Regrasp Map: A State-Space Graph for Manipulation

• Regrasp Map is a state-space abstraction for sequential manipulation that links grasp states and placements through transitions such as transit, transfer, and handover.
• It employs robust filtering—considering kinematics, collisions, stability, and contact mechanics—to ensure feasible transitions between manipulation states.
• Recent approaches combine classical graph search with learning-based and differentiable methods to optimize complex regrasp sequences for robotic tasks.

Searching arXiv for papers on regrasp maps and related regrasp planning formulations. A regrasp map, often called a regrasp graph in the manipulation literature, is a state-space abstraction for sequential manipulation in which feasible grasp states are connected by transitions such as transit, transfer, handover, placement change, or in-hand adjustment. Across the literature, the precise state encoded by the map varies with the manipulation regime: nodes may represent stable object placements, grasp instances bound to placements, whole-body humanoid states, in-hand object poses, grasp groups indexed by closing directions, or connected regions of object pose space with identical feasible-grasp signatures. The common role is to expose shared-grasp connectivity and thereby support planning when a single pick-and-place or a single grasp cannot achieve the task (Cao et al., 2015, Wan et al., 2017, Levit et al., 16 Jul 2025).

1. Classical graph semantics and the placement–grasp viewpoint

In the classical pick-and-place setting, a regrasp map is built from stable intermediate placements and grasps associated with those placements. A widely used formulation distinguishes a placement layer from a grasp layer. In the support-pin formulation, layer-1 nodes are placements of the object on the workspace, while layer-2 nodes are grasp instances associated to a particular placement; layer-1 edges connect placements that share at least one common grasp, and layer-2 edges are split into transit edges, which change grasp at a fixed placement, and transfer edges, which move the object between placements while maintaining the same grasp (Cao et al., 2015). The same transit/transfer distinction also underlies the large-scale database-backed roadmap for “10,000s of grasps,” in which each node corresponds to a discrete robot-object grasp configuration at a specific object placement on a table, and edges are induced either by shared placement or by shared free-air grasp identity (Wan et al., 2017).

This formulation is closely tied to stable-placement reasoning. In the support-pin work, a valid pin placement is generated by letting the object touch the table along a convex-hull edge and the pin at a sampled surface point, then validating collision, static stability, and friction conditions; the support polygon becomes the triangle formed by the two edge endpoints and the pin base, and the center-of-mass projection must lie strictly inside that triangle (Cao et al., 2015). In tabletop regrasp with large grasp sets, stable placements are obtained by posing the object on supporting facets and requiring the projection of the center of mass to lie in the support polygon; grasps are then transformed to each placement and filtered for collisions and inverse-kinematics feasibility before being inserted into the graph (Wan et al., 2017).

A central consequence of the placement–grasp construction is that connectivity depends not only on how many grasps or placements are sampled, but on how many shared grasps survive physical and kinematic filtering. The support-pin study shows that introducing a vertical pin expands the feasible placement set far beyond flat-surface-only support and increases the number of shared grasps across placements, which in turn improves graph connectivity and success rates for non-convex objects (Cao et al., 2015). The large-scale database formulation reaches interactive-time querying by precomputing grasps, placements, and robot-specific inverse-kinematics feasibility into relational tables and then constructing transit and transfer connectivity through indexed joins (Wan et al., 2017).

2. Generalized state abstractions: from discrete placements to pose-space regions

Later work generalizes the notion of a regrasp map beyond enumerated placements. In humanoid regrasp planning, the graph connects nodes between given initial and goal placements for an object and searches for a sequence of pick-and-place sub-tasks; a node is an inverse-kinematics-feasible, collision-free, and stable whole-body state, while edges correspond to transit, transfer, and handover motions (Sanchez et al., 2018). In in-hand manipulation, the term may not be used explicitly, but the planner constructs an equivalent map: in stable prehensile pushing, nodes are discretized grasp poses $q=[X,Z,\theta_y]\in \mathbb{R}^3$, and edges are feasible stable pushes that concatenate into a T-RRT* tree of reachable grasp states (Chavan-Dafle et al., 2017). In geometric in-hand regrasp, the graph is implicit rather than explicitly materialized: grasp states $G_i=(X_i,o_i)$, where $X_i$ is the fingertip contact set on the mesh and $o_i$ the object pose in the palm frame, are connected by finger-gait edges and in-grasp manipulation edges validated by continuous constrained optimization (Sundaralingam et al., 2018).

A more explicit state-space abstraction appears in “Regrasp Maps for Sequential Manipulation Planning,” where the object free space $X_o\subset SE(3)$ is discretized into voxels, each voxel is assigned a binary signature of feasible grasp anchors, and a regrasp area is defined as a connected component of adjacent voxels with identical signatures. The resulting map $M=(M_v,M_e)$ has nodes $(a,u)$, where $a$ is a regrasp area and $u$ a feasible grasp in that area; regrasp edges connect $(a,u)$ and $G_i=(X_i,o_i)$0 within the same area, while transport edges connect $G_i=(X_i,o_i)$1 and $G_i=(X_i,o_i)$2 across adjacent areas (Levit et al., 16 Jul 2025). The feasibility map is written as

$G_i=(X_i,o_i)$3

with $G_i=(X_i,o_i)$4 derived from local sampling and collision checking (Levit et al., 16 Jul 2025).

