Stable Rearrangement Planning (SRP)

• Stable Rearrangement Planning (SRP) is a framework for planning manipulation sequences that safely transition objects between configurations while ensuring physical stability and collision-free placements.
• SRP formulations range from tabletop pick-and-place to nonprehensile pushing, incorporating constraints like buffer usage, mode transitions, and objective functions to optimize action cost and travel distance.
• SRP integrates combinatorial optimization with physical simulation and graph search to manage dependencies and stability, improving practical manipulation in cluttered and dynamic environments.

Searching arXiv for recent and foundational papers relevant to Stable Rearrangement Planning and adjacent rearrangement formulations. arXiv search query: "stable rearrangement planning tabletop rearrangement stacking mobile manipulation" Stable Rearrangement Planning (SRP) is typically understood as the problem of finding a sequence of manipulation actions that moves a set of objects from an initial arrangement to a goal arrangement while all intermediate configurations are physically stable, collision constraints are respected, and dependency or precedence constraints induced by blocking or stacking are satisfied (Hu et al., 2024). Across tabletop rearrangement, cluttered nonprehensile manipulation, multi-layer 3D piles, dense storage systems, and online packing, the common requirement is that the system moves through stable, realizable intermediate states rather than purely symbolic reorderings (Song et al., 2019, Xu et al., 2023, Gao et al., 12 Jul 2025).

1. Formal scope and problem classes

In a standard tabletop formulation, an arrangement is

$A = \{p_1, p_2, \dots, p_n\},$

where each $p_i$ is the pose of object $i$ on the table, and an arrangement is valid iff no objects collide with each other and no object collides with the table boundary (Hu et al., 2024). A system state may explicitly include both robot pose and object poses,

$s = \{p_r, p_1, p_2, \ldots, p_n\},$

with $p_r$ denoting either an end-effector configuration for a stationary robot or a base pose for a mobile robot, and actions are pick-and-place primitives that move one object at a time (Hu et al., 2024).

A broader 3D formulation is the Multi-layer Object Rearrangement on a Tabletop (MORT) problem, where the workspace is $\mathcal W \subset \mathcal W_t \times [0,H]$, objects are generalized cylinders with identical height $h$, each object pose is $x_i \in SE(3)$, and a pick-and-place action

$a = (i, x_i', x_i'')$

is allowed only when the moved object is unblocked from above, the target pose is stable and collision-free, and the resulting arrangement remains stable and collision-free (Xu et al., 2023). MORT seeks a feasible plan

$P = (a_1,a_2,\dots,a_k)$

with minimum number of actions (Xu et al., 2023).

SRP also appears in nonprehensile and abstracted forms. In nested nonprehensile rearrangement, the joint configuration space is

$p_i$0

and plans alternate between Stable, Transit, and Push modes with legal mode changes (Song et al., 2019). In scene rearrangement planning, the state can be a fully observable grid tensor $p_i$1, and actions are atomic object translations and rotations on a 2D floor-plane abstraction (Wang et al., 2021). This suggests that SRP is best treated as a family of rearrangement formulations sharing a stability requirement, rather than a single canonical state representation.

2. Stability models and feasible intermediate states

In planar, non-stacking tabletop rearrangement, stability is often implicit. STRAP assumes that objects are placed directly on the table without stacking, an action is valid only if it does not cause any collisions upon placing the object, and a valid arrangement has no collisions with other objects or workspace boundaries (Hu et al., 2024). Under these assumptions, every intermediate state is a stable, collision-free table-supported configuration.

In nonprehensile rearrangement, stability is expressed as a mode condition: stable means that all the objects rest on the surface and the robotic arm is idle, transit means collision-free arm motion with static objects, and push means simultaneous pushing of a subset of objects under quasi-static physics (Song et al., 2019). The planning architecture accepts only legal mode changes, and pushing segments are rejected if the final state of a receding-horizon segment deviates from the desired waypoint by more than a tolerance $p_i$2 (Song et al., 2019).

MORT and SIPP treat stability as a black-box physical predicate evaluated by simulation. After each action in a candidate plan, the system is simulated for a fixed duration; if any object moves beyond a small threshold from its expected pose, the arrangement is deemed unstable (Xu et al., 2023). SIPP then adds a constraint forbidding the unstable prefix, so stability becomes a set of cutting planes over the discrete ordering problem (Xu et al., 2023).

