Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models

Ferdinando Fioretto; Jacob K Christopher; Jinhao Liang; Sven Koenig

REVIEW 4 major objections 5 minor 5 cited by

Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read SMD projects diffusion sampling into feasible multi-robot trajectories.

desk verdict Real empirical gains, but the feasibility guarantee in the text doesn't hold up because Algorithm 2's stopping condition is inverted and the multipliers never update. read the letter →

arxiv 2502.03607 v2 pith:ULMV4MAM submitted 2025-02-05 cs.RO cs.AIcs.LG

Jinhao Liang , Jacob K Christopher , Sven Koenig , Ferdinando Fioretto This is my paper · ORCID

classification cs.ROcs.AIcs.LG

keywords multi-robotmotionplanningdiffusionmodelsconstrainedoptimizationaugmentedLagrangianmethodcollisionavoidancetrajectorygenerationMRMPbenchmark

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to prove that diffusion models can plan for multiple robots simultaneously, not just generate candidate trajectories, if the sampling loop is interleaved with a constrained-optimization projection. It introduces SMD, which alternates score-based denoising with an augmented-Lagrangian project-and-dual-update step, and claims this yields collision-free, kinematically feasible plans where gradient-guided and rejection-sampling diffusion planners fail. The reported experiments back this with near-perfect success rates across a new 4,000-instance benchmark, including 96% success in the hardest dense 9-robot maps. If the claim holds, learning-based planners become a practical option for high-density, unstructured multi-robot environments.

What carries the argument

The central object is the projected diffusion sampler (Algorithm 1) combined with an augmented-Lagrangian dual-ascent projection (Algorithm 2). The projection maps a noisy trajectory to the nearest point in the convex set $\Omega_c$ (start, goal, and velocity limits) while iteratively raising Lagrangian multipliers on the nonconvex inter-robot and obstacle-avoidance residuals $H_a$ and $H_o$, with tolerances $\delta_a$ and $\delta_o$ as stopping criteria. The relaxation replaces inequality constraints by equalities using nonnegative auxiliary variables $d$, which the paper never updates; the theoretical guarantee (Proposition 4.2) covers distance to $\Omega_c$, while Remark 4.3 extends the guarantee to the collision residuals only through the user-defined stopping criterion.

What would settle it

Run SMD on the corridor swap task with tight tolerances ($\delta_a=\delta_o=10^{-4}$), then compute the true collision inequalities $(\pi_i^h-\pi_j^h)^2 \ge (R_a)^2$ and $(\pi_i^h-o_j)^2 \ge (R_o)^2$ directly; if any pair of robots or a robot and an obstacle violates these while the residual check reports success, the stopping criterion is not a certificate of collision-freeness.

Watch

Extended reading notes

Core claim

The paper introduces SMD, a diffusion-based multi-robot motion planner that alternates score-based denoising with a projection operator; each projection solves a Lagrangian relaxation of the MRMP constraints over a convex set of start, goal, and velocity-feasible trajectories, then updates dual variables on the nonconvex collision residuals. The central claim is that this produces trajectories satisfying $\|H_a(\Pi)\| \le \delta_a$ and $\|H_o(\Pi)\| \le \delta_o$ for user-defined tolerances, and empirically yields collision-free, kinematically feasible plans at success rates no other tested learning-based method reaches, including 100% success on corridor swaps, 96% success with 9 robots in dense maps, and a 3.6x success-rate improvement over the prior best in the hardest setting.

Load-bearing premise

The load-bearing premise is that the augmented-Lagrangian dual-ascent loop, which only minimizes over the convex set $\Omega_c$, actually drives the original nonconvex collision inequalities to zero, so that a small residual means a genuinely collision-free trajectory.

