Dual Quaternion Based Contact Modeling for Fast and Smooth Collision Recovery of Quadrotors

Valentin Gaucher; Wenlong Zhang

cs.ROMar 16, 2026

Dual Quaternion Based Contact Modeling for Fast and Smooth Collision Recovery of Quadrotors

Authors: Valentin Gaucher, Wenlong Zhang

Organizations: School of Manufacturing Systems and Networks, Ira A. Fulton Schools of Engineering, Arizona State University, Mesa, AZ, 85212, USA.

Abstract

Unmanned aerial vehicles (UAVs) operating in cluttered environments require efficient and accurate impact modeling to maintain stability post collisions, however classical impulse contact models decouple the normal and tangential components. This letter presents a dual quaternion impulse reset map directly on the SE(3) manifold. By operating on the unified spatial twist (unified linear and angular velocities), the proposed formulation retains the cross-coupling between normal and tangential impulse components in a single closed-form expression, and recovers the classical decoupled Newton impulse model as a special case. A recovery controller is designed that couples linear and angular momentum to enforce kinetic energy dissipation across impacts. Hardware-in-the-loop benchmarks demonstrate a 24% reduction in execution latency compared to an optimized matrix-based implementation, and a 20% reduction relative to a position-plus-quaternion (PQ) formulation. MuJoCo simulations across Monte Carlo sweeps over impact angles and friction coefficients show a 50.8%-75.1% reduction in position root-mean-square error (RMSE) and a 68.7%-85% decrease in peak kinetic energy compared to published linear-admittance baselines.

Figures & tables

Fig. 1 : UAV collision recovery in MuJoCo simulation. The proposed dual quaternion framework (blue) mitigates linear and angular state oscillations post-impact, preventing drift seen in the traditional matrix-based approach (green).

Panel of Figure 3 — Fig. 3 : Matlab simulations performed under impulse contact model.

Fig. 4 : MuJoCo results for an initial position $(x,y)=(-0.5,0.5)$ and friction $\mu=0.3$ . Impact velocity $\approx 2$ m/s.

Panel of Figure 5 — Fig. 5 : Monte Carlo results ( $N=50$ ) for the recovery phase.

Variation	Metric	vs Published	vs Strong Baseline
Angle	$L_{2}$ RMSE (m)	50.8%	12.4%
Angle	$E_{k}$ RMSE (J)	68.7%	4.0%
Friction	$L_{2}$ RMSE (m)	75.1%	24.7%
Friction	$E_{k}$ RMSE (J)	85.0%	12.7%

TABLE I : Improvement of the proposed DQ controller using post-impact recovery metrics from Monte Carlo simulation (

N=50

) against two baseline methods.

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Autonomous Drone Racing Model Predictive Control Quadrotor Control

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Quadrotor racing demands aggressive attitude and progress control while passing through every gate, and conventional quadrotor MPCC formulations state the prediction model in inertial coordinates and the attitude error in the body frame. We present a Dual-Quaternion Model Predictive Contouring Control (DQ-MPCC) for quadrotor racing in which the pose is a unit dual quaternion and the contouring errors are projected onto the tangent space of the dual quaternion manifold, expressed in the desired body frame: the same rigid-body dynamics as the conventional model, in unified pose-twist coordinates in the body frame. We compare DQ-MPCC against a baseline MPCC through Monte Carlo software-in-the-loop simulations and real-world racing on an eight-gate circuit of 11x4.5x3.65 m. With the same gains in simulation and hardware, DQ-MPCC keeps every crossing of its completed flights within the prescribed geometric margin, whereas the baseline exceeds it, its median worst-gate offset growing by 71.5% sim-to-real against a 10.1% decrease for DQ-MPCC. Among the configurations that keep every simulated gate crossing within the geometric margin, DQ-MPCC also reduces the minimum lap time by 6.7%, and by 10.5% in the real-world flights, while running onboard at 100 Hz.

Abstract

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