Analysis of a Fast Control Allocation approach for nonlinear over-actuated systems

Autonomous Robots with multiple directional thrusters are normally over-actuated systems that require nonlinear control allocation methods to map the forces that drive the robot's dynamics and act as virtual control variables to the actuators. This process demands computational efforts that, sometimes, are not available in small robotic platforms. The present paper introduces a new control allocation approach with fast convergence, high accuracy, and dealing with complex nonlinear problems, especially in embedded systems. The adopted approach divides the desired nonlinear system into coupled linear problems. For that purpose, the Real Actions (RAs) and Virtual Control Variables (VCVs) are broke in two or more sets each. While the RA subsets are designed to linearize the system according to different input subspaces, the VCV is designed to be partially coupled to overlap the output subspaces. This approach generates smaller linear systems with fast and robust convergence used sequentially to solve nonlinear allocation problems. This methodology is assessed in mathematical tutorial cases and over-actuated UAV simulations.