Long-Horizon Multi-Robot Rearrangement

• Long-horizon multi-robot rearrangement is a domain focused on planning and executing sequences of coordinated object and robot reconfigurations over extended time horizons.
• Key methodologies include Rubik Table abstractions, hypergraph decompositions, and layered logical planning to reduce joint search complexity and enhance task efficiency.
• Empirical benchmarks in simulated and hardware settings demonstrate improvements in execution time, plan efficiency, and robustness across diverse environments such as warehouses, homes, and factories.

Long-horizon multi-robot rearrangement encompasses the computational and algorithmic foundations for planning and executing sequences of object relocations or robot reconfigurations involving multiple robot agents over extended temporal horizons. The field addresses high-dimensional, tightly coupled task and motion spaces, requiring scalable abstractions and coordination frameworks to ensure success in complex environments such as homes, warehouses, factories, or construction sites. State-of-the-art solutions integrate symbolic reasoning, powerful combinatorial representations, trajectory optimization, and self-adaptive mechanisms, with rigorous evaluation in simulated and hardware settings.

1. Formal Problem Definitions and Objective Criteria

Long-horizon multi-robot rearrangement problems are formally specified by a tuple describing:

• An environment $\mathcal{E}$ comprising $N$ robots $R = \{R_1, \ldots, R_N\}$, $M$ (potentially labeled) movable objects $O = \{o_1, \ldots, o_M\}$, and fixed structures.
• A state space $S$ representing the joint configuration space $\{q_t^{(r)}\}$ of all robots and the states (poses, occupancy) of all objects at time $t$.
• Action spaces $A_r$ for each robot, including pick-and-place, open/close, delivery, or handoff primitives; atomic joint actions $a_t = \{a_t^{(r)}\}$.
• High-level instructions $I$ (often structured as language commands or formal task grammars).
• The objective to decompose $I$ into a sequence of $K$ subtasks $T = \{T_1, \ldots, T_K\}$, assign and schedule them over the robot team (with possible parallelism), and produce physically and logically feasible joint trajectories that maximize task success rate, minimize makespan, and reduce plan length or cumulative execution cost.

Evaluation is typically via

• Task success rate (fraction of trials completing all subtasks).
• Subtask completion rate.
• Makespan or wall-clock time.
• Plan efficiency, e.g., number of pick-and-place operations or execution length, often with explicit reward functions that penalize failure, plan length ($\lambda$), and execution time ($\mu$) (Yuan et al., 28 Mar 2025).

2. Algorithmic Abstractions and Decomposition Schemes

Scalability is achieved through combinatorial abstractions that reduce joint search complexity:

Rubik Table and High-Dimensional Shuffle Abstractions: The Rubik Table framework treats large-scale object or agent rearrangement as a series of row/column/slice shuffles, providing sharp upper bounds on the number of moves required. For an $n \times n$ Rubik Table, at most $2n$ shuffles suffice for colored sorting, and $3n$ for fully labeled sorting. These results generalize to higher dimensions, with $(2^R-1)n^{R-1}$ slice shuffles for $R$-dimensional arrays, translating directly into constant-factor-optimal stack and multi-robot motion plans in grid environments (Szegedy et al., 2020).

Hypergraph Decomposition: Traditional rearrangement planners suffer exponential scaling because they represent every possible assignment of robots to objects in a composite graph. Hypergraph-based planners instead encode only atomic task modes (robot-alone, object-alone, robot-holding-object), yielding $O(RO)$ vertices and $O(R^2O)$ hyperarcs for $R$ robots and $O$ objects—exponential reductions compared to composite-mode graphs. Transitions (pick, place, handoff) are modeled as directed hyperarcs, supporting efficient extraction of feasible action sequences (Motes et al., 2022).

Logical and Partial-Order Layering: Many solvers employ layered or partial-order decompositions over the induced dependency graph (DG) of the rearrangement task, assigning subtasks to robots as soon as their prerequisites are satisfied. Layered "peeling" handles non-monotonic dependencies and cyclic entanglements, using specialized strategies (e.g., swaps, buffer-introducing) for cycles in the DG (Zhang et al., 9 Dec 2025).

3. Planning and Coordination Architectures

Several coordination paradigms dominate the literature:

Self-Reflective and Self-Evolving Planning: REMAC (Yuan et al., 28 Mar 2025) exemplifies a vision-language-based framework where robots decompose high-level language instructions using LLMs and VLMs, conduct pre-/post-condition checks in a closed loop, and accumulate "reflections" (diagnoses of plan failures or inefficiencies) to iteratively synthesize improved task decompositions. After convergence, subtasks are partially ordered for maximally parallel assignment. Coordination proceeds via blackboard systems for task requests and dynamic bipartite matchings for robot-task allocation.

Three-Layered Task and Motion Planning: Hypergraph planners such as DaSH (Motes et al., 2022) follow a separation of concerns:

• Task-space hypergraph search yields a skeleton with minimal assignment constraints.
• Motion-space grounding samples feasible configurations and short trajectory segments within each task mode.
• A transition-extended search refines the solution to resolve inter-agent conflicts, with feedback mechanisms for constraint insertion or lazy refinement.

