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A Dual Quaternion Framework for Collision Recovery of Quadrotor

Valentin Gaucher, Wenlong Zhang

Abstract

Unmanned aerial vehicles (UAVs) operating in cluttered environments require accurate impact modeling to maintain stability. However, conventional contact models decouple linear and angular impulses, risking manifold inconsistency during rapid state transitions. This article presents a dual quaternion reset map that resolves rigid-body impacts directly on the SE(3) manifold. By operating on the unified spatial twist (linear and angular velocities as a single dual entity), our formulation is algebraically equivalent to the classical Newton impulse model while preserving manifold consistency during discrete state jumps. Building on this framework, we design a hybrid recovery controller that couples linear and angular momentum to ensure strict energy dissipation across impacts. Hardware-in-the-loop benchmarks demonstrate a 24% reduction in execution latency compared to an optimized matrix-based implementation. High-fidelity MuJoCo simulations validate the controller's robustness to complex contact dynamics, showing a 56.6% reduction in post-impact root-mean-square error (RMSE) and a 41.2% decrease in peak kinetic energy compared to decoupled recovery methods.

A Dual Quaternion Framework for Collision Recovery of Quadrotor

Abstract

Unmanned aerial vehicles (UAVs) operating in cluttered environments require accurate impact modeling to maintain stability. However, conventional contact models decouple linear and angular impulses, risking manifold inconsistency during rapid state transitions. This article presents a dual quaternion reset map that resolves rigid-body impacts directly on the SE(3) manifold. By operating on the unified spatial twist (linear and angular velocities as a single dual entity), our formulation is algebraically equivalent to the classical Newton impulse model while preserving manifold consistency during discrete state jumps. Building on this framework, we design a hybrid recovery controller that couples linear and angular momentum to ensure strict energy dissipation across impacts. Hardware-in-the-loop benchmarks demonstrate a 24% reduction in execution latency compared to an optimized matrix-based implementation. High-fidelity MuJoCo simulations validate the controller's robustness to complex contact dynamics, showing a 56.6% reduction in post-impact root-mean-square error (RMSE) and a 41.2% decrease in peak kinetic energy compared to decoupled recovery methods.
Paper Structure (23 sections, 47 equations, 5 figures, 2 tables)

This paper contains 23 sections, 47 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivation and Problem Statement
  3. Related Work
  4. Contributions
  5. Preliminaries
  6. Notation and Algebra
  7. Standard Quaternion Flight Dynamics
  8. Matrix-Based Reset Model
  9. Dual Quaternion formulation
  10. Dual Quaternion Flight Dynamics
  11. The Dual Quaternion Reset Map
  12. Dual Quaternion Impact Recovery Control
  13. Numerical Validation and Simulation
  14. Computational Complexity Analysis
  15. Validation Simulations
  16. ...and 8 more sections

Figures (5)

  • Figure 1: UAV collision recovery performance in MuJoCo simulation. The proposed Dual Quaternion framework (blue, dashed) effectively mitigates linear and angular state oscillations post-impact, preventing drift seen in the traditional matrix-based approach (green, solid).
  • Figure 2: Geometric interpretation of the Dual Quaternion Reset Map. The reset map in \ref{['eq:DQM-reset']} is solved directly on the dual manifold.
  • Figure 3: MATLAB simulation results for an impact velocity of $2$ m/s: position and attitude responses to an idealized impulse.
  • Figure 4: MuJoCo simulation results for an impact velocity of $2$ m/s: high-fidelity kinematic response demonstrating the significant lateral cross-coupling of the baseline controller.
  • Figure 5: Monte Carlo results in MuJoCo during the post-impact recovery phase.