Editorial extensions

If this is right

In dense maps with 20 obstacles and 9 robots, SMD reports 96% success, a 3.6x improvement over the best prior method, with a near-zero collision ratio.
In corridor maps, SMD is the only tested method with any successful plans, achieving 100% success on the two-robot swap.
The projection guarantees output within user-set tolerances $\delta_a$ and $\delta_o$ for nonconvex collision residuals, and arbitrarily small distance to the convex constraint set $\Omega_c$.
The introduced benchmark gives 4,000 standardized instances across empty, basic, dense, corridor, shelf, and room maps, with success rate, path length, acceleration, and collision ratio metrics.
Because no rejection sampling or post-hoc repair is needed, SMD's per-sample pipeline is a single forward pass with interleaved projections.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the residual bounds are genuine certificates, the same projection wrapper could be dropped onto any generative trajectory model, not only score-based diffusion, turning them into constrained planners without retraining.
The auxiliary variables $d$ in Eq. (8) are never updated in Algorithm 2; whether the stopping criterion can be fooled by stale $d$ is an open stress test the paper does not run.
The runtime growth (from about 30 seconds for 3 robots to about 550 seconds for 9 robots in dense maps) suggests the dual-ascent projection, not the diffusion sampling, is the bottleneck; warm-started multipliers or learned initialization could be a natural next step.
The 4,000-instance benchmark, with corridor, shelf, and room maps, looks usable as a shared evaluation suite for future MRMP planners, including classical anytime planners compared on the same metrics.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Hey, here's the deal with 2502.03607. The empirical story is strong: SMD beats the baselines by a wide margin across all map types, including the hard 9-robot dense maps where MMD collapses to 27%. On sheer results, this is a useful advance. The benchmark of 4,000 instances is also a real contribution; code is up.

But the theory section does not back up the paper's feasibility claims. Algorithm 2 has a load-bearing bug as written: the while loop continues while \nabla\nu_a < \delta_a, which is backwards (you want to loop until the residual is below tolerance, not while it's below). The multipliers \nu_a and \nu_o are never updated inside the loop, and line 4 uses \nu^*_a,\nu^*_o that are never defined. The auxiliary variables d in Eq. (8) are introduced but never touched again, so the equality relaxation is incomplete. Proposition 4.2's proof relies on Eq. (15), which is asserted without proof, and on a theorem from your prior NeurIPS paper without checking its conditions. Remark 4.3 then claims the output satisfies ||Ha||≤δa etc., but that's exactly what Algorithm 2 doesn't establish. At best, the proposition covers the convex set \Omega_c, not the collision constraints.

The weak theory doesn't kill the empirical result—the trends are monotonic and the success-rate gaps are big—but it means the paper overstates its guarantees. There are also minor issues: no error bars on success rates/path lengths, and calling the benchmark 'the first' is wrong since Shaoul et al. already had practical maps; the paper even evaluates on those later, which undercuts the claim.

Who should read it: people working on learning-based MRMP or constrained diffusion sampling. The method idea—repeated projection with an augmented-Lagrangian dual-ascent loop inside diffusion sampling—is worth taking seriously, but right now the details are too sloppy to reproduce from the text alone.

My call: this deserves a proper peer review, not a desk reject. The empirical core is valuable and the flaws are fixable in revision. But I'd push for a major revision: rewrite Algorithm 2 correctly, either prove the collision-constraint guarantee under the actual nonconvex constraints or cut the Remark 4.3 claim down to what's proven, and add error bars. If the authors fix the algorithm description and keep the results, it could be a solid publication.

Referee Report

4 major / 5 minor

Summary. The paper proposes Simultaneous MRMP Diffusion (SMD), a diffusion-based multi-robot motion planner that alternates denoising steps with a projection operator designed to enforce collision avoidance and kinematic feasibility. The projection is cast as a Lagrangian relaxation over convex constraints (start/goal, velocity) and nonconvex constraints (inter-robot and obstacle avoidance), solved by a dual-ascent procedure (Algorithm 2). The authors claim a feasibility guarantee: the projection output satisfies ||Ha(Π)|| ≤ δa and ||Ho(Π)|| ≤ δo for user-specified tolerances (Remark 4.3). They also introduce a new MRMP benchmark with empty, basic, dense, corridor, shelf, and room maps, and report extensive experiments showing that SMD outperforms standard diffusion (DM), Motion Planning Diffusion (MPD), and Multi-robot Motion Planning Diffusion (MMD), with high success rates and near-zero collision ratios across most settings. Classical baselines (EECBS) are also compared in the appendix.

Significance. If the feasibility guarantee and the experimental results hold, SMD would be an important advance: it would be the first diffusion-based planner to produce collision-free, kinematically feasible multi-robot trajectories in cluttered environments without rejection sampling or post-hoc filtering. The paper ships code, provides a standardized benchmark with 4,000 test instances, and reports consistent, monotonic improvements across all six map types and all robot counts, including a 3.6x success-rate improvement over the prior state of the art in dense 9-robot maps (96% vs. 27%). The sensitivity analysis of the projection scaling factor is a useful addition. However, the theoretical justification is not yet sound: the stated algorithm and proof do not establish the advertised nonconvex feasibility guarantee, and the relaxation with auxiliary variables is not fully specified. The empirical claim is credible on its own, but the paper's central formal contribution—the tolerance-bounded feasibility guarantee—is not supported by the current writeup.

major comments (4)

[§4.3, Algorithm 2] The stopping criterion in Algorithm 2 checks the wrong quantity. The while condition is '∇ν_a < δa and ∇ν_o < δo', but lines 3 and 5 set ∇ν_a and ∇ν_o to H_a(Π̂) and H_o(Π̂), i.e., primal constraint residuals, not the dual gradients. This conflates the dual residual with the primal violation. Moreover, the loop never updates ν_a or ν_o, and line 4 uses ν*_a, ν*_o, which are never defined in the algorithm. As written, the loop terminates immediately if the initial residuals are below tolerance, and it does not implement the dual ascent described in Eq. (12). Consequently, Remark 4.3's claim that the output satisfies ||H_a(Π)|| ≤ δa and ||H_o(Π)|| ≤ δo is not established by the stated procedure.
[§4.3, Eq. (8)-(12)] The auxiliary variables d_a and d_o introduced in Eq. (8) to convert inequalities into equalities are never optimized. The Lagrangian in Eq. (9) and the primal update in Eq. (12a) minimize over Π ∈ Ω_c only, with no minimization or update over d_a, d_o. Thus the equality constraints H_a(Π) = 0 and H_o(Π) = 0 as defined in Eq. (8) are not enforced; the residuals computed in Algorithm 2 are not equality residuals of the relaxed system. Without an update rule for d, the relaxation does not correspond to the original nonconvex inequalities, and a trajectory with small H_a(Π) (interpreted as the inequality violation f(Π) − R_a²) may still violate the original constraints, or the equalities may be infeasible for any Π. The paper should either explicitly minimize over d, or justify why the inequality-violation form is sufficient for the claimed guarantee.
[§4.4 and Appendix B, Proposition 4.2] The proof of Proposition 4.2 is incomplete and does not support Remark 4.3. Eq. (15) asserts the existence of an iteration index Ī and a bound involving ‖F_t‖ without proof, and the conditions of Theorem 5.2 of Christopher et al. (2024) are not verified in the present setting. More importantly, Proposition 4.2 only bounds dist(Π, Ω_c), the distance to the convex set; it says nothing about the nonconvex constraints H_a(Π) and H_o(Π). Remark 4.3's guarantee on nonconvex residuals therefore does not follow from Proposition 4.2. The paper needs either a complete proof that the dual-ascent procedure drives the nonconvex residuals below δ, or a revised claim that clearly separates the convex guarantee from the empirical/heuristic treatment of nonconvex constraints.
[§6.1 and §5, Baseline comparison] The claim in Section 6.1 that 'SMD is the only known method that provides feasible solutions for the largest number of robots in complex environments' is an overclaim relative to the evidence. The paper compares SMD only with DM, MPD, MMD, and (in the appendix) EECBS; other learning-based MRMP or optimization-based planners are not included. Similarly, the contribution stating 'the first benchmark for MRMP evaluation' is contradicted by Section C, which evaluates on maps introduced by Shaoul et al. (2025). These statements should be scaled back to 'among the methods compared' and 'a new benchmark,' respectively.

minor comments (5)

