This paper discusses an optimal controller for small satellites that are required to perform large-angle maneuvers with two reaction wheels. If a reaction wheel malfunctions, a satellite control system satellite with no redundancy must control the attitude on three axes with only two reaction wheels. The most difficult problem is control around the axis that has no available reaction wheel. The maneuver should be performed with as little energy as possible. It is, however, impossible for small satellites to calculate the minimum energy trajectory with the onboard computer. Proposed is a simple optimal algorithm that performs the reorientation on the no-wheel axis with the two wheels on the other axes. The controller is applied to the Rest-to-Rest reorientation around the no-wheel axis. Under such conditions, the optimal solution has symmetry characteristics according to its orbit and time. Thus, the proposed algorithm is designed by using the symmetric characteristics. This paper first presents the optimal numerical solution for asymmetrical terminal conditions and then discusses the symmetry of the solution and the capability of the proposed algorithm for asymmetrical conditions.
A case study of optimal reorientation for large attitude maneuvers on two wheels under asymmetrical terminal conditions
