Convergent EKF-based control allocation: general formulation and application to a Control Moment Gyro cluster

This paper addresses control allocation for redundant systems with the Extended Kalman Filter formalism. This method is compatible with the low computational power available in space environment, and presents a flexible framework to include constraints such as singularity avoidance. The convergence domain of the allocator is derived from the contraction theory framework, depending on specific parameters of the system. A general formulation is proposed to maximize the convergence domain with regard to these parameters. The method is applied to design a steering law of Control Moment Gyroscopes. Experimental tests show that the control allocation allows the actuators to work efficiently along nominal trajectories while avoiding singularities when necessary