SE(3) Neural Potential Fields for 6-DoF Trajectory Planning Directly from Images Without Explicit 3D Reconstruction

Reaching a 6-DoF grasp pose in clutter requires a collision-free trajectory, conventionally obtained by reconstructing the scene in 3D and planning inside that reconstruction, at the cost of its accuracy and compute. Potential fields learned directly from images remove that dependency but inherit the classical weakness of artificial potential fields: where attractive and repulsive gradients cancel, the descent grazes the obstacle instead of going around it, and can stall short of the goal. We present an SE(3) neural potential field learned from posed RGB images and supervised with a navigation function, the geodesic distance to the grasp through free space recovered from those same images during training, which removes both failures. On two tabletop scenes, from obstacle-blocked starts executed on a UR10, the field converges within 3 cm of the grasp from every start and every path it executes is collision-free against the ground-truth geometry, against 25% and 0% under image supervision alone; mean clearance rises from under a centimeter to 8.6-8.8 cm and arm-link contacts fall from 20.6-50.4% to 2.7-5.5% of executed configurations. Executed grasp success is 90.0% and 40.0% on the two scenes, the residual failures being refusals of the Cartesian executor rather than of the field. Planning takes about 2 s against 67-133 s for RRT* on a reconstruction of the same images, though under a common offline harness the two are comparable: the deployed margin is the cost of collision-checking a dense reconstruction, not planner complexity.