[§2, Related Work] Typo: 'especifically' should be 'especially'.
[Table 4, Shelf Maps, 9 robots] In the Shelf Maps 9-robot rows, the 'C ↓' and 'A ↓' entries appear swapped: the collision-ratio row contains acceleration values and the acceleration row contains collision-ratio values. This makes Table 4 hard to read and should be corrected.
[Figures 9 and 10, Appendix C] The y-axis of the sensitivity analysis plots is labeled 'Gradient,' but the text refers to 'gradient convergence.' Please clarify whether the plotted quantity is the constraint residual, the multiplier gradient, or the norm of the augmented-Lagrangian gradient, since the distinction matters for interpreting the convergence behavior.
[§4.3, Eq. (12c)] Eq. (12c) contains a typo: the update for ν_o is written as 'ν_o^{k+1} = ν_a^k + ρ_o^k H_o(Π^k)', which reuses the subscript 'a' instead of 'o'. The intended update should be ν_o^{k+1} = ν_o^k + ρ_o^k H_o(Π^k).
[§4.2, Eq. (6)-(7)] The nonconvex constraints are written as squared-distance inequalities, but they are not qualified by whether the trajectories are continuous or discretized in time. Please state explicitly whether (6) and (7) are required at every discrete time step h only, or over continuous time, and how the benchmark evaluates collisions between time steps.

Circularity Check

2 steps flagged · score 6.0 of 10

The nonconvex feasibility 'guarantee' in Remark 4.3 is exactly Algorithm 2's stopping condition, and the convex guarantee's proof leans on the authors' prior theorem; the measured benchmark results are independent.

self definitional [Section 4.4, Remark 4.3; Section 4.3, Algorithm 2 (lines 2 and 5)]
"Specifically, SMD ensures the output of the projection operator Π: ||Ha(Π)|| ≤δa, ||Ho(Π)|| ≤δo, for some tolerances δa, δo > 0. (Remark 4.3) ... while ∇ν a < δa and ∇ν o < δo do ... ∇ν a ← Ha( ˆΠ), ∇ν o ← Ho( ˆΠ) (Algorithm 2)."

The claimed guarantee is exactly the loop's exit condition: Algorithm 2 loops while ∇νa < δa and ∇νo < δo, and lines 3 and 5 set those variables to Ha(Π̂) and Ho(Π̂). Therefore any output of the loop satisfies the 'guarantee' by construction; the Lagrangian/dual-ascent derivation in Eqs. (9)-(12) plays no role in establishing it. The residual Ha/Ho is defined in Eq. (8) in terms of auxiliary variables da, do that never appear in Algorithm 2, so the link between this stopping test and the original collision constraints (6)-(7) is asserted, not derived. The theoretical claim is thus a restatement of the termination test rather than a first-principles guarantee.
self citation load bearing [Appendix B.1, proof of Proposition 4.2, Eq. (16)]
"Using Theorem 5.2 in (Christopher et al., 2024), for any i ≥ I, we have: E[Error(U(PΩc(Π^i_t)), Ωc)] ≤ ξ ≤ E[Error(U(Π^i_t), Ωc)]."

Proposition 4.2 is the paper's convex-feasibility guarantee, but its proof is not self-contained: it invokes Theorem 5.2 from the authors' own prior NeurIPS 2024 paper (Christopher, Baek, and Fioretto; the first and last authors overlap with the present paper). The proof also relies on an unproved assertion, Eq. (15), before applying that theorem. Thus the convex guarantee is carried by a self-citation chain rather than derived here; if Theorem 5.2's hypotheses are not met, the guarantee has no independent support in this paper.