This broader view makes clear that a regrasp map is not tied to a single discretization primitive. It may be a graph over stable placements, a graph over placement–grasp pairs, an implicit graph induced by local optimizers, a tree of reachable in-hand states, or a partition of pose space into grasp-equivalence regions. What remains invariant is the role of the map as a compressed representation of where grasp continuity is possible and where explicit grasp changes must occur (Sundaralingam et al., 2018, Levit et al., 16 Jul 2025).

3. Feasibility filters: kinematics, collisions, stability, and contact mechanics

Regrasp maps are only useful insofar as their nodes and edges encode admissible manipulation states. In the humanoid formulation, candidate states are discarded if they are inverse-kinematics-unfeasible, colliding, or unstable, and stability is assessed through the center of mass of the robot–object system,

$G_i=(X_i,o_i)$5

whose vertical projection must lie inside the support polygon with a minimum distance to the boundary above a user-defined threshold (Sanchez et al., 2018). This is a quasi-static center-of-mass-in-support-polygon test rather than a dynamic ZMP or contact-wrench formulation (Sanchez et al., 2018).

For in-hand and extrinsic manipulation, contact mechanics play the analogous pruning role. Stable prehensile pushing models point contacts with Coulomb friction, derives a generalized friction cone for each pusher, and keeps an edge only if the required motion wrench lies inside the pusher’s generalized friction cone, or if the relevant polyhedral wrench sets intersect in the mixed sticking/sliding case (Chavan-Dafle et al., 2017). Fixtureless fixturing specializes this to pushes against environmental contacts under gravity-balancing orientation, yielding a convex polyhedral robust motion cone in object-twist space; membership in that cone is then used as a fast feasibility oracle for tree expansion (Chavan-Dafle et al., 2018). In geometric in-hand regrasp, by contrast, the solver enforces surface-contact and collision constraints through signed-distance conditions on the mesh and uses a conservative small-step condition as a surrogate for grasp stability, without explicit friction or wrench-feasibility constraints (Sundaralingam et al., 2018).

Stable placement generation also serves as a map filter in extrinsic manipulation on a support plane. There, predicted placements are labeled stable by physics simulation if orientation and height do not change significantly after settling, with the reported criteria $G_i=(X_i,o_i)$6 and $G_i=(X_i,o_i)$7 cm, and only high-score placements are retained as graph nodes for downstream shared-grasp computation (Xu et al., 2022). In classical support-pin regrasp, stability and friction are checked analytically through support geometry and friction-cone conditions at the pin contact (Cao et al., 2015).

These variants differ in mechanics, but they agree on one design principle: the map is not merely topological. It is a feasibility-filtered graph whose adjacency is produced only after kinematic, collision, and task-specific physical admissibility checks (Cao et al., 2015, Sanchez et al., 2018, Chavan-Dafle et al., 2017).

4. Domain-specific regrasp maps

Humanoid regrasp planning extends the classical graph to whole-body balance and handover structure. The planner distinguishes single-arm and dual-arm regrasps, includes handover states such as “Start-left End-right” and “Start-right End-left,” and uses an RRT-inspired task-related stability ratio to choose among hand configurations and stances. Simulation and real-world experiments on the 35-DoF HRP5P show that stance and hand sequence strongly affect the set of stable graph paths (Sanchez et al., 2018).

For long and heavy objects, the map can integrate discrete regrasp with continuous support-assisted in-hand motion. The hierarchical planner for repose of long objects formulates the task-level graph with grasp poses as nodes and object poses for edges, and incorporates both regrasping at stably placed states and constrained drooping transitions generated by a height-change criterion. Shared connecting nodes allow switching between the drooping subgraph and the regrasp subgraph within a unified map (Raessa et al., 2021). This is a significant departure from classical maps that only admit release-and-regrasp operations on stable placements.

Bimanual uncertainty-reduction uses a different node semantics again. In the sensorless two-arm method based on flat finger pads, nodes are grasp groups indexed by opening/closing direction vectors $G_i=(X_i,o_i)$8, and edges are bimanual handover transitions executed under admittance control. Each grasp contributes a midplane constraint

$G_i=(X_i,o_i)$9

with $X_i$0, and three approximately orthogonal grasps collectively determine a unique object pose through the intersection of the three grasp-induced planes and axes (Nagahama et al., 28 Mar 2025). Here the regrasp map is not primarily a placement-graph for reorientation; it is a constraint-stacking structure for active reduction of pose uncertainty.

Dual-arm tool-use planning with a suction cup employs two layered regrasp graphs: one for the tool alone and one for the tool–object complex. Nodes are inverse-kinematics-feasible, collision-free grasp states grouped into initial, handover, and goal layers; edges are candidate transitions retained only if RRT-Connect finds a collision-free motion. Backtracking over alternative suction poses couples the suction-pose sub-planner to graph construction (Chen et al., 2019). In simPLE, a related but more perception-centric graph connects a localized table grasp, a set of in-air grasps, and a goal-placement node; shortest-path planning on this hand-to-hand regrasp graph supports high-precision placement with 1 mm clearance (Bauza et al., 2023).