Other SRP variants instantiate stability differently. In online 3D bin packing, an item is stable if its center-of-gravity uncertainty set $p_i$3 lies entirely inside its support polygon $p_i$4, where $p_i$5 is derived from Load Bearable Convex Polygons (LBCPs) (Gao et al., 12 Jul 2025). In Dynamic Buffer planning, stack stability is determined by a predefined lookup table over functional categories, and each base supports at most one object (Barghi et al., 26 Sep 2025). In ReloPush, stable pushing is enforced indirectly by selecting a minimum turning radius $p_i$6 so that Dubins paths respect quasi-static stable pushing constraints (Ahn et al., 2024). Taken together, these formulations show that SRP stability can be encoded by direct support constraints, simulation-based validation, category-level compatibility rules, or conservative kinematic surrogates.

3. Dependencies, buffers, and non-monotonicity

A central SRP difficulty is that object order is not arbitrary. In STRAP, dependencies are represented implicitly by goal availability: if an object’s goal position is available, it is moved there; if the goal position is not available, it is moved to a buffer location (Hu et al., 2024). All buffers are internal to the table, buffer capacity is limited implicitly by free space, and the search avoids immediately moving the same object again or re-buffering it to a region that was already possible earlier in the search tree (Hu et al., 2024).

MORT makes dependency structure explicit. Start pose contact constraints require that an object above another must be removed first; goal pose vertical dependency constraints and start-goal collision constraints determine whether an object must be buffered (Xu et al., 2023). The ILP variables $p_i$7 encode removal order and $p_i$8 encode whether object $p_i$9 must be moved through a buffer, so the total number of moves is

$i$0

Thus minimizing action count is equivalent to minimizing buffer usage (Xu et al., 2023).

Dynamic Buffer extends the buffer concept from static placements to temporary, movable stacks. When an object $i$1 is moved, all objects stacked upon it and their transitive dependents move accordingly, maintaining their relative stacking relationships (Barghi et al., 26 Sep 2025). Static stacking uses an object as a buffer but freezes the base until its top is clear; dynamic stacking instead turns the stack into a movable cluster that can be transported as a unit (Barghi et al., 26 Sep 2025).

Dense storage results show that the need for non-monotone rearrangement can depend on workspace topology itself. For an $i$2 grid with $i$3, there is an offline storage and retrieval solution that avoids relocations if and only if $i$4; for $i$5, there exist instances with no rearrangement-free solution (Geft et al., 28 May 2025). This suggests that, in SRP, precedence structure is not only object-induced but also geometry-induced.

4. Algorithmic paradigms

A large branch of SRP uses informed graph search with lazy geometric realization. STRAP is an enhanced A*-based algorithm that improves state representation by including robot pose, employs incremental goal attempts with lazy evaluation at each iteration, uses TRLB as a fast local rearrangement solver, and prunes nodes whose $i$6 exceeds the cost of the current best complete plan (Hu et al., 2024). The mobile extension further introduces multiple relocation actions, manipulation regions, implicit and explicit objects, state re-exploration, and tree rewriting so that multiple operations can be executed from a single standing position instead of forcing the robot to move to the closest available location for each pick and place operation (Hu et al., 24 May 2025).

A second family couples combinatorial optimization with physical verification. SIPP formulates the discrete ordering problem as an ILP with permutation variables $i$7 and buffer flags $i$8, then interleaves solving with pyBullet-based stability checking and instability cuts that remove unsafe prefixes from the solution space (Xu et al., 2023). The paper characterizes this as a stability-constrained branch-and-cut pattern (Xu et al., 2023).

A third family uses search over macro-actions or receding-horizon dynamics. NRS recursively searches over subsets of remaining objects and permutations of nested chains, using NESTED-PUSH macro-actions and an offline MDP-based local policy for pushing one or more similar objects (Song et al., 2019). dhRRT instead treats rearrangement as kinodynamic planning with dynamic planning horizons, a heuristic $i$9, a progress threshold $s = \{p_r, p_1, p_2, \ldots, p_n\},$0, and replanning after short execution segments, so continuous contact-rich rearrangement is handled without explicit enumeration of stable placements (Ren et al., 2022).