full rationale

The empirical evaluation is not circular: SMD's success rates, collision ratios, and path lengths are measured on held-out test instances (Section 5 and Appendix A.3) and compared against external baselines; no parameter is fitted to those test outcomes. The diffusion model is trained on MMD-generated trajectories, but that is data generation, not fitting the target result, and the test instances are separate. Circularity appears in the theoretical support. Remark 4.3 asserts ||Ha(Π)|| ≤ δa and ||Ho(Π)|| ≤ δo as a 'theoretical guarantee,' but Algorithm 2's while condition is exactly '∇νa < δa and ∇νo < δo', with ∇νa and ∇νo assigned Ha(Π) and Ho(Π) inside the loop. Hence the guarantee is the loop's exit test by construction; it does not by itself establish the original nonconvex constraints (6)-(7), especially because the auxiliary variables da and do from Eq. (8) are never updated in Algorithm 2. Additionally, Proposition 4.2's proof relies on Theorem 5.2 from the authors' prior paper (Christopher et al. 2024) without verifying Eq. (15) or the theorem's conditions, making the convex guarantee load-bearing on a self-citation. These issues affect the formal guarantee, not the measured benchmark results, so the circularity is partial rather than total.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The method's load-bearing free choices are the projection tolerances and penalty parameters, which are hand-tuned but unreported in the main text. The theoretical claims rest on an unverified convexity assumption, an unproven nonconvex dual-ascent convergence premise, and a theorem from the authors' prior work. No new physical entities are introduced; the auxiliary slack variables d are mathematical constructs whose treatment is incomplete.

free parameters (4)

Projection tolerances δa, δo = Not reported.
User-defined stopping criteria for the dual-ascent loop (Algorithm 2, Remark 4.3). They set the allowed residual on collision constraints; reported success rates depend on their values, which are not stated.
Penalty scaling factor ζ = 1.05 (recommended).
Multiplicative growth of the augmented penalty in Algorithm 2. Sensitivity analysis (Figures 9-10) shows 1.00-1.09 all converge, but the exact choice affects iteration count and runtime.
Initial penalty weight ρ = Not reported.
Starting augmented Lagrangian penalty in Algorithm 2; never specified, yet it controls how strongly constraints are enforced in early iterations.
Diffusion sampling steps = 25.
Number of denoising steps used in all experiments (Table 1); a hand-chosen hyperparameter of the score-based diffusion model.

assumptions (3)

domain assumption Assumption 4.1: the relaxed MRMP cost L(Π, νa, νo) is continuously differentiable and convex over Ωc.
Stated as 'commonly satisfied' but not verified. Convexity is questionable because the augmented Lagrangian contains squared residuals of nonconvex collision constraints, which are not guaranteed convex over Ωc.
ad hoc to paper Dual ascent on the nonconvex MRMP constraints converges to a point with residuals below the user-specified tolerances.
The paper acknowledges strong duality does not hold, yet relies on Algorithm 2 terminating with ||Ha(Π)|| ≤ δa and ||Ho(Π)|| ≤ δo. No convergence proof is provided for the nonconvex case.
standard math Theorem 5.2 of Christopher et al. (2024) about projected diffusion convergence.
Used as the foundation for Proposition 4.2 (Appendix B). The paper does not show that the conditions of that theorem hold when the projection is implemented via the approximate Lagrangian loop rather than an exact projection onto Ωc.

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Pith. "Pith review of Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models." pith.science (2026). https://pith.science/paper/ULMV4MAM

@misc{pith2026250203607,
  author       = {Pith},
  title        = {Pith review of: Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ULMV4MAM}},
  note         = {Machine review of arXiv:2502.03607}
}

read the original abstract

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes Simultaneous MRMP Diffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments.

Figures

Figures reproduced from arXiv: 2502.03607 by the authors.

**Figure 1.** SMD incorporates a projection operator to enforce constraints within the diffusion process. During sampling, the projection operator iteratively corrects trajectories by mapping them to the nearest feasible points, resulting in final collision-free paths. The infeasible paths are marked with red circles and only occur in the initial random trajectory. In the experiments, the red objects appear at sampling time only,… view at source ↗

**Figure 2.** Examples of random maps used for MRMP experiments, with increasing complexity. Colorful spheres and plates denote the start and goals of robots. White objects indicate obstacles. (a) Corridor Maps. (b) Shelf Maps. (c) Room Maps [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 4.** Results for each method on random maps with three different numbers of robots. Gray bars represents the failure rate, and values on top of the bars indicate average path length per robot. 6. Experiments In this section, we evaluate the performance of various MRMP algorithms using our proposed benchmark. In most cases, regular projection methods cannot be applied to obtain solutions in MRMP due to the huge computati… view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: Trajectories generated by SMD on random maps. maps. Next, we focus on Motion Planning Diffusion (MPD). While it reports near-perfect success rates for the 3-robots setting (the smallest in our benchmark), this approach is highly ineffective when scaled to additional ro…

