Abstract
Safe navigation within a workspace is a fundamental skill for autonomous robots to accomplish more complex tasks. Harmonic potentials are artificial potential fields that are analytical, globally convergent and provably free of local minima. Thus, it has been widely used for generating safe and reliable robot navigation control policies. However, most existing methods do not allow customization of the harmonic potential fields nor the resulting paths, particularly regarding their topological properties. In this paper, we propose a novel method that automatically finds homotopy classes of paths that can be generated by valid harmonic potential fields. The considered complex workspaces can be as general as forest worlds consisting of numerous overlapping star-obstacles. The method is based on a hybrid optimization algorithm that searches over homotopy classes, selects the structure of each tree-of-stars within the forest, and optimizes over the continuous weight parameters for each purged tree via the projected gradient descent. The key insight is to transform the forest world to the unbounded point world via proper diffeomorphic transformations. It not only facilitates a simpler design of the multi-directional D-signature between non-homotopic paths, but also retain the safety and convergence properties. Extensive simulations and hardware experiments are conducted for non-trivial scenarios, where the navigation potentials are customized for desired homotopic properties. Project page: this https URL.
Abstract (translated)
工作空间内的安全导航是自主机器人完成更复杂任务的一项基本技能。谐波势场是一种人工势场，具有解析性、全局收敛性和无局部极小值的特性，因此被广泛用于生成安全可靠的机器人导航控制策略。然而，现有大多数方法不允许对谐波势场及其路径进行定制化调整，尤其是在拓扑性质方面。本文提出了一种新的方法，可以自动寻找由有效谐波势场所产生的同伦类路径。所考虑的复杂工作空间可以是一片包含大量重叠星形障碍物的森林世界。 该方法基于一种混合优化算法，在这种算法中搜索同伦类、选择森林中的每棵树结构，并通过投影梯度下降法对每个去除障碍后的树进行连续权重参数的优化。关键见解在于，通过适当的微分同胚变换将森林世界转换为无界点世界。这不仅简化了不同非同伦路径之间的多向D签名的设计，而且还保留了安全性和收敛性属性。 进行了广泛的仿真和硬件实验，涵盖了非平凡场景，在这些场景中导航势场被定制化以满足所需同伦性质。项目主页在此链接: [此链接应为实际的URL地址]。
URL
https://arxiv.org/abs/2507.09858
