Control allocation for gimballed/fixed thrusters

Some overactuated control systems use a control distribution law between the controller and the set of actuators, usually called control allocator. Beyond the control allocator, the configuration of actuators may be designed to be able to operate after a single point of failure, for system optimization and/or decentralization objectives. For some type of actuators, a control allocation is used even without redundancy, being a good example the design and operation of thruster configurations. In fact, as the thruster mass flow direction and magnitude only can be changed under certain limits, this must be considered in the feedback implementation. In this work, the thruster configuration design is considered in the fixed (F), single-gimbal (SG) and double-gimbal (DG) thruster cases. The minimum number of thrusters for each case is obtained and for the resulting configurations a specific control allocation is proposed using a nonlinear programming algorithm, under nominal and single-point of failure conditions.