Harmonic potentials provide globally convergent potential fields that are provably free of local minima. Due to its analytical format, it is particularly suitable for generating safe and reliable robot navigation policies. However, for complex environments that consist of a large number of overlapping non-sphere obstacles, the computation of associated transformation functions can be tedious. This becomes more apparent when: (i) the workspace is initially unknown and the underlying potential fields are updated constantly as the robot explores it; (ii) the high-level mission consists of sequential navigation tasks among numerous regions, requiring the robot to switch between different potentials. Thus, this work proposes an efficient and automated scheme to construct harmonic potentials incrementally online as guided by the task automaton. A novel two-layer harmonic tree (HT) structure is introduced that facilitates the hybrid combination of oriented search algorithms for task planning and harmonic-based navigation controllers for non-holonomic robots. Both layers are adapted efficiently and jointly during online execution to reflect the actual feasibility and cost of navigation within the updated workspace. Global safety and convergence are ensured both for the high-level task plan and the low-level robot trajectory. Known issues such as oscillation or long-detours for purely potential-based methods and sharp-turns or high computation complexity for purely search-based methods are prevented. Extensive numerical simulation and hardware experiments are conducted against several strong baselines.

翻译：调和势场提供全局收敛且可证明无局部极小值的势场。由于其解析形式，它特别适用于生成安全可靠的机器人导航策略。然而，对于由大量重叠非球形障碍物构成的复杂环境，相关变换函数的计算可能十分繁琐。这在以下情况下尤为明显：(i) 工作空间初始未知，且随着机器人探索不断更新底层势场；(ii) 高层任务包含多个区域间的顺序导航任务，要求机器人在不同势场间切换。因此，本文提出一种高效自动的方案，在任务自动机引导下在线增量式构建调和势场。引入一种新颖的两层调和树结构，该结构促进了面向任务规划的定向搜索算法与面向非完整机器人的基于调和势场的导航控制器的混合集成。在线执行过程中，两层结构均能高效协同调整，以反映更新后工作空间内导航的实际可行性与成本。高层任务规划与底层机器人轨迹均确保全局安全性与收敛性。该方法避免了纯势场方法常见的振荡或绕远问题，以及纯搜索方法存在的急转弯或高计算复杂度问题。针对多个强基线模型，进行了广泛的数值仿真与硬件实验。