Fast Pseudoinverse-Based Control Allocation Using Variant of Cholesky Decomposition

Pseudoinverse-based control allocation (CA) methods like redistributed scaled pseudoinverse are popular options for control allocation of safety-critical systems with limited computational power, such as aircraft, unmanned aerial vehicles, and spacecraft. Those methods may require the online computation of the pseudoinverse of the control effectiveness matrix, which results in a significant computational load using the standard singular value decomposition (SVD). This paper presents the [Formula: see text] decomposition, a variant of the Cholesky decomposition, as a viable replacement for the SVD in CA. The [Formula: see text] decomposition is known to be computationally less expensive while being numerically unstable. This study evaluates a nonpivoted, a pivoted, and a rank-1 update [Formula: see text] algorithm and demonstrates their implementability according to coding standards. The results show that the developed [Formula: see text] -based algorithms are applicable for full-rank and rank-deficient input matrices while reducing the computational effort significantly. Despite the theoretically inferior numerical properties, the [Formula: see text] -based algorithms reach the same level of precision as the SVD for real-world applications such as a multicopter, a cyclocopter, and a transition electrical vertical takeoff and landing vehicle.