Efficient optimal constrained control allocation via multiparametric programming

Constrained control allocation is studied, and it is shown how an explicit piecewise linear representation of the optimal solution can be computed numerically using multiparametric quadratic programming. Practical benefits of the approach include simple and efficient real-time implementation that permits software verifiability. Furthermore, it is shown how to handle control deficiency, reconfigurability, and flexibility to incorporate, for example, rate constraints. The algorithm is demonstrated on several overactuated aircraft control configurations, and the computational complexity is compared to other explicit approaches from the literature. The applicability of the method is further demonstrated using overactuated marine vessel dynamic position experiments on a scale model in a basin.