Data-augmented Learning of Geodesic Distances in Irregular Domains through Soner Boundary Conditions
This work addresses training stability issues for geodesic distance solvers in robotics, offering an incremental improvement through a hybrid data-physics approach.
The paper tackled the problem of unstable convergence in neural network-based geodesic distance learning for irregular domains by proposing a framework using Soner boundary conditions and data losses, resulting in significantly improved convergence robustness and reduced training instabilities.
Geodesic distances play a fundamental role in robotics, as they efficiently encode global geometric information of the domain. Recent methods use neural networks to approximate geodesic distances by solving the Eikonal equation through physics-informed approaches. While effective, these approaches often suffer from unstable convergence during training in complex environments. We propose a framework to learn geodesic distances in irregular domains by using the Soner boundary condition, and systematically evaluate the impact of data losses on training stability and solution accuracy. Our experiments demonstrate that incorporating data losses significantly improves convergence robustness, reducing training instabilities and sensitivity to initialization. These findings suggest that hybrid data-physics approaches can effectively enhance the reliability of learning-based geodesic distance solvers with sparse data.