用对偶四元数建模无人机碰撞，实现更快更平滑的恢复。
Dual Quaternion Based Contact Modeling for Fast and Smooth Collision Recovery of Quadrotors
- 在SE(3)流形上直接使用对偶四元数统一处理碰撞冲量。
- 实验显示执行延迟降低24%，位置误差减少超50%。
- 适合需要高鲁棒性飞行控制的复杂环境无人机系统。
在复杂环境中运行的无人机需高效精确的碰撞建模以维持稳定性，但传统冲量模型将法向与切向分量解耦。本文提出一种基于对偶四元数的SE(3)流形上冲量重置映射，通过统一空间速度（线速度与角速度）在单一闭式表达中保留法向与切向冲量的交叉耦合，并将经典解耦的牛顿冲量模型作为特例恢复。设计了一种耦合线动量与角动量的恢复控制器，确保碰撞过程中动能耗散。软硬件联合测试表明，相比优化的矩阵实现，执行延迟降低24%；相较于位置+四元数（PQ）方法，降低20%。在MuJoCo中对碰撞角度与摩擦系数进行蒙特卡洛模拟，位置均方根误差（RMSE）降低50.8%–75.1%，峰值动能下降68.7%–85%，优于已发表的线性阻抗基线。
原文摘要 · Abstract (English)
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.
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