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Adaptive Multirobot Virtual Structure Control using Dual Quaternions

Juan I. Giribet, Alejandro S. Ghersin, Ignacio Mas, Harrison Neves Marciano, Daniel Khede Dourado Villa, Mario Sarcinelli-Filho

TL;DR

This paper addresses multi-UAV formation control by unifying translation and rotation through dual quaternions and a virtual-structure formation model, enabling consistent handling of pose and geometry with compact representations such as the unit dual quaternion ${\tilde{q}}$.The authors introduce cluster-space control (CSC) that decouples geometry control from pose control and derives cluster-to-robot transformations via forward/inverse kinematics, applying it to 2R and 3R formations.A geometry-based adaptive gain scheduling mechanism adjusts controller gains $K_{\omega,p}(\rho)$, $K_{\omega,i}(\rho)$, $K_{v,p}(\rho)$, $K_{v,i}(\rho)$, and $K_{\eta}(\rho)$ on a compact set $C$, with Lyapunov-based proofs ensuring convergence of pose and shape errors.Both simulations and indoor experiments with UAVs validate accurate trajectory and attitude tracking while preserving formation geometry, and demonstrate robustness gains when adapting to geometry variations.Overall, the work delivers a practical, robust framework for adaptive UAV formation control that leverages dual-quaternion pose representation and cluster-space decoupling to manage 6-DOF coordination in changing geometries.

Abstract

This paper presents a control strategy based on dual quaternions for the coordinated formation flying of small UAV groups. A virtual structure is employed to define the desired formation, enabling unified control of its position, orientation, and shape. This abstraction makes formation management easier by allowing a low-level controller to compute individual UAV commands efficiently. The proposed controller integrates a pose control module with a geometry-based adaptive strategy, ensuring precise and robust task execution. The effectiveness of the approach is demonstrated through both simulation and experimental results.

Adaptive Multirobot Virtual Structure Control using Dual Quaternions

TL;DR

This paper addresses multi-UAV formation control by unifying translation and rotation through dual quaternions and a virtual-structure formation model, enabling consistent handling of pose and geometry with compact representations such as the unit dual quaternion ${\tilde{q}}$.The authors introduce cluster-space control (CSC) that decouples geometry control from pose control and derives cluster-to-robot transformations via forward/inverse kinematics, applying it to 2R and 3R formations.A geometry-based adaptive gain scheduling mechanism adjusts controller gains $K_{\omega,p}(\rho)$, $K_{\omega,i}(\rho)$, $K_{v,p}(\rho)$, $K_{v,i}(\rho)$, and $K_{\eta}(\rho)$ on a compact set $C$, with Lyapunov-based proofs ensuring convergence of pose and shape errors.Both simulations and indoor experiments with UAVs validate accurate trajectory and attitude tracking while preserving formation geometry, and demonstrate robustness gains when adapting to geometry variations.Overall, the work delivers a practical, robust framework for adaptive UAV formation control that leverages dual-quaternion pose representation and cluster-space decoupling to manage 6-DOF coordination in changing geometries.

Abstract

This paper presents a control strategy based on dual quaternions for the coordinated formation flying of small UAV groups. A virtual structure is employed to define the desired formation, enabling unified control of its position, orientation, and shape. This abstraction makes formation management easier by allowing a low-level controller to compute individual UAV commands efficiently. The proposed controller integrates a pose control module with a geometry-based adaptive strategy, ensuring precise and robust task execution. The effectiveness of the approach is demonstrated through both simulation and experimental results.

Paper Structure

This paper contains 17 sections, 2 theorems, 42 equations, 23 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. DUAL QUATERNIONS
  3. Quaternions
  4. Dual Quaternions and Unit Dual Quaternions
  5. Applications of Quaternions and Dual Quaternions for Rigid Body Pose Representation
  6. Dual Quaternions and UAV formation control
  7. CLUSTER SPACE CONTROL
  8. Three-vehicle formation
  9. Two-Vehicle Formation
  10. CONTROL ADAPTATION BASED UPON GEOMETRY
  11. SIMULATION RESULTS
  12. Two Robot System (2R)
  13. Three Robot System (3R)
  14. EXPERIMENTAL VALIDATION
  15. Tracking Control Performance for UAV Formation
  16. ...and 2 more sections

Key Result

Theorem 2.1

Let $C\subseteq\mathbb{R}^d$ be compact. Let $K_{\omega,i}$, $K_{v,i}$ be self-adjoint, and $K_{\omega,p}$, $K_{v,p}$, $K_\eta$, $K_\xi:\mathbb{R}^d\to\mathbb{R}^{3\times 3}$ be continuous, symmetric positive definite, uniformly bounded functions on $C$; there exist constants ${k}_{min}$, ${k}_{max} Then every solution of the closed-loop system satisfies $({\delta q}, {\delta p}, {\eta}, {\xi}) \t

Figures (23)

  • Figure 1: 3R cluster geometry.
  • Figure 3: Axis/angle representation for the ${z}$ to ${z_d}$ error.
  • Figure 4: Formation hovering with variable $d$ (left) and obstacle avoidance maneuver (right).
  • Figure 5: 2R formation statistic plot. Top: Azimuth in hovering. Bottom: Azimuth in tracking.
  • Figure 6: Variable geometries emphasizing characteristics for: roll/yaw GS (left) and pitch GS (right).
  • ...and 18 more figures

Theorems & Definitions (4)

  • Theorem 2.1
  • proof
  • Theorem 3.1
  • proof