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

Omayra Yago Nieto, Alexandre Anahory Simoes, Juan I. Giribet, Leonardo Colombo

TL;DR

The paper presents a learning-based trajectory tracking controller for rigid-body motion on $SE(3)$ using unit dual quaternions. It integrates Gaussian Process disturbances into a geometric, velocity-level controller, providing probabilistic Lyapunov guarantees for pose tracking despite unknown, state-dependent effects. The approach preserves the SE(3) structure, supports online/offline learning, and demonstrates robust, data-efficient pose control under sensor-induced disturbances such as magnetometer perturbations. The results highlight the value of combining geometric modeling with probabilistic learning for robust autonomous robotics, with potential extensions to multi-agent coordination and large-scale experiments.

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.

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

TL;DR

The paper presents a learning-based trajectory tracking controller for rigid-body motion on using unit dual quaternions. It integrates Gaussian Process disturbances into a geometric, velocity-level controller, providing probabilistic Lyapunov guarantees for pose tracking despite unknown, state-dependent effects. The approach preserves the SE(3) structure, supports online/offline learning, and demonstrates robust, data-efficient pose control under sensor-induced disturbances such as magnetometer perturbations. The results highlight the value of combining geometric modeling with probabilistic learning for robust autonomous robotics, with potential extensions to multi-agent coordination and large-scale experiments.

Abstract

We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on . 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.
Paper Structure (17 sections, 5 theorems, 81 equations, 13 figures, 3 tables, 1 algorithm)

This paper contains 17 sections, 5 theorems, 81 equations, 13 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Nominal controller in dual quaternions
  3. Nomenclature
  4. Generalities on dual quaternions
  5. Dual quaternion error dynamics
  6. Nominal control design
  7. Disturbance and measurement error model
  8. Learning-based trajectory tracking control based on Gaussian processes
  9. Learning with Gaussian Processes
  10. Control design
  11. Online learning-based tracking algorithm
  12. Simulation Results
  13. Open-Loop Experiment (Without GP Compensation)
  14. Close-Loop Experiment (With GP Compensation)
  15. Quantitative Performance Evaluation on Different Trajectories
  16. ...and 2 more sections

Key Result

Lemma 1

The dual quaternion $\bm{Q}=\mathcal{P}(\bm{Q}) + \varepsilon \mathcal{D}(\bm{Q})$ has unit-norm if and only if its principal part $\mathcal{P}(\bm{Q})$ is a unit-norm quaternion and the dual part can be written as $\mathcal{D}(\bm{Q})=\frac{1}{2}\widetilde{\bm p}\circ\mathcal{P}(\bm{Q})$, where $\w

Figures (13)

  • Figure 1: Block diagram of the proposed control law
  • Figure 2: Nominal reference trajectory for position and attitude.
  • Figure 3: External disturbance affecting yaw and altitude when the vehicle approaches the center of the trajectory. GP estimation of the angular-velocity disturbance.
  • Figure 4: External disturbance affecting yaw and altitude when the vehicle approaches the center of the trajectory. GP estimation of the linear velocity disturbance.
  • Figure 5: Open-loop yaw tracking performance in the presence of external magnetic disturbances.
  • ...and 8 more figures

Theorems & Definitions (17)

  • Lemma 1
  • Remark 1
  • Lemma 2
  • Remark 2
  • Theorem 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • ...and 7 more