Sampling+Optimization for Continuous-Time Collaboration: For highly articulated and temporally coupled assembly problems, hybrid strategies augment task-logic decomposition with kinematic sampling (for handover events), nonlinear optimization for contact constraints, and bi-directional space-time RRTs for path generation in robot-object configuration × time spaces. Iterative decomposition into object-wise subproblems, with dynamic freezing/unfreezing of robots and objects, enables scalability to $>100$ parts and $>10$ robots (Hartmann et al., 2021).

Dual-Arm and Multi-Arm Synchronization: Dedicated frameworks for 2-arm (or $k$-arm) rearrangement, such as SDAR (Zhang et al., 9 Dec 2025) and MODAP (Gao et al., 2024), tightly couple combinatorial layered skeletons, systematic multi-arm grasp and motion sampling (often accelerated with GPU SIMD kernels), and continuous trajectory optimization honoring dynamics (velocity, acceleration, jerk limits). Candidates are ranked via collision-free feasibility and cost scores, with asynchronous fallback and tie-breaking for intractable subproblems.

4. Empirical Benchmarks and Evaluation Metrics

Systematic benchmarking is integral to validating methods:

System / Setting	Success Rate	Subtask Completion	Efficiency Gain	Coverage
REMAC/Multi-Robot (Yuan et al., 28 Mar 2025)	43%	81%	$+$52.7% exec. eff.	RoboCasa, 4 task types, $>50$ objects
SDAR (Zhang et al., 9 Dec 2025)	100%	–	$10{-}30$\% fewer actions	40 test cases, up to 18 objects, 2 UR-5e arms
MODAP (Gao et al., 2024)	–	–	$21.8$s makespan ($-44\%$ BL)	$n{=}6\ldots18$ objects, 2 arms, tabletop

Key conclusions include that reflective evolution (planning $\to$ execution $\to$ reflection) reduces plan redundancy and increases subtask reliability, that multi-robot parallelism yields substantial speedups, and that GPU-accelerated layered planners maintain near-real-time response for complex tasks.

5. Scalability, Limitations, and Generalization

Method scalability relies on abstraction strength (hypergraphs, Rubik tables), careful subproblem decomposition, and parallelism. For example, stack rearrangement using fat Rubik tables achieves $O(nd)$ optimality for $n$ stacks of depth $d$ with a buffer, provided $d$ is subpolynomial in $n$ (Szegedy et al., 2020). In construction assembly domains, iterative object-wise planning yields practical compute times even for $n\approx100$ (Hartmann et al., 2021).

Limitations include:

• Dependence on robust low-level controllers—failures or inaccuracies can cascade through high-level plans.
• Centralized blackboard or scheduling architectures may not scale or generalize to distributed heterogeneous teams.
• Text-buffer-based reflection may degrade performance for large-scale, nuanced logs (Yuan et al., 28 Mar 2025).
• Even quadratic hypergraph task representations may be impractical for $R,O\gg 100$ without further compression (Motes et al., 2022).
• Simulated benchmarks may not fully capture real-world issues such as sensor noise, unmodeled contacts, or runtime uncertainties.

6. Extensions, Open Challenges, and Theoretical Perspectives

Research continues toward:

• $k$-arm and heterogeneous multi-agent generalizations with synchronous and asynchronous execution models, leveraging maximal matching and conflict sampling techniques (Zhang et al., 9 Dec 2025, Gao et al., 2024).
• Hierarchical/hybrid decompositions and implicit (on-demand) expansion of constraint graphs to support orders of magnitude more objects or robots.
• Integrating robust uncertainty management, e.g., via multi-hypothesis IK sampling or probabilistic collision models (Gao et al., 2024).
• Generalizing abstractions (e.g., Rubik Tables) to three-dimensional rearrangement, transport, and fully-coupled multi-modal coordination (Szegedy et al., 2020).

Theoretical advances establish that combinatorial abstractions (Rubik Tables, hypergraphs) deliver constant-factor optimality, completeness, and polynomial time construction for otherwise intractable instances. A plausible implication is that further reductions in empirical runtime will hinge upon adaptive abstraction selection and online decomposition strategies.

7. Concluding Synthesis

Long-horizon multi-robot rearrangement synthesizes techniques from task and motion planning, combinatorial optimization, and self-reflective reasoning to address scalable autonomous coordination in high-dimensional, dynamic domains. Recent frameworks such as REMAC, hypergraph planners, SDAR, and MODAP demonstrate substantial improvements in efficiency and robustness by integrating symbolic decomposition, layered continuous planning, parallel execution, and adaptive self-evolution (Yuan et al., 28 Mar 2025, Motes et al., 2022, Zhang et al., 9 Dec 2025, Gao et al., 2024, Szegedy et al., 2020, Hartmann et al., 2021). Progress in this domain continues to be driven by advances in abstraction, algorithmic design, and empirical validation on complex rearrangement and assembly tasks.