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 in which 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 Pontryagin's principle. For the case in which the three components of the control are independently constrained, we discover six- and seven-switch solutions for reorientation angles of less than 72 deg 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. Wefind 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 that illustrate and validate the new findings are summarized. Although no conclusive proof is available to date, we believe the six-switch maneuvers to be global extrema.
ASJC Scopus subject areas
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics