Error-State LQR Formulation for Quadrotor UAV Trajectory Tracking

TL;DR

The paper addresses robust quadrotor trajectory tracking by formulating an error-state LQR that uses exponential coordinates for orientation errors, enabling a linearized model around the current tracking error. It derives the error-state dynamics, computes Jacobians and the ARE-based gain $\mathbf{K}$ (with $\mathbf{u}_t = \mathbf{u} - \mathbf{K} \delta \mathbf{x}$), and integrates a cascaded bodyrate controller to handle actuator dynamics via time-scale separation. Key contributions include explicit Jacobians for the error-state model, a practical ARE-based gain computation, and a cascaded control architecture for real-time robustness. This approach offers accurate, stable trajectory tracking for quadrotors in dynamic environments with computationally tractable online updates.

Abstract

This article presents an error-state Linear Quadratic Regulator (LQR) formulation for robust trajectory tracking in quadrotor Unmanned Aerial Vehicles (UAVs). The proposed approach leverages error-state dynamics and employs exponential coordinates to represent orientation errors, enabling a linearized system representation for real-time control. The control strategy integrates an LQR-based full-state feedback controller for trajectory tracking, combined with a cascaded bodyrate controller to handle actuator dynamics. Detailed derivations of the error-state dynamics, the linearization process, and the controller design are provided, highlighting the applicability of the method for precise and stable quadrotor control in dynamic environments.

Figures (1)

• Figure 1: Tracking performance of the error-state LQR controller on a lemniscate trajectory while tracking yaw angles. The tracking error at the beginning of the trajectory is due to the fact that the UAV begins with a flat initial orientation $q_0 = (1, 0, 0, 0)^T$.