**Figure 7.** Figure 7: Results for each method on practical maps with three different numbers of robots. Gray bars represents the failure rate, and values on top of the bars indicate average path length per robot. (a) Shelf Maps. (b) Room Maps [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Trajectories generated by SMD on practical maps. is even more noticeable. These results shows the adaptability of the proposed algorithm to multiple environments and challenging scenarios (such as the narrow passages). Finally, [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: Sensitivity analysis of the scaling factor ζ on gradient convergence for inter-agent collision avoidance constraints in ALM-based projection, evaluated for each map with different numbers of robots. The scaling factor ζ determines how the coefficient of the augmented t…

**Figure 10.** Figure 10: Sensitivity analysis of the scaling factor on gradient convergence for obstacle collision avoidance constraints in ALM-based projection, which leads to similar conclusions with inter-agent collision avoidance constraints. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]

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Reference graph

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

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P., and D’Andrea, R

Augugliaro, F., Schoellig, A. P., and D’Andrea, R. Gen- eration of collision-free trajectories for a quadrocopter fleet: A sequential convex programming approach. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1917–1922,

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For collision-free cases, we analyze path length and acceleration

Summary of MRMP Benchmark Instances Map Type Obstacle Variations Number of Robots Variations Start & Goal Variations Number of Instances Empty Maps 25 3 10 750 Basic Maps 25 3 10 750 Dense Maps 25 3 10 750 Corridor Maps 25 1 10 250 Shelf Maps 25 3 10 750 Room Maps 25 3 10 750 Total 4000 For each generated path, we first check for collisions and compute th...

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S is the success rate, L denotes the average path length per robot, A is the average acceleration, and C is the collision ratio (see Section 5)

Additional results for classical algorithms and learning-based algorithms in random maps. S is the success rate, L denotes the average path length per robot, A is the average acceleration, and C is the collision ratio (see Section 5). We omit acceleration and collision information for multi-agent path finding methods, as they assume constant velocities an...

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Additional results for classical algorithms and learning-based algorithms in practical maps. Map Robots Metric EECBS DM MPD MMD Ours Corridor Maps 2 S ↑ 1 0 0 0 1 L ↓ 1.4208 – – – 1.6619 A ↓ – – – – 0.0012 C ↓ – 1 1 1 0 Shelf Maps 3 S ↑ 1 0.1200 0.5960 0.5960 1 L ↓ 1.1697 0.7884 0.8825 0.9371 0.9017 A ↓ – 0.0030 0.0081 0.0030 0.0060 C ↓ – 0.5027 0.2493 0....

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In addition, Table 6 shows evaluation results on practical maps introduced by (Shaoul et al., 2025)

Notably, more challenging tasks typically take longer to solve, thus increasing the average running time. In addition, Table 6 shows evaluation results on practical maps introduced by (Shaoul et al., 2025). SMD still maintains a zero collision rate. These results further confirm the practical applicability and reliability of our approach. In Figures 9 and...

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Additional results for MMD and SMD in maps used in (Shaoul et al., 2025). Map Robots Metric MMD Ours Highways Maps 3 S ↑ 1 1 L ↓ 1.1638 1.1391 A ↓ 0.0026 0.0030 C ↓ 0 0 6 S ↑ 1 1 L ↓ 1.1669 1.1775 A ↓ 0.0028 0.0022 C ↓ 0 0 9 S ↑ 1 1 L ↓ 1.1792 1.1802 A ↓ 0.0028 0.0031 C ↓ 0 0 Conveyor Maps 3 S ↑ 1 1 L ↓ 1.1529 1.1499 A ↓ 0.0030 0.0029 C ↓ 0 0 6 S ↑ 1 1 L ...

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Shaoul, Y ., Mishani, I., Vats, S., Li, J., and Likhachev, M

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