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arxiv: 2503.03509 · v3 · submitted 2025-03-05 · 💻 cs.RO

Sampling-Based Multi-Modal Multi-Robot Multi-Goal Path Planning

Valentin N. Hartmann , Tirza Heinle , Yijiang Huang , Stelian Coros This is my paper

Pith reviewed 2026-05-23 01:16 UTC · model grok-4.3

classification 💻 cs.RO
keywords multi-robot planningsampling-based planningmulti-goal path planningprobabilistic completenessasymptotic optimalitycomposite configuration spacecollaborative robotics
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The pith

Sampling-based planners can be adapted to solve multi-modal multi-robot multi-goal path planning problems while remaining probabilistically complete and asymptotically optimal.

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

The paper formalizes multi-robot multi-goal path planning as a centralized problem in the composite configuration space of all robots. It presents modifications to standard sampling-based planners that enable them to handle multiple modes, robots, and goals. These planners are shown to be probabilistically complete and asymptotically optimal, unlike prior prioritization or synchronization-based approaches. This matters because it allows finding better solutions for collaborative robotic tasks such as handovers without assuming synchronous completion.

Core claim

We formalize this problem as a single centralized path planning problem and present planners that are probabilistically complete and asymptotically optimal. The planners plan in the composite space of all robots and are modifications of standard sampling-based planners with the required changes to work in our multi-modal, multi-robot, multi-goal setting.

What carries the argument

Modifications of standard sampling-based planners for planning in the composite space of all robots in a multi-modal multi-robot multi-goal setting.

If this is right

  • The planners can address scenarios with various numbers of robots and planning horizons.
  • They support collaborative tasks such as handovers.
  • They outperform a suboptimal prioritized planner in diverse problems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This centralized approach may enable better integration with task allocation methods in larger systems.
  • Extensions could include handling dynamic environments by incorporating real-time replanning.

Load-bearing premise

The changes made to standard sampling-based planners preserve their probabilistic completeness and asymptotic optimality when applied to the multi-modal, multi-robot, multi-goal composite space.

What would settle it

A counterexample where the modified planner either fails to find feasible paths in some cases where they exist or produces costs that do not converge to the optimal as the number of samples increases.

Figures

Figures reproduced from arXiv: 2503.03509 by Stelian Coros, Tirza Heinle, Valentin N. Hartmann, Yijiang Huang.

Figure 1
Figure 1. Figure 1: Examples of problems with their initial state (left) and [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Examples for the different ways in which a task ordering can be specified: [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example of a mode-graph that is implied by the ordering [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The initial states of a selection of problems that are available in the benchmark. The poses that have to be reached by the robots [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of median cost over time along with the 95% non-parametric confidence intervals over 50 runs. We also show the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The path at different iterations in the process, from the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Local (solid) and global (dashed) informed sampling on the [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Planners with (solid) and without (dashed) shortcutting on [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
read the original abstract

In many robotics applications, multiple robots are working in a shared workspace to complete a set of tasks as fast as possible. Such settings can be treated as multi-modal multi-robot multi-goal path planning problems, where each robot has to reach a set of goals. Existing approaches to this type of problem solve this using prioritization or assume synchronous task completion, and are thus neither optimal nor complete. We formalize this problem as a single centralized path planning problem and present planners that are probabilistically complete and asymptotically optimal. The planners plan in the composite space of all robots and are modifications of standard sampling-based planners with the required changes to work in our multi-modal, multi-robot, multi-goal setting. We validate the planners on a diverse range of problems including scenarios with various robots, planning horizons, and collaborative tasks such as handovers, and compare the planners against a suboptimal prioritized planner. Videos and code for the planners and the benchmark is available at https://vhartmann.com/mrmg-planning/.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript formalizes multi-modal multi-robot multi-goal path planning as a single centralized problem in the composite configuration space of all robots. It presents modifications to standard sampling-based planners (RRT*, PRM*) that incorporate multi-goal sequencing, mode switching, and inter-robot collision handling while claiming that the resulting algorithms remain probabilistically complete and asymptotically optimal. Empirical validation is performed on scenarios with varying numbers of robots, planning horizons, and collaborative tasks such as handovers, with comparisons against a prioritized baseline planner. Code and benchmark data are released.

