WCA: A New Efficient Nonlinear Adaptive Control Allocation for Planar Hexacopters

Abstract

This paper presents an efficient control allocation (CA) strategy which significantly improves the flight performance of a planar hexacopter. This allocation maps the desired control vector v = [ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T, L,M,N</i> ]⟙ composed of the thrust and torques in roll, pitch, and yaw axis, respectively, to propellers’ speed. This paper shows that a CA strategy based on the classical approach of pseudo-inverse matrix only exploits a limited range of the vehicle capabilities to generate thrust and moments. A novel approach is presented, which is based on a weighted pseudo-inverse matrix method, called WCA, capable of exploiting a much larger domain in v. The three weights involved in WCA are adapted online according to nonlinear laws which are analytically derived by solving symbolically the equivalent constraint least-squares problem, thus removing the need for online-optimization calculations. This solution allows for very fast real-time operations, suitable for autopilots with limited computing resources. This paper provides 1) a detailed analysis of the limitations of the classical control allocation scheme, 2) the mathematical development of the WCA algorithm, 3) simulations and real experiments which show that this WCA strategy outperforms the classical CA approach in terms of a) capability to generate the maximum roll and pitch torques possible, without generating undesired yaw torques, b) prioritizing the generation of thrust over attitude torques, thus achieving better altitude tracking despite aggressive maneuvers or the presence of a payload, and c) better behavior in case of actuator saturation, faults or even failures.