Parametric verification of a quadrotor angular rate control law using the least squares method

Abstract

This paper proposes a verification method for a nonlinear angular rate control law for a quadrotor UAV based on the least squares method (LSM). The paper considers a compensation-based angular rate control law for a quadrotor UAV using a nominal inertia matrix, reference angular velocity, and tracking error. During controller synthesis, it was assumed that the inertia matrix of the platform was known exactly. Under this assumption, the closed-loop system acquires linear dynamic properties and provides exponential convergence of angular velocity tracking errors. However, under practical operating conditions, the actual inertia parameters may differ from nominal values due to payload variations, structural modifications, modeling uncertainties, or preliminary identification errors. Therefore, an additional procedure is required to assess whether the controller parameters remain consistent with the actual physical characteristics of the platform. It is shown that the Euler equations for a rigid body with a diagonal inertia matrix admit a linear parameterization with respect to inertia components. As a result, the parameter estimation problem can be reformulated as an overdetermined linear system and solved using the least squares method directly from closed-loop operation data. A distinctive feature of the proposed approach is that it does not require dedicated identification maneuvers. Parameter estimation is performed during normal operation of the control system without introducing additional excitation procedures. A verification criterion based on comparing the identified and nominal inertia matrices and on analyzing the identification residual is proposed. Numerical simulations were carried out for a 450 mm class quadrotor platform with parameter mismatch and MPU-6000 gyroscope measurement noise taken into account. The obtained results demonstrate the applicability of the proposed approach and confirm its capability for quantitative assessment of inertial parameter deviations over a wide range of inertia variations.