A Dual Quaternion Framework for Collision Recovery of Quadrotor

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.