Dual-quaternion learning control for autonomous vehicle trajectory tracking with safety guarantees

TL;DR

This paper introduces a dual-quaternion based learning controller for autonomous robots that ensures stable trajectory tracking with safety guarantees by integrating Gaussian Process regression for online disturbance compensation.

Contribution

It presents a novel geometric control framework combining dual quaternions and probabilistic learning to achieve robust, model-free trajectory tracking with formal stability guarantees.

Findings

Accurate trajectory tracking under disturbances demonstrated in simulations.

The controller maintains stability with probabilistic bounds on pose error.

Effective disturbance compensation using Gaussian Processes in a geometric setting.

Abstract

We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on $\mathrm{SE}(3)$. The controller is formulated in the dual quaternion framework and operates at the velocity level, assuming direct command of angular and linear velocities, as is standard in many aerial vehicles and omnidirectional mobile robots. Gaussian Process (GP) regression is integrated into a geometric feedback law to learn and compensate online for unknown, state-dependent disturbances and modeling imperfections affecting both attitude and position, while preserving the algebraic structure and coupling properties inherent to rigid-body motion. The proposed approach does not rely on explicit parametric models of the unknown effects, making it well-suited for robotic systems subject to sensor-induced disturbances, unmodeled actuation couplings, and environmental uncertainties. A Lyapunov-based analysis establishes probabilistic ultimate boundedness of the pose tracking error under bounded GP uncertainty, providing formal stability guarantees for the learning-based controller. Simulation results demonstrate accurate and smooth trajectory tracking in the presence of realistic, localized disturbances, including correlated rotational and translational effects arising from magnetometer perturbations. These results illustrate the potential of combining geometric modeling and probabilistic learning to achieve robust, data-efficient pose control for autonomous robotic systems.