Graph-based and learned formulations add further variants. ReloPush constructs a Push-Traversability graph whose vertices are pushing poses and whose edges are optimal, kinematically feasible, and stable transitions between them (Ahn et al., 2024). Structural Concept Learning (SCL) uses a Graph Attention Network to infer a dependency DAG for multi-level structures and then topologically sorts that graph to obtain a placement order (Kulshrestha et al., 2023). MO-SeGMan combines an ATSP with precedence constraints, Selective Guided Forward Search (SGFS), and subgoal refinement to handle highly constrained, non-monotone rearrangement (Tuncer et al., 3 Nov 2025). At the most combinatorial extreme, Rubik Tables abstract dense rearrangement as row, column, or slice shuffles and yield constant-factor optimal algorithms for stack rearrangement and dense multi-robot grids (Szegedy et al., 2020).

Learning-based search also appears in explicitly stochastic settings. PEARL models scene rearrangement as an MDP and trains an apprentice policy with expert-assisted MCTS, while the OBPP SRP module uses MCTS to decide unpacking and rollout packing order and then applies $s = \{p_r, p_1, p_2, \ldots, p_n\},$1 to shorten the resulting unpack, pack, and repack sequence (Wang et al., 2021, Gao et al., 12 Jul 2025).

5. Objective functions and cost models

SRP objective functions vary sharply across formulations. In STRAP, the goal is to minimize total cost consisting of travel cost and manipulation cost; for a mobile robot, travel cost between two object poses is measured by distance along the table boundary between the corresponding closest boundary points (Hu et al., 2024). The mobile manipulation extension generalizes this to multiple relocation actions, where cost accumulates over sequences of standing locations and the number of operations executed at each standing location (Hu et al., 24 May 2025).

MORT uses a different objective: minimum number of actions. Because every object must be removed from its start pose at least once and every buffered object incurs one additional move, the objective becomes minimizing $s = \{p_r, p_1, p_2, \ldots, p_n\},$2 (Xu et al., 2023). NRS, by contrast, defines

$s = \{p_r, p_1, p_2, \ldots, p_n\},$3

so the planner favors nested pushes that reduce total end-effector path length (Song et al., 2019).

Dynamic Buffer planning is explicitly travel-centric. For an action $s = \{p_r, p_1, p_2, \ldots, p_n\},$4, the action cost is

$s = \{p_r, p_1, p_2, \ldots, p_n\},$5

and the total objective is

$s = \{p_r, p_1, p_2, \ldots, p_n\},$6

which includes returning the manipulator to its home position (Barghi et al., 26 Sep 2025). The paper emphasizes that dynamic stacks may increase the number of pick-and-place actions while still reducing total manipulator travel (Barghi et al., 26 Sep 2025).

In reinforcement and online packing settings, cost is reward-shaped rather than directly encoded as path length. PEARL uses Distance $s = \{p_r, p_1, p_2, \ldots, p_n\},$7, Arrival $s = \{p_r, p_1, p_2, \ldots, p_n\},$8, Leave $s = \{p_r, p_1, p_2, \ldots, p_n\},$9, and Success $p_r$0 as reward components (Wang et al., 2021). The OBPP SRP module evaluates rollouts with

$p_r$1

so rearrangement is guided jointly by predicted future value and final utilization (Gao et al., 12 Jul 2025). These differences are not superficial: they determine whether the planner prefers shorter travel, fewer actions, fewer buffers, better utilization, or lower failure risk.

6. Empirical patterns across domains

In tabletop A*-based rearrangement, STRAP can provide superior solutions compared to orla*, in a shorter time, for both stationary and mobile robots (Hu et al., 2024). The mobile extension reports that its planner outperforms existing planners both in terms of solution quality and planning time (Hu et al., 24 May 2025). Dynamic Buffer further reports reductions in manipulator travel cost of 11.89% in dense scenarios with a stationary robot and 5.69% in large, low-density settings with a mobile manipulator (Barghi et al., 26 Sep 2025).

