Executor-aware Candidate Selection via a Feasibility Certificate

Planners on graphs of convex sets return trajectories that are collision-free by construction, provided the convex regions are collision-free. The region generator only promises that property probabilistically, and no planner in the family verifies it. We report the first measurement of what the gap costs. On a scaled 14-DOF bimanual library, $3.2\%$ of interface samples are in collision, and a search-based GCS planner (\gcsstar) turns that volume error into a $62\%$ answer error: $18$ of $29$ pick-and-place queries return trajectories that drive the arms through the shelves, up to $91$,mm deep, reported as successes. Repairing the library does not work; a ten times stricter acceptance contract, sums-of-squares certified regions, and uniform margins each destroy the connectivity planning needs before they deliver soundness. We instead build a planner that certifies its answers. It samples the overlaps and shared faces of the decomposition, prunes with an admissible informed bound, and verifies the one candidate each search round proposes, continuously, by a chain of clearance certificate balls with no resolution parameter; failures are repaired with local in-region detours, and the convex polish is re-verified. Head-to-head on all $29$ task queries it delivers zero invalid answers against $21$ for the reference, reaches its first certified answer in $0.11$,s against $1.59$,s for the reference's unverified one, and reproduces the reference optimum exactly on every query whose reference answer is physically valid.

Reactive task-space planners such as Bug2 operate with fixed Cartesian step sizes and are unaware of the manipulator's joint-angle limits. When the Jacobian is poorly conditioned, even small Cartesian steps can demand joint changes that exceed admissible bounds; clipping the joints to their limits causes tracking drift and can prevent goal reaching entirely. We address this by computing, at each planning step, the largest Cartesian hyperrectangle that is \emph{certifiably reachable} under joint displacement bounds. Using a second-order polynomial approximation of the inverse kinematics and the S-procedure, we formulate a small semidefinite program whose solution yields the certified half-width~$λ^\star$. An equivalent bisection procedure exploiting the quadratic structure solves the certification in sub-millisecond time. Integrating this certificate with Bug2 yields a planner whose step size adapts to local kinematic conditioning. In a statistical evaluation over 94 adversarial scenarios spanning six joint-limit settings, the SOS-verified planner achieves \emph{zero} joint-limit violations with a 100% goal-reaching rate, whereas a standard Bug2 planner violates joint limits in 6--11% of steps and fails to reach the goal in up to 18% of scenarios.

A geometrically valid placement can still be difficult to execute because the selected grasp changes the required end-effector pose, collision geometry, and transport motion. Placement is formulated as a pre-execution ranking problem in which supplied grasp-placement candidates are scored before planning. The model combines a typed target-conditioned point cloud with three pose descriptors and hierarchical heads for planning success and execution success conditioned on planning. On a 30-object, 1,235-scene dataset with scene-group-held-out splits, three-seed top-1 success on covered test groups reaches 85.63 +/- 1.08% for joint selection and 79.84 +/- 0.16% for fixed-target ranking. For the designated frozen seed-42 checkpoint, top-1 success improves from 72.84% to 85.78% over full-pool cuMotion for joint ranking and from 59.65% to 79.67% for fixed-target ranking. Frozen transfer to xArm7/MoveIt requires no xArm-specific retraining. Across 27 locked cases, 13 complete end to end (48.15%). Of the 16 cases that pass Top-5 preflight and begin execution, 13 succeed (81.25%). Candidate-level deployment-feasibility prediction reaches 81.25% recall, 85.20% specificity, and 83.23% balanced accuracy.