Underactuated attitude reorientation method based on a novel decoupled characteristic of the plane-axis rotation

Abstract

Adequate understanding of rotational properties is significant for the orientation and control of solar energy, robotic, and spacecraft. This paper investigates a rotational decoupled characteristic for a rigid body's plane-axis rotation with an eigenvalue analysis-based approach. In the beginning, we define the quasi-eigenvalue and quasi-eigenvector and analyze their existence. On this basis, we provide two properties for the decoupled characteristic with complete proof when two quasi-eigenvectors exist. One property is that the quasi-eigenvector is unchanged during the rotation of its orthogonal axis. The other property is that the eigenvalue of the other quasi-eigenvector is unchanged during the same rotation. For the application of the decoupled characteristic, we apply it to the attitude reorientation problem using only two-dimensional controls. For validation, we introduce two simulation cases. One is to validate the characteristic, and the other is to check its application in attitude reorientation. Simulation results show that the eigenvalue of one quasi-eigenvector and the other quasi-eigenvector itself is unchanged, which coincides with the theorems, and meanwhile, the decoupled characteristic-based attitude reorientation method is effective.