Connecting Sequential Least Squares Active Set, Exact Redistributed, and Redistributed Scaled Pseudoinverse Control Allocation

Control allocation methods such as redistributed scaled pseudoinverse (RSPI), exact redistributed pseudoinverse (ERP), and sequential least squares active set (SLS-AS) are crucial for safety-critical overactuated systems. This paper addresses the need for efficient and reliable control allocation in these systems. While the RSPI and ERP are based on the cascaded generalized inverses (CGI) method, SLS-AS is derived from quadratic programming optimization techniques. Despite the fact that RSPI and ERP were developed independently and differ in formulations, we demonstrate that they are equivalent. Additionally, we show significant parallels between RSPI with null space transition (NST) and SLS-AS, suggesting that RSPI is a special variant of SLS-AS. This paper evaluates the similarities and differences between RSPI and SLS-AS. Numerical comparisons are conducted using data from a real multicopter. This analysis gives valuable insight into both algorithms and lays the basis for further improvement towards a compromise between computational effort and optimal results.