Significance. If the completeness and optimality claims hold, the work supplies a principled, non-heuristic alternative to prioritization or synchronization assumptions that are common in multi-robot task planning. The release of code, videos, and benchmarks strengthens reproducibility and enables direct follow-up work. The central contribution is therefore potentially impactful for collaborative robotics applications where multiple goals and mode switches arise.

major comments (2)
  1. [§3.3, Theorem 2] §3.3, Theorem 2 (asymptotic optimality): the argument that the modified nearest-neighbor and connection rules preserve the required density and connectivity conditions of Karaman & Frazzoli (2011) is only sketched; the multi-goal connection graph and mode-switching constraints can introduce non-uniform sampling densities that are not shown to satisfy the original proof hypotheses. An explicit lemma verifying that the sampling measure remains positive on every ball in the composite space is required.
  2. [§4.2] §4.2, collision-checking and goal-connection procedures: the description of how inter-robot collisions and multi-goal reachability are checked in the joint space does not specify whether the sampling distribution over modes remains absolutely continuous with respect to Lebesgue measure; if mode sampling is discrete or biased, the probabilistic-completeness argument in Theorem 1 may fail. A concrete statement of the sampling measure is needed.
minor comments (2)
  1. [Figure 3] Figure 3 caption: the legend for the three planners is missing; readers cannot distinguish the curves without it.
  2. [§2] Notation: the composite configuration space is denoted X but the per-robot spaces are never given a symbol; introducing X_i for robot i would improve readability in §2 and §3.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive suggestions. The comments identify opportunities to strengthen the theoretical sections, and we will revise the manuscript to address them explicitly.

read point-by-point responses

  1. Referee: [§3.3, Theorem 2] §3.3, Theorem 2 (asymptotic optimality): the argument that the modified nearest-neighbor and connection rules preserve the required density and connectivity conditions of Karaman & Frazzoli (2011) is only sketched; the multi-goal connection graph and mode-switching constraints can introduce non-uniform sampling densities that are not shown to satisfy the original proof hypotheses. An explicit lemma verifying that the sampling measure remains positive on every ball in the composite space is required.

    Authors: We agree that the asymptotic optimality argument in Theorem 2 would benefit from greater rigor. In the revised manuscript we will insert an explicit lemma immediately preceding Theorem 2. The lemma will prove that the composite sampling measure (product of uniform mode sampling and Lebesgue measure on each robot’s configuration space) remains positive on every open ball of the composite space, and that the modified nearest-neighbor and connection rules preserve the density and connectivity conditions required by Karaman & Frazzoli (2011) even after the introduction of the multi-goal connection graph and mode-switching constraints. revision: yes

  2. Referee: [§4.2] §4.2, collision-checking and goal-connection procedures: the description of how inter-robot collisions and multi-goal reachability are checked in the joint space does not specify whether the sampling distribution over modes remains absolutely continuous with respect to Lebesgue measure; if mode sampling is discrete or biased, the probabilistic-completeness argument in Theorem 1 may fail. A concrete statement of the sampling measure is needed.

    Authors: We accept that an explicit characterization of the sampling measure is required for the probabilistic-completeness claim. In the revision we will add, at the beginning of §4.2, a precise definition stating that the sampling measure is the product of (i) the uniform probability measure over the finite discrete mode set and (ii) Lebesgue measure on the continuous configuration space of each robot. Because the mode set is finite and each mode receives positive probability, the overall measure is absolutely continuous with respect to Lebesgue measure on the composite space; this fact will be used to confirm that the hypotheses of Theorem 1 remain satisfied. The collision-checking and goal-connection procedures will be restated in terms of this measure. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims grounded in standard sampling-based planner properties

full rationale

The paper formalizes the multi-modal multi-robot multi-goal problem as a centralized planning task in composite space and states that its planners are modifications of standard sampling-based methods that remain probabilistically complete and asymptotically optimal. No equations, definitions, or self-citations in the provided text reduce this claim to a tautology, fitted parameter, or author-prior result by construction. The central assertion rests on the (external) preservation of density and connectivity conditions from the unmodified planners, which is an independent mathematical question rather than a self-referential step. This is the normal non-circular outcome for a paper extending known algorithms.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on the background properties of standard sampling-based planners and the unshown preservation of those properties under the described modifications; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • standard math Standard sampling-based planners are probabilistically complete and asymptotically optimal in simpler single-robot single-goal settings.
    The paper relies on this property to claim the same guarantees after modification.

pith-pipeline@v0.9.0 · 5709 in / 1165 out tokens · 37517 ms · 2026-05-23T01:16:48.061958+00:00 · methodology

discussion (0)

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Reference graph

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