在无奇异性引导向量场中将物理速度与路径参数化解耦
Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields
- Hunan University（湖南大学）
- Hunan Normal University（湖南师范大学）
- National University of Defense Technology（国防科技大学）
- Information Support Force Engineering University（信息支援部队工程大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对SF-GVF中期望速度依赖路径参数化且部分归一化可能引入新奇异点的问题，提出具有指定物理速度的新型SF-GVF，实现指数收敛和物理速度可控，仿真与实验验证有效性。
AI中文摘要：
现有的带有额外虚拟坐标的无奇异性引导向量场（SF-GVF）可以消除传统GVF中固有的奇异点（即向量场消失的点），并保证机器人轨迹全局收敛到闭合和自交的期望路径。然而，GVF在原始低维空间中沿期望路径给出的期望速度不能任意指定，而是依赖于路径参数化。一种可能的解决方法是部分归一化SF-GVF的物理投影并分配用户设计的速度。然而，我们表明这种解决方法可能会引入新的奇异性，因为归一化分母可能变为零。为解决此问题，我们提出了一种具有指定物理速度（PPS）的新型SF-GVF。新SF-GVF的积分曲线从高维空间（包括虚拟维度）中的任何初始条件指数收敛到期望路径；更重要的是，机器人的物理速度收敛到PPS，而路径误差动力学在期望路径的规则重参数化下保持不变。我们进一步为二阶运动学模型开发了一种饱和加速度控制律。最后，在不同PPS剖面下与四旋翼进行的比较仿真和3D路径跟踪实验验证了理论结果，并证明了所提出方法的有效性。
英文摘要：
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.
