用角度自适应优化路径平滑性，提升视觉导航路径匹配度。

Path smoothness is often overlooked in path imitation learning from expert demonstrations. In this paper, we introduce a novel learning method, termed deep angular A* (DAA*), by incorporating the proposed path angular freedom (PAF) into A* to improve path similarity through adaptive path smoothness. The PAF aims to explore the effect of move angles on path node expansion by finding the trade-off between their minimum and maximum values, allowing for high adaptiveness for imitation learning. DAA* improves path optimality by closely aligning with the reference path through joint optimization of path shortening and smoothing, which correspond to heuristic distance and PAF, respectively. Throughout comprehensive evaluations on 7 datasets, including 4 maze datasets, 2 video-game datasets, and a real-world drone-view dataset containing 2 scenarios, we demonstrate remarkable improvements of our DAA* over neural A* in path similarity between the predicted and reference paths with a shorter path length when the shortest path is plausible, improving by 9.0% SPR, 6.9% ASIM, and 3.9% PSIM. Furthermore, when jointly learning pathfinding with both path loss and path probability map loss, DAA* significantly outperforms the state-of-the-art TransPath by 6.3% SPR, 6.0% PSIM, and 3.7% ASIM. We also discuss the minor trade-off between path optimality and search efficiency where applicable. Our code and model weights are available at https://github.com/zwxu064/DAAStar.git.