Optimization of under-constrained control effector allocations

An alternative method for dealing with the travel limitations of control surfaces arranged in an X-configuration on underwater vehicles is presented. The X-configuration uses four effectors to implement three functions: roll, pitch, and yaw moment generation. Each effector saturates due to stall at some angle of attack. As a result, the desired set of roll, pitch and yaw moments may not be achievable in all cases. The simplest procedure for handling these cases simply truncates any commanded fin angle beyond saturation. The resulting set of roll, pitch and yaw moments may not be the most desirable combination. Even when all three functions are achievable, the fin angles resulting from the simplest fin mixing scheme are not necessarily optimized. The proposed technique determines the combination of fin angles that minimizes fin drag when the manoeuvring moments are achievable and maintains proportionality between the actual moments when the desired set are unachievable. A comparison of results with simple truncation is presented and the computational penalties discussed