提出3D空间中避免局部陷阱的导航函数构造方法
Feedback-Based Mobile Robot Navigation in 3-D Environments Using Artificial Potential Functions Technical Report
- 用多项式隐式函数建模障碍物，设计平滑导航函数
- 理论证明目标点有唯一非退化最小值，可避局部极小
- 适用于球形/柱形障碍物相交的复杂3D环境，适合机器人路径规划
本技术报告构建并分析了用于三维工作空间中运动规划的多项式导航函数，该空间由球形和圆柱形障碍物构成。工作区被建模为有界球体区域，障碍物通过光滑的多项式隐式函数编码。文中建立了在存在成对相交障碍物情况下，所提导航函数在目标点具有唯一非退化最小值且避免局部极小的充分条件。提供了梯度与海森矩阵分析，并通过密集障碍物环境中的数值模拟验证了理论结果。
原文摘要 · Abstract (English)
This technical report presents the construction and analysis of polynomial navigation functions for motion planning in 3-D workspaces populated by spherical and cylindrical obstacles. The workspace is modeled as a bounded spherical region, and obstacles are encoded using smooth polynomial implicit functions. We establish conditions under which the proposed navigation functions admit a unique non-degenerate minimum at the target while avoiding local minima, including in the presence of pairwise intersecting obstacles. Gradient and Hessian analyses are provided, and the theoretical results are validated through numerical simulations in obstacle rich 3-D environments.
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