We formulate grasp learning as a neural field and present Neural Grasp Distance Fields (NGDF). Here, the input is a 6D pose of a robot end effector and output is a distance to a continuous manifold of valid grasps for an object. In contrast to current approaches that predict a set of discrete candidate grasps, the distance-based NGDF representation is easily interpreted as a cost, and minimizing this cost produces a successful grasp pose. This grasp distance cost can be incorporated directly into a trajectory optimizer for joint optimization with other costs such as trajectory smoothness and collision avoidance. During optimization, as the various costs are balanced and minimized, the grasp target is allowed to smoothly vary, as the learned grasp field is continuous. We evaluate NGDF on joint grasp and motion planning in simulation and the real world, outperforming baselines by 63% execution success while generalizing to unseen query poses and unseen object shapes. Project page: https://sites.google.com/view/neural-grasp-distance-fields.

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