Time-optimal spacecraft reorientation: A quasi closed-form control law

The problem of slewing a spacecraft from an arbitrary initial orientation to a desired target state in minimum time is addressed. The nature of the time optimal trajectories 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 (Quaternion) Parameters is examined for systems in which the applied torque is much greater than the nonlinear gyroscopic terms in Euler's equations. An approximate solution to these equations is used to construct the state transition matrix for a desired maneuver. This allows the solution of the required switch times for an assumed control sequence. The rapid solution of all admissible sequences permits the selection of the minimum time solution in near-real-time. Given the approximate switch times, uncoupled switching functions are generated for feedback control. The resulting feedforward/feedback control law is simulated using a model of the Advanced Structure Technology Research Experiment (ASTREX) test article at the USAF Astronautics Laboratory. Finally, the robustness of the feedback control in the presence inertia matrix uncertainty is considered.