Sparse online Gaussian process regression-based robust nonlinear dynamic inversion for multirotor with forward flight ground effect

Abstract

This paper proposes a sparse online Gaussian process-based robust nonlinear dynamic inversion (SOGPR-RNDI) to compensate for ground effect during forward flight. Ground effect is challenging to model as it varies with altitude, thrust, propeller radius, platform movement, and surface quality. Its characteristics change significantly during forward flight due to aerodynamic effects. To address this problem, sparse online Gaussian process regression (SOGPR), a non-parametric modeling method, is employed to estimate and compensate for ground effect in real-time. SOGPR updates the mean and variance through a recursive process and uses a kernel linear independence test to maintain a meaningful dataset while reducing a computational burden. The proposed controller integrates a baseline control input, a Gaussian process regression (GPR) control input, and a robust control input, which is designed using the time derivative of the uncertainty error to ensure tracking performance and mitigate chattering issues. In addition, finite-time asymptotic convergence of the closed-loop system is proved using Lyapunov stability. Simulation results demonstrate that the proposed method effectively compensates for ground effect during forward flight and achieves superior tracking performance compared to nonlinear disturbance observer (NDO), deep neural network (DNN), modified GPR (MGPR), and SOGPR-based nonlinear dynamic inversion (SOGPR-NDI). Notably, SOGPR-RNDI reduces altitude root mean square error (RMSE) by 18.7% and velocity RMSE by 12.4% compared to SOGPR-NDI. Moreover, the computational efficiency of SOGPR-RNDI is analyzed, demonstrating its real-time applicability through better training and execution times compared to other methods.