Grasp Execution Without a Planner

Mainstream plan-then-track approaches to multifingered grasp execution entail selecting a grasp, planning a collision-free trajectory, and tracking the resulting trajectory via a feedback controller. Pose-estimation error during execution or scene motion can invalidate this open-loop commitment and trigger replanning. We thus present Grasp Distance Fields (GDFs), smooth softmin distances to finite sets of arm-hand grasp configurations. Using their negative gradients as feedback, we jointly select and execute grasps without planning a trajectory. A CBF-CLF quadratic program (QP) enforces self-collision, workspace, object, and obstacle-clearance constraints, while its CLF slack quantifies obstruction of task progress. We bound the softmin approximation error by $\log N/\rho$ and prove forward invariance of the filtered safe set. To handle changes in contact topology, we combine a hysteretic contact-mode transition with a wrench-quality CBF that limits degradation of the realized force-closure margin relative to hold onset. Using our method, a fixed-base manipulator and a Unitree G1 equipped with the same underactuated hand grasp and lift 46 of 50 test objects amid clutter and moving obstacles. The realized grasps also retain a median 94% of their synthesized quality margin, and each QP solve requires 0.09 ms within a 20 ms control interval.

Our wrench-quality constraint prevents the controller from lifting after the realized closure certificate degrades beyond its hold-relative bound. We repeat the descriptor-set evaluation with this constraint active and every other parameter fixed. Because the constraint activates only at entry into HOLD and the controller is deterministic, the quality-neutral and quality-constrained configurations reach HOLD identically on every record. The quality-constrained controller completes 45 lifts, one fewer than the quality-neutral configuration. In the single changed box trial, the hand forms a three-finger contact set whose realized margin falls from $1.51\times10^{-3}$ at hold onset to $-0.32$, against a descriptor certified at $1.83\times10^{-3}$. The quality-neutral controller proceeds through the certificate loss and lifts the grasp, whereas the wrench-quality constraint makes the program infeasible 25 control steps after hold onset and the trial stops in HOLD.

Physics simulation separates the two outcomes. We transfer each held configuration at entry into LIFT to a Drake simulation with a fixed wrist and implicit proportional-derivative finger actuation, then increase an upward force on the object to $1.5\,mg$ over one second. The certified grasp holds through the full force increase with at most $1.5~\mathrm{mm}$ of lateral drift, while the uncertified three-finger configuration drops the object under gravity alone. All 45 completed quality-constrained lifts end within $k_{\mathrm{wq}}=0.02$ of their hold-onset margins, and 44 satisfy the bound at every evaluated control step. One contact-set change violates the bound transiently and recovers to a $0.006$ deficit by the end of the lift. Median end-of-lift quality ratios are $0.932$ with the constraint and $0.936$ without it, so the constraint leaves the median essentially unchanged while acting on the large-degradation case.

Our controller completes the full reach-grasp-lift sequence on 46 of the 50 objects${}^{\dagger}$, each behind a rectangular obstacle placed next to its approach path. The test set contains four geometric primitives, 17 YCB household objects, and 29 adversarial EGAD meshes. Because the hand still forms a contact set in the two HOLD failures, we evaluate 48 realized grasps in all. Of these, 37 satisfy $\varepsilon_{\mathrm{exec}}^{(\beta)} \ge 0$ at $\beta = 0.9$, while the min-weight baseline classifies 39 as force closed and places 30 above $\bar{\ell}^{*} \ge 0.3$. This descriptor-set evaluation runs without the wrench-quality constraint, so the $\varepsilon_{\mathrm{exec}}^{(\beta)}$ values score the realized grasps post hoc.