  Constrained Motion Planning (CMP) aims to find a collision-free path between
the given start and goal configurations on the kinematic constraint manifolds.
These problems appear in various scenarios ranging from object manipulation to
legged-robot locomotion. However, the zero-volume nature of manifolds makes the
CMP problem challenging, and the state-of-the-art methods still take several
seconds to find a path and require a computationally expansive path dataset for
imitation learning. Recently, physics-informed motion planning methods have
emerged that directly solve the Eikonal equation through neural networks for
motion planning and do not require expert demonstrations for learning. Inspired
by these approaches, we propose the first physics-informed CMP framework that
solves the Eikonal equation on the constraint manifolds and trains neural
function for CMP without expert data. Our results show that the proposed
approach efficiently solves various CMP problems in both simulation and
real-world, including object manipulation under orientation constraints and
door opening with a high-dimensional 6-DOF robot manipulator. In these complex
settings, our method exhibits high success rates and finds paths in
sub-seconds, which is many times faster than the state-of-the-art CMP methods.
