  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.
