Grasp Execution Without a Planner: Configuration-Space Grasp Distance Fields with Certified Safety & Guaranteed Quality

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Article Summary

Standard multifingered grasp execution architectures plan a collision-free trajectory to a selected grasp pose and track it with a feedback law. Execution-time object pose uncertainty or perturbations may invalidate the planned trajectory, forcing a costly replanning step. We present Grasp Distance Fields (GDFs), a smooth softmin distance field over grasp configurations in the arm-hand configuration space. Our controller executes a grasp by following this field's negative gradient with a stationary feedback law, eliminating the need for a planner, stored trajectory, or grasp selection. For safety, we filter this command through a CBF-CLF quadratic program (QP) constraining self-collision, workspace, object, and obstacle clearance, reporting impeded progress as explicit slack. We prove that the softmin tracks the true set distance within \(\log N/ρ\) for \(N\) candidates and smoothing parameter \(ρ\), and that the filtered loop renders the safe set forward invariant. Since no smooth field captures hand-object contact switching, we switch modes with hysteresis at a pregrasp configuration, trading object collision avoidance for contact admission. A wrench-quality barrier then keeps the realized grasp's force-closure margin within a prescribed tolerance of its value at hold onset. We evaluate in kinematic simulation on a fixed-base arm and a Unitree G1 humanoid, both fitted with the same underactuated hand. Our controller navigates cluttered and dynamic scenes to safely reach for, grasp, and lift 46 of 50 objects spanning primitive, household, and adversarial classes. Across those lifts, the executed grasps retain a median 94\% of their synthesized quality margin, at 0.09 ms QP solve time per 20 ms control step. Per-step softmax weights confirm that our controller executes the nearest candidate, obviating a separate selection step. Project page: www.clintonenwerem.com/gdf.

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