Motion planning (MP) is one of the core robotics problems requiring fast methods for finding a collision-free robot motion path connecting the given start and goal states. Neural motion planners (NMPs) demonstrate fast computational speed in finding path solutions but require a huge amount of expert trajectories for learning, thus adding a significant training computational load. In contrast, recent advancements have also led to a physics-informed NMP approach that directly solves the Eikonal equation for motion planning and does not require expert demonstrations for learning. However, experiments show that the physics-informed NMP approach performs poorly in complex environments and lacks scalability in multiple scenarios and high-dimensional real robot settings. To overcome these limitations, this paper presents a novel and tractable Eikonal equation formulation and introduces a new progressive learning strategy to train neural networks without expert data in complex, cluttered, multiple high-dimensional robot motion planning scenarios. The results demonstrate that our method outperforms state-of-the-art traditional MP, data-driven NMP, and physics-informed NMP methods by a significant margin in terms of computational planning speed, path quality, and success rates. We also show that our approach scales to multiple complex, cluttered scenarios and the real robot set up in a narrow passage environment. The proposed method's videos and code implementations are available at https://github.com/ruiqini/P-NTFields.

翻译：运动规划（MP）是机器人学的核心问题之一，需要快速找到连接给定起始状态和目标状态的无碰撞机器人运动路径。神经运动规划器（NMP）在寻找路径解时展现出快速计算速度，但需要大量专家轨迹进行学习，从而增加了显著的训练计算负担。相比之下，最新进展催生了一种直接求解Eikonal方程的物理信息NMP方法，该方法无需专家示范即可进行学习。然而，实验表明，物理信息NMP方法在复杂环境中表现不佳，且在多种场景和高维真实机器人设置中缺乏可扩展性。为克服这些局限，本文提出一种新颖且易于处理的Eikonal方程公式，并引入一种新的渐进式学习策略，以在复杂、拥挤、多高维机器人运动规划场景中无需专家数据即可训练神经网络。结果表明，我们的方法在计算规划速度、路径质量和成功率方面显著优于最先进的传统MP、数据驱动NMP和物理信息NMP方法。我们还展示了该方法可扩展至多种复杂、拥挤场景以及狭窄通道环境中的真实机器人设置。所提方法的视频和代码实现可在https://github.com/ruiqini/P-NTFields获取。