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

2026-01-06

arXiv.org

AI Summary

This work addresses the challenge of achieving high-precision and safe six-degree-of-freedom trajectory tracking for autonomous vehicles under state-dependent disturbances and modeling uncertainties. The authors propose a geometric feedback controller based on dual quaternions, integrated with Gaussian process regression at the velocity level to learn and compensate in real time for unknown position-pose coupled disturbances while preserving the SE(3) rigid-body motion structure. This approach represents the first integration of dual quaternion-based geometric control with Gaussian process learning, enabling structure-preserving online disturbance compensation and offering probabilistic stability guarantees grounded in Lyapunov theory. Experimental results demonstrate that, even under realistic local perturbations such as magnetometer disturbances, the system maintains accurate, smooth, and safe trajectory tracking, confirming the method’s robustness and data efficiency.

Technology Category

Intelligent Robots: State EstimationPlanning, Routing, and Scheduling: Replanning and Plan RepairSearch and Optimization: Learning to Search

Application Category

Responsible Web: Machine-in-the-loop, human agency and autonomySemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• trajectory tracking
• safety guarantees
• disturbance compensation
• modeling uncertainty
• autonomous vehicles

Innovation

• dual quaternion
• Gaussian Process regression
• geometric control
• learning-based control
• SE(3) trajectory tracking