A Dual Quaternion Framework for Collision Recovery of Quadrotor

2026-03-15

AI Summary

This work addresses the instability and state discontinuities in quadrotor collision recovery caused by traditional methods that decouple linear and angular impulses, thereby violating geometric consistency on the SE(3) manifold. To resolve this, the paper introduces dual quaternions for the first time in quadrotor post-collision dynamics, formulating a unified reset map on SE(3) that fuses linear and angular velocities into a single dual twist. This approach preserves geometric consistency during discrete impacts and is paired with a hybrid recovery controller designed to dissipate energy effectively. Experimental validation via hardware-in-the-loop tests demonstrates a 24% reduction in control latency, while high-fidelity MuJoCo simulations show a 56.6% decrease in post-collision RMSE and a 41.2% reduction in peak kinetic energy.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• collision recovery
• quadrotor
• impact modeling
• manifold consistency
• contact dynamics

Innovation

• dual quaternion
• SE(3) manifold
• impact modeling
• hybrid recovery controller
• spatial twist