In nonprehensile and kinodynamic rearrangement, the same pattern appears with different primitives. NRS reduces the traveled distance of the end-effector compared to mono-object pushing and other baselines, and on the real robot it is substantially faster as the number of objects grows (Song et al., 2019). dhRRT improves robustness under limited time budgets; on the reported real-robot grasping task with $p_r$2, dhRRT achieves $p_r$3 success versus $p_r$4 for kdRRT and $p_r$5 for r-kdRRT, and on relocating with $p_r$6 it achieves $p_r$7 versus $p_r$8 and $p_r$9 respectively (Ren et al., 2022).

For multi-layer structures and nonholonomic pushing, scaling claims are also strong. SIPP readily scales to optimally solve complex rearrangement problems of 3D structures with over 60 building blocks, with solution quality significantly outperforming natural greedy best-first approaches (Xu et al., 2023). ReloPush exhibits orders of magnitude faster runtimes and lower execution times and fewer losses of object contact than baselines, with planning success rates of 89% at 6 objects and 86% at 8 objects in the reported scenarios (Ahn et al., 2024).

Learning-based approaches show mixed but important empirical behavior. PEARL’s apprentice reaches Success Rate $\mathcal W \subset \mathcal W_t \times [0,H]$0 and Length $\mathcal W \subset \mathcal W_t \times [0,H]$1, compared with RL at Success Rate $\mathcal W \subset \mathcal W_t \times [0,H]$2 and Length $\mathcal W \subset \mathcal W_t \times [0,H]$3, while the PEARL expert reaches Success Rate $\mathcal W \subset \mathcal W_t \times [0,H]$4 and Length $\mathcal W \subset \mathcal W_t \times [0,H]$5 (Wang et al., 2021). In online 3D bin packing, SRP improves utilization to about 80.5%, the MCTS search succeeds in 83.9% of cases, and A* refinement reduces sequence length from 5.8 to 4.0 operations (Gao et al., 12 Jul 2025). SCL reports 95.1% success and 98.7% completion on unseen multi-level structures (Kulshrestha et al., 2023). MO-SeGMan reports feasible motion plans in all evaluated benchmark cases and consistently faster solution times and superior solution quality compared to its baselines (Tuncer et al., 3 Nov 2025).

7. Scope, limitations, and research directions

A recurring misconception is that SRP refers only to overhand pick-and-place on a single tabletop. The literature includes stable-mode nonprehensile pushing, grid-based scene rearrangement, multi-layer 3D pile reconfiguration, dense storage and retrieval, and rearrangement modules embedded in online packing (Song et al., 2019, Wang et al., 2021, Xu et al., 2023, Geft et al., 28 May 2025). Another misconception is that stability must always be written as explicit force-balance inequalities; many practical systems instead use table-support constraints, categorical lookup rules, or black-box simulation with cutting planes (Xu et al., 2023, Barghi et al., 26 Sep 2025, Gao et al., 12 Jul 2025).

At the same time, most current formulations remain highly specialized. STRAP and the mobile tabletop planners assume planar, non-stacking scenes, overhand grasps, rigid objects, known geometries, and deterministic execution (Hu et al., 2024, Hu et al., 24 May 2025). MORT abstracts away robot kinematics and assumes enough buffers on the tabletop, NRS focuses on monotone tasks and similar objects, Dynamic Buffer uses a coarse functional taxonomy with one-object-per-base, and PEARL uses a 2D occupancy abstraction without explicit tipping or friction (Xu et al., 2023, Song et al., 2019, Barghi et al., 26 Sep 2025, Wang et al., 2021).

The literature explicitly points toward several extensions. STRAP notes that handling stacking would require 3D stable placement checks and richer support representations; MORT discusses integrating motion planning and graspability; SCL identifies independent substructures for future multi-manipulator task allocation; MO-SeGMan names multi-robot extensions as future work; and the OBPP SRP framework discusses cost-aware operation modeling and adaptive search budgeting (Hu et al., 2024, Xu et al., 2023, Kulshrestha et al., 2023, Tuncer et al., 3 Nov 2025, Gao et al., 12 Jul 2025). This suggests that the next phase of SRP research is likely to be hybrid: global combinatorial reasoning over dependencies and buffers, coupled to physically grounded stability validation and task-and-motion realization in richer 3D, uncertain, and multi-robot environments.