New Results for Time-Optimal Three-Axis Reorientation of a Rigid Spacecraft

Some new results for a classical minimum time, rest-to-rest maneuver problem are presented. An inertially symmetric rigid body is considered. For the case that the magnitude of the control is constrained while the control direction is left free, we analytically prove that the eigenaxis maneuver is the time minimum solution by using the Pontryagin’s principle. For the case that the three components of the control are independently constrained, we discover six switch and seven switch solutions for reorientation angles less than 72 degrees by using a hybrid numerical approach. The seven switch solutions are consistent with the classical results and the six switch solutions are reported here for the first time. We find that the two sets of solutions are widely separated in state and control spaces. However, the two locally optimum maneuver times are very close to each other although the six switch control always has a slightly shorter time. Simulation results are summarized that illustrate and validate the new ∗Current Affiliation:Graduate Research Assistant, Department of Aerospace Engineering, TAMU-3141; [email protected]; phone: 979-862-3394; fax: 979-845-6051. Student Member AIAA. †Regents Professor, Distinguished Professor of Aerospace Engineering, Holder of the Royce E. Wisenbaker ’39 Chair in Engineering, Department of Aerospace Engineering, TAMU-3141. Fellow AIAA. 1 findings. While no conclusive proof is available to date, we believe the six switch maneuvers to be global extrema.