence. The resulting feedforward/feedback control is suitable for online computation.