## 1 Introduction  
In recent years, there has been a growing demand for earth observation satellites equipped with highly accurate observation sensors to capture high-resolution images of certain points on the ground. For example, earth observation satellites including IKONOS which is launched in 1999, have made emergency observations to determine the detailed situation of disaster areas, and made efforts to utilize this information to prevent secondary disasters and aid in prompt reconstruction. In order to direct the sensors to the ground in comparison with sweeping the earth's surface, such earth observation satellites need to improve their agility in large-angle attitude maneuvers. Moreover, methods that enable highly accurate attitude determination by online sensors such as the star tracker (ST) and inertial measurement unit (IMU), as well as global positioning system (GPS) based methods [1; 2] have been proposed. Thus, high accuracy of attitude control is also needed using this information. To achieve the above-described agile large-angle attitude maneuver, a single-gimbal control moment gyro (SGCMG) should be mounted as a modern-type actuator. The SGCMG (as shown in Figure 1a) is an internal force actuator that outputs a large torque owing to the gyro effect generatedby rotating a gimbal. Normally, from the viewpoint of the redundancy and symmetry of angular momentum, the SGCMG should be equipped on a four-skew array like a pyramid, as shown in Figure 1b. In the conventional works on agile attitude maneuvers of a satellite using SGCMGs as actuators, the gimbal angular velocity is calculated by solving the pseudo inverse matrix of the SGCMGs Jacobian matrix from the torque command value calculated by the satellite attitude control system and input to the SGCMGs system (upper part of Figure 2). This control system structure has been extensively studied because of the shape of the Jacobian matrix with respect to the SGCMGs and the strong nonlinearity depending on its time variation. As usual, the singularity problem always exists for SGCMGs during the large-angle maneuvering of satellites. In the singularity, input may not be sometimes required, in which the possible output direction is degenerated owing to the combination of the gimbal angle, as shown in Figure 3. Therefore, it was necessary to design the attitude control system and the SGCMG control system separately. Figure 1: The scheme of a single-gimbal control moment gyro (SGCMG) (**a**) and four-skew array single-gimbal control moment gyros (SGCMGs) (**b**). Figure 3: Relationship between the output torque and singularity of SGCMGs. Figure 2: Block diagram of conventional method and proposed method. As a countermeasure to the singularity problem, a number of avoidance/escape steering laws have been proposed. The singularity avoidance law of null motion by the projection matrix [3] and Jacobian cofactor [4] were firstly proposed, followed by a steering law for avoiding singularity to reduce the error of the output torque [5]. After that, a nondiagonal singularity robust steering law to escape the singular surface with torque error [6] and a generalized singularity robust (GSR) steering law [7], as well a method to make it possible to adjust the design parameters of the GSR steering law [8] were put forward. Furthermore, methods combining multiple singularity avoidance/escaping steering laws [9; 10] were proposed. Subsequently, methods to avoid singularity by feed-forward inputs using a Fourier basis algorithm [11], path planning of angular momentum [12] or gimbal angle [13] appeared. In such conventional methods, it is possible that the desired control torque cannot provide output to the satellite determined by the attitude control system, and it cannot guarantee the attitude stability of the satellite under the singularity of SGCMGs. These issues caused by the singularity avoidance/escape cannot be taken into account in the attitude control system.