标题： 通过同伦路径上的混合优化定制谐波势场 显示英文标题

标题： Customize Harmonic Potential Fields via Hybrid Optimization over Homotopic Paths

摘要： 在工作空间内进行安全导航是自主机器人完成更复杂任务的基本技能。 调和势场是人工势场，它们是解析的、全局收敛的，并且可证明没有局部最小值。 因此，它已被广泛用于生成安全可靠的机器人导航控制策略。 然而，大多数现有方法不允许自定义调和势场及其产生的路径，特别是关于它们的拓扑特性。 在本文中，我们提出了一种新方法，可以自动找到由有效调和势场生成的路径的同伦类。 所考虑的复杂工作空间可以像由许多重叠的星形障碍物组成的森林世界一样一般。 该方法基于一种混合优化算法，在同伦类中搜索，选择森林中每个星树的结构，并通过投影梯度下降对每个清除的树进行连续权重参数优化。 关键见解是通过适当的微分同胚变换将森林世界转换为无界点世界。 这不仅有助于在非同伦路径之间设计更简单的多方向D签名，还能保留安全性和收敛性。 进行了大量仿真和硬件实验，针对非平凡场景，其中导航势场被定制以实现期望的同伦性质。 项目页面：https://shuaikang-wang.github.io/CustFields. 显示英文摘要

摘要： 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: https://shuaikang-wang.github.io/CustFields.