Adaptive Neural Network Stochastic-Filter-based Controller for Attitude Tracking with Disturbance Rejection

Abstract

This paper proposes a real-time neural network (NN) stochastic filter-based controller on the Lie Group of the Special Orthogonal Group $SO(3)$ as a novel approach to the attitude tracking problem. The introduced solution consists of two parts: a filter and a controller. Firstly, an adaptive NN-based stochastic filter is proposed that estimates attitude components and dynamics using measurements supplied by onboard sensors directly. The filter design accounts for measurement uncertainties inherent to the attitude dynamics, namely unknown bias and noise corrupting angular velocity measurements. The closed loop signals of the proposed NN-based stochastic filter have been shown to be semi-globally uniformly ultimately bounded (SGUUB). Secondly, a novel control law on $SO(3)$ coupled with the proposed estimator is presented. The control law addresses unknown disturbances. In addition, the closed loop signals of the proposed filter-based controller have been shown to be SGUUB. The proposed approach offers robust tracking performance by supplying the required control signal given data extracted from low-cost inertial measurement units. While the filter-based controller is presented in continuous form, the discrete implementation is also presented. Additionally, the unit-quaternion form of the proposed approach is given. The effectiveness and robustness of the proposed filter-based controller is demonstrated using its discrete form and considering low sampling rate, high initialization error, high-level of measurement uncertainties, and unknown disturbances. Keywords: Neuro-adaptive, estimator, filter, observer, control system, trajectory tracking, Lyapunov stability, stochastic differential equations, nonlinear filter, attitude tracking control, observer-based controller.