Mind the Gap: Online Control Allocation for Multirotors with Low-Speed Deadbands

In this work, we present a novel optimizationbased input allocation strategy for fully-actuated multirotor aerial vehicles with N propellers that explicitly respects box constraints on the control inputs in both positive and negative actuation values while accounting for a deadband around zero. The resulting optimization problem belongs to the fundamental class of NP-hard global optimization problems, which can be recast as a Mixed-Integer Linear Program (MILP). We show that feasible solutions to this formulated MILP can efficiently be computed using a standard branch-and-bound algorithm. Building on that algorithm, the proposed method also robustly handles cases in which the desired allocation is infeasible by introducing several fallback instances. The method is experimentally validated on an octo-rotor platform, demonstrating the effectiveness of the proposed approach and its superior performance compared to the conventional QPbased allocation method.