The pathfinding problem, which aims to identify a collision-free path between two points, is crucial for many applications, such as robot navigation and autonomous driving. Classic methods, such as A$^*$ search, perform well on small-scale maps but face difficulties scaling up. Conversely, data-driven approaches can improve pathfinding efficiency but require extensive data labeling and lack theoretical guarantees, making it challenging for practical applications. To combine the strengths of the two methods, we utilize the imperative learning (IL) strategy and propose a novel self-supervised pathfinding framework, termed imperative learning-based A$^*$ (iA$^*$). Specifically, iA$^*$ is a bilevel optimization process where the lower-level optimization is dedicated to finding the optimal path by a differentiable A$^*$ search module, and the upper-level optimization narrows down the search space to improve efficiency via setting suitable initial values from a data-driven model. Besides, the model within the upper-level optimization is a fully convolutional network, trained by the calculated loss in the lower-level optimization. Thus, the framework avoids extensive data labeling and can be applied in diverse environments. Our comprehensive experiments demonstrate that iA$^*$ surpasses both classical and data-driven methods in pathfinding efficiency and shows superior robustness among different tasks, validated with public datasets and simulation environments.

翻译：路径规划问题旨在寻找两点间无碰撞路径，对于机器人导航和自动驾驶等众多应用至关重要。A$^*$搜索等经典方法在小规模地图上表现良好，但在扩展时面临困难。相反，数据驱动方法能提高路径规划效率，但需要大量数据标注且缺乏理论保证，使其在实际应用中面临挑战。为融合两类方法优势，我们利用指令学习策略提出了名为基于指令学习A$^*$（iA$^*$）的新型自监督路径规划框架。具体而言，iA$^*$是一个双层优化过程：下层优化通过可微A$^*$搜索模块寻找最优路径，上层优化则通过数据驱动模型设置合适的初始值来缩小搜索空间以提高效率。此外，上层优化中的模型是一个全卷积网络，通过下层优化计算出的损失进行训练。因此，该框架避免了大量数据标注，可适用于多种环境。全面实验表明，iA$^*$在路径规划效率上超越经典方法和数据驱动方法，并在不同任务中展现出卓越的鲁棒性，这已在公共数据集和仿真环境中得到验证。