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arXiv · 2609.19726

Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields

Zhouru Xiao·Sha Luo·Yang Lu·Mingliang Xiao·Weijia Yao·Bohuan Lin·Xianzhe Cheng·Yaonan Wang
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Abstract

The existing singularity-free guiding vector field (SF-GVF) with an additional virtual coordinate can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-intersecting desired paths. However, the desired speed given by the GVF along the desired path in the original lower-dimensional space cannot be arbitrarily specified but depends on path parameterizations. One possible workaround is to partially normalize the physical projection of the SF-GVF and assign a user-designed speed. However, we show that this workaround may introduce new singularities since the normalization denominator can become zero. To address this issue, we propose a new SF-GVF with prescribed physical speed (PPS). The integral curves of the new SF-GVF converge exponentially to the desired path from any initial condition in the higher-dimensional space (including virtual dimension); more importantly, the robot's physical speed converges to the PPS, while the path-error dynamics remain invariant under regular reparameterizations of the desired path. We further develop a saturated acceleration control law for second-order kinematic models. Finally, comparative simulations and 3D path-following experiments with a quadrotor under different PPS profiles validate the theoretical results and demonstrate the effectiveness of the proposed approach.

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Zhouru Xiao, Sha Luo, Yang Lu, Mingliang Xiao, Weijia Yao, Bohuan Lin, Xianzhe Cheng, Yaonan Wang. 2026-09-17. Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields. https://arxiv.org/abs/2609.19726

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