Taken together, these examples show that “regrasp map” is a family resemblance term rather than a single data structure. The family includes balance-aware whole-body graphs, support-assisted graphs, bimanual handover graphs, tool-use graphs, and in-hand reachability trees, each tailored to the dominant constraints of its manipulation regime (Sanchez et al., 2018, Raessa et al., 2021, Chen et al., 2019, Bauza et al., 2023).

5. Learning, perception, and task-dependent connectivity

Recent work shifts part of regrasp-map construction from analytic enumeration to learned prediction. “Learning to Regrasp by Learning to Place” defines a regrasp graph whose nodes are stable poses of objects and whose edges are single grasping-and-placement operations; the crucial learned component is a neural stable placement predictor operating on partial point clouds of the object and surrounding environment (Cheng et al., 2021). The regrasp map is thus expanded by leveraging environmental affordances that would be cumbersome to enumerate manually.

Extrinsic manipulation on a support plane makes this idea explicit. A three-stage framework of orientation generation, placement refinement, and placement discrimination predicts diverse stable placements from point clouds; placements with discriminator score $X_i$1 become graph nodes, and edges connect nodes when a shared grasp exists between them. The reported placement predictor achieves 90.4% accuracy and 81.3% diversity on unseen test objects, and the resulting graph supports sequential pick-and-place steps for goal poses unattainable in a single step (Xu et al., 2022). simPLE similarly combines task-aware grasping, visuotactile localization, and a graph of hand-to-hand regrasps, achieving successful placements into structured arrangements with 1 mm clearance over 90% of the time for 6 objects and over 80% of the time for 11 objects (Bauza et al., 2023).

Task-dependent connectivity can also be computed directly from object motion requirements rather than from stable placements alone. In “Synthesizing Grasps and Regrasps for Complex Manipulation Tasks,” a manipulation plan skeleton is represented as a sequence of constant screw motions; for each screw segment $X_i$2, the method computes a set $X_i$3 of feasible grasps on the object’s point-cloud surface, and the overlaps $X_i$4 determine where a single grasp can be maintained and where regrasps are necessary (Patankar et al., 30 Jan 2025). This formulation turns the regrasp map into a graph over task-segment-specific graspability rather than over a support-surface placement lattice.

Learning also enters the map through feedback-driven online adjustment. For unknown objects grasped with tactile and visual sensing, slip detection and a center-of-mass-based regrasp planner can be reformulated as an online graph of grasp states and regrasp transitions, where nodes store grasp pose, slip label, sensor histories, and robustness score, and edges correspond to slip-conditioned grasp adjustments along the grasp normal. Although the source work does not explicitly define a regrasp map, it provides a natural state-transition structure and reports 76.88% slip-detection accuracy on 5 unknown test objects and a 31.0% increase in grasp success rate over a state-of-the-art vision-based grasping algorithm (Feng et al., 2020).

6. Differentiable regrasp maps and open problems

The most explicit departure from discrete graph search appears in differentiable pose-connectivity models. “Differentiable Object Pose Connectivity Metrics for Regrasp Sequence Optimization” replaces brittle shared-grasp tests with a continuous connectivity score derived from a learned grasp-feasibility energy $X_i$5. For a pair of object poses $X_i$6 and $X_i$7, connectivity is measured by

$X_i$8

and multi-step planning optimizes intermediate poses by minimizing a sequence cost built from these pairwise terms plus a regularizer that discourages bottlenecks (Qin et al., 16 Apr 2026). Adaptive iterative deepening increases the number of intermediate poses only when shorter sequences fail verification, thereby searching for minimum-step regrasp plans in a continuous optimization loop (Qin et al., 16 Apr 2026).

This continuous view clarifies several long-standing limitations of discrete regrasp maps. Classical placement–grasp graphs are sensitive to discretization density, grasp sampling coverage, and narrow shared-grasp regions; the continuous formulation is designed precisely to provide smooth, informative gradients where thresholded set intersections become brittle (Qin et al., 16 Apr 2026). Yet discrete and hybrid formulations remain dominant because they are easy to combine with robot-specific collision checkers, inverse kinematics, and symbolic task skeletons (Wan et al., 2017, Levit et al., 16 Jul 2025).

Across the literature, several limitations recur. Many planners do not provide completeness or optimality guarantees; several rely on quasi-static assumptions, flat support surfaces, or simplified contact models; and learned variants depend on placement-label quality, grasp sampling coverage, or energy-model calibration (Sanchez et al., 2018, Raessa et al., 2021, Xu et al., 2022, Qin et al., 16 Apr 2026). A plausible implication is that future regrasp maps will remain hybrid objects: discrete enough to encode task structure, handovers, and admissible placements, but continuous enough to refine pose choices, absorb perception uncertainty, and expose differentiable connectivity information during optimization (Levit et al., 16 Jul 2025, Qin et al., 16 Apr 2026).