Control allocation problem transformation approaches for over-actuated vectored thrust VTOLs

One main challenge of vectored thrust VTOLs is actuator thrust control saturation because it may lead to undesired behaviour and loss of control if the control channels are not prioritised. Another challenge of vectored thrust VTOLs is that the vectored thrust results in non-linear effector mapping preventing the direct use of standard linear control allocation approaches. Linear control allocation approaches have lower online computational and complexity burden, and have simplier requirements for fault tolerance and reconfigurability than nonlinear control allocation approaches. This paper proposes three real-time control allocation approaches for transforming a nonlinear control allocation problem to a linear problem so that classical linear control allocation approaches can then be used. The approaches which addresses the two main challenges of the particular VTOL configuration are then tested using three selected flight test manoeuvres on a generic over-actuated vectored thrust three degrees of freedom planar VTOL with no aerodynamics. The first approach transfers the non-linearity from the effector mapping to the computation of the actuator limits by formulating the real controls in cartesian form and then converts the physical actuator limits from polar to cartesian form. The second approach transforms the non-linear effector mapping to a linear mapping via numerical linearisation of the non-linear effector mapping in real-time. The third approach is similar to second approach except an extra step which transforms the virtual controls from cartesian to polar before performing an analytical linearisation resulting in a different and more complicated linear Effector mapping. The results demonstrate the effectiveness of the proposed control allocation schemes to allocate remaining control authority to higher priority and critical control channels in order to maintain operational safety and stability during certain flight conditions while there is limited control authority.