Singularity Analysis of Variable Speed Control Moment Gyros

Single-gimbal control moment gyros (CMGs) have many advantages over other actuators for attitude control of spacecraft. For instance, they act as torque amplifiers and, thus, are suitable for slew maneuvers. However, their use as torque actuators is hindered by the presence of singularities, that, when encountered, do not allow a CMG cluster to generate torques about arbitrary directions. One method to overcome this drawback is to use variable-speed single-gimbal control moment gyros (VSCMGs). Whereas the wheel speed of a conventional CMG is constant, VSCMGs are allowed to have variable wheel speed. Therefore, VSCMGs have extra degrees of freedom that can be used to achieve additional objectives, such as singularity avoidance and/or power tracking, as well as attitude control. The singularity problem of a VSCMGs cluster is studied in detail for the cases of attitude tracking, with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. This criterion can be used to size the wheels and develop appropriate momentum damping strategies tailored to the specific mission requirements. I. Introduction A CONTROL moment gyro (CMG) is a device used as an actuator for attitude control of spacecraft. It generates torques through angular momentum transfer to and from the main spacecraft body. This is achieved by changing the direction of the angular momentum vector of a gimballed flywheel. Because a CMG operates in a continuous manner, contrary to the gas jet’s on/off operation, it can achieve precise attitude control. Moreover, as with other momentum exchange devices, for example, reaction wheels, it does not consume any propellant, thus prolonging the operational life of the spacecraft. Single-gimbal CMGs essentially act as torque amplifiers. 1 This torque amplification property makes them especially advantageous as attitude control actuators for large space spacecraft and space structures, for example, a space station. In fact, single-gimbal and double-gimbal CMGs have been used for attitude control of the Skylab, the MIR and the International Space Station (ISS). An obstacle when using a CMG system in practice is the existence of singular gimbal angle states for which the CMGs cannot generate a torque along arbitrary directions. At each singular state, all admissible torque directions lie on a two-dimensional surface in the three-dimensional angular momentum space; therefore, the CMG system cannot generate a torque normal to this surface. The CMG singularities can be classified into two categories: 1) external or saturated singularities in which the total angular momentum sum of the CMGs lies on the maximum momentum envelope and 2) internal singularities in which the total momentum lies inside this envelope. The external singularities can be easily anticipated from the given CMG configuration and mission profile; therefore, they can be taken into account at the design step. A properly designed momentum management scheme can also relieve the external singularity problem. The internal CMG singularities, on the other hand, are in general difficult to anticipate. Avoiding such internal singularities has, thus, been a long-standing problem in the CMG