Grasp Execution Without a Planner

GDF combines feedback grasp selection with collision-constrained execution across fixed-base, humanoid, and bimanual robot platforms. The robot approaches, grasps, and lifts an object while accommodating static or dynamic obstacles without a precomputed trajectory. The four-panel demonstration compares these execution settings. After hold onset, a wrench-quality control barrier function constrains degradation of the realized force-closure margin, coupling collision avoidance with grasp-quality preservation.

We represent the grasp target by a finite set $\mathcal{G} = \{q_i^{\text{pre}}\}_{i=1}^{N}$ of arm-hand pregrasp configurations. The hard set distance $d_{\min}(q)=\min_i \lVert q_i^{\text{pre}}-q\rVert_{\Lambda}$ is nonsmooth on candidate Voronoi boundaries, so the controller uses the smooth softmin $d_G(q)=-\tfrac{1}{\rho}\log\sum_i\exp(-\rho\,\lVert q_i^{\text{pre}}-q\rVert_{\Lambda})$. It satisfies $d_{\min}(q)-\log N/\rho \le d_G(q) \le d_{\min}(q)$, and its gradient is a softmax-weighted convex combination of the candidate-distance gradients. The nominal command $v_{\mathrm{nom}}=-k\nabla d_G$ therefore requires no discrete grasp-selection step; the softmax weights interpolate candidate selection at every evaluation. At each control step, a CLF-CBF quadratic program filters this nominal velocity through the active safety constraints, while an admission test rejects candidates whose pregrasp or closure violates a barrier constraint.

The REACH, CLOSE, HOLD, and LIFT modes change the active constraints as object contacts form. At hold onset, the wrench-quality CBF limits degradation of the realized risk-adjusted force-closure margin relative to its hold-onset value. Dependent-joint equalities represent the underactuated hand.

For the Unitree G1 humanoid, we specify the rigid-body model and a grasp record synthesized for that platform.

The controls below play recorded execution data from three representative reach-avoid-stay trials: static-obstacle and moving-obstacle trials with a fixed-base arm-hand system, and a static-obstacle trial with the Unitree G1. Use the tabs to switch trials and the playback controls to inspect the timeline. The readouts report time, active mode, Grasp Distance Field value $d_G$, minimum barrier value, and contact count through REACH, CLOSE, HOLD, and LIFT.

In a reference trial, we place a sphere from the descriptor set behind a pair of $6 \times 6 \times 50$ cm rectangular obstacles. No unobstructed approach to the object exists. The filtered closed loop avoids the obstacles, with the palm deviating by up to 20.5 cm from the nominal path, and completes the 12 cm rise. Both obstacle constraints remain positive at every control step, with a minimum of 6.7 mm. The realized grasp retains $r=0.912$ of the descriptor's certified risk-adjusted margin, $3.05\times10^{-3}$ versus $3.35\times10^{-3}$, while the corresponding min-weight margins are 0.446 and 0.468.

Our controller updates obstacle poses at every control step and handles a moving obstacle without changing the feedback law. We translate a $5 \times 5 \times 45$ cm obstacle at 0.05 m/s across the arm's approach path. The filtered closed loop steers around the obstacle and continues the approach, with the palm path deviating by up to 19.1 cm from the nominal path and true surface clearance remaining positive at a minimum of +8.4 mm. Because the implemented constraint omits the $\partial h/\partial t$ term, the obstacle CBF can fall below zero by at most $v/\alpha_0=10$ mm in this trial; the measured minimum is $-6.6$ mm, within the 1.5 cm obstacle margin.

We instantiate the controller on a humanoid to test whether the platform-specific structure comes from the rigid-body model alone. We combine the 29-degree-of-freedom Unitree G1 body with an 11-joint hand at the right wrist and fix the legs and left arm, leaving a 21-dimensional fixed-pelvis chain. With a $4 \times 4 \times 36$ cm obstacle on the palm-to-object line, the closed loop completes the 12 cm rise in 434 steps with no infeasible step. The minimum obstacle-constraint value is 3.8 mm, true surface clearance is 3.4 cm, the filtered palm path deviates by up to 9.7 cm from the nominal path, and torso rotation remains below 18 degrees through the lift.