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Bundle Length Tradeoffs in Decentralized Multi-Robot Task Allocation Under Degraded Communications

James Lott, Vahraz Honary

arXiv:2609.06273v1cs.ROcs.MA

TL;DR

Bundle length’s role in the MinSum–MinMax tradeoff and the transfer of nominal settings under packet loss are not established. The paper compares three allocators across bundle lengths and communication conditions; deeper bundles trade lower MinSum cost for higher MinMax cost under ideal communication, while packet loss changes the MinSum-preferred region for ACBBA and PI.

  • Problem

    It is unresolved whether bundle length changes the MinSum–MinMax response within an allocator and whether a nominally selected bundle length remains performance-preferred under degraded communication.

    Source: §I · p. 1

  • Method

    The study compares ACBBA, PI, and HIPC across six bundle lengths in 300 paired ten-target scenarios under ideal communication and 25% independent Bernoulli loss, using cross-fitting to assess transfer.

    Source: §I · p. 2

  • Results

    Under ideal communication, B = 1 to 12 trades MinSum reductions (19.0%, 23.0%, 31.8%) for MinMax increases (45.6%, 94.3%, 67.6%) across ACBBA, PI, and HIPC; packet loss shifts ACBBA and PI’s MinSum preference.

    Source: A. Objective-Specific Bundle Depth · p. 3, §V · p. 5

  • Takeaways & Limitations

    Bundle length should be reported together with its configuration objective and communication condition.

    Source: §V · p. 5

    The study is limited to grid-based simulation with four homogeneous robots, static known targets, three allocators, six bundle lengths, and one independent packet-loss level; additional-load extensions are exploratory.

    Source: C. Limitations · p. 5

Abstract

from arXiv · show

Bundle length B is commonly fixed when configuring multi-task multi-robot task allocation (MRTA) algorithms. MinSum and MinMax are known to favor different task distributions, but the role of B in this objective tradeoff has not been systematically characterized. Additionally, degraded-communication evaluations also often retain settings selected under ideal communication, leaving whether nominal bundle-length tuning transfers under message loss unresolved. We examine both questions for ACBBA, PI, and HIPC across six bundle lengths in 300 paired ten-target Collaborative Visit scenarios under ideal communication and 25% Bernoulli packet loss. Under ideal communication, increasing B from 1 to 12 reduces MinSum cost by 19.0%, 23.0%, and 31.8% for ACBBA, PI, and HIPC, respectively, while increasing MinMax cost by 45.6%, 94.3%, and 67.6%. Under packet loss, the lowest-mean MinSum setting shifts from B = 12 to B = 2 for ACBBA and PI. Repeated paired cross-fitting shows that retaining the ideal-network setting incurs held-out MinSum penalties of 14.4% and 7.2%, respectively, and increases MinMax cost by 30.0% and 41.8% relative to the loss-conditioned MinSum setting. HIPC retains a deep MinSum operating region, while the MinMax setting remains stable for all three allocators. Experiments at two additional target loads reproduce the ACBBA and PI MinSum shifts.

I. INTRODUCTION

Bundle length links route construction to the tradeoff between aggregate efficiency and final-robot completion, while its response under degraded communication remains unresolved. The study characterizes that tradeoff across allocators and tests whether bundle settings selected under ideal communication transfer under packet loss.

I. INTRODUCTION

  • MinSum emphasizes aggregate route cost, whereas MinMax emphasizes completion of the final robot; spatial consolidation can favor the former while degrading the latter.This motivates examining whether bundle depth induces the same distinction within decentralized allocators.Source: §I · p. 1
  • Prior degraded-communication evaluations often retain nominal settings, but do not establish whether bundle-length response changes within an allocator or quantify configuration-transfer costs.The unresolved question is whether a setting selected under one communication condition remains performance-preferred under another.Source: §I · p. 1
  • The primary experiment compares six bundle lengths on 300 paired ten-target scenarios under ideal delivery and 25% independent Bernoulli loss.Repeated paired cross-fitting separates configuration selection from evaluation.Source: §I · p. 2
  • Bundle growth exchanges aggregate route efficiency for parallel completion, with workload concentration and held-out objective-transfer analysis supporting the characterization.The study examines this tradeoff across ACBBA, PI, and HIPC.Source: §I · p. 2
  • Under 25% packet loss, the MinSum-preferred bundle region shifts for ACBBA and PI, with held-out transfer costs and additional-load checks.The introduction frames the robustness check as scoped to two additional target loads.Source: §I · p. 2

A. Objectives

The section defines aggregate effort and makespan as the two route objectives, then applies a common per-robot bundle-depth bound while leaving task selection to each allocator’s native procedure.

A. Objectives

  • JΣ is the MinSum route cost, or total effort, and Jmax is the MinMax route cost, or makespan.The team is R and L_i denotes the grid steps taken by robot i before mission completion.Source: A. Objectives · p. 2

B. Bundle Length

  • For every allocator, the same constraint |P_i| ≤ B bounds each robot’s active ordered future-task list, while native logic determines which tasks occupy the available positions.ACBBA and PI use their native marginal procedures; HIPC first constructs a local team allocation with sequences capped at B.Source: B. Bundle Length · p. 2
  • When fewer than B uncompleted tasks remain, the bound is nonbinding, making B = 12 effectively unrestricted in the five- and ten-target experiments.The common bound therefore controls bundle depth only when enough tasks remain.Source: B. Bundle Length · p. 2

C. Mission Design

The study holds the allocators and simulator conditions fixed while varying bundle length and communication, then uses paired comparisons and cross-fitting to assess response and transfer.

C. Mission Design

  • Four homogeneous robots perform ten-target Collaborative Visit missions on a 19 × 19 obstacle-free grid, with ideal delivery or independent 25% packet loss per receiver.The allocators share the motion planner, scheduler, allocation triggers, and completion logic; non-bundle parameters remain fixed.Source: C. Mission Design · p. 2

D. Experimental Design

  • Each of 300 ten-target instances is tested across three allocators, six bundle lengths, and two communication conditions, yielding 10,800 primary runs.Separate five- and twenty-target campaigns use 25 paired scenarios each and are not pooled with the primary data.Source: D. Experimental Design · p. 2

E. Response and Transfer Analysis

  • Bundle-length response is reported as percentage change from B = 1, while communication transfer compares ideal-network references with loss-conditioned references.Paired bootstrap intervals and repeated paired ten-fold cross-fitting separate configuration selection from held-out evaluation.Source: E. Response and Transfer Analysis · p. 3

A. Objective-Specific Bundle Depth

Under ideal communication, deeper bundles reduce aggregate route effort but increase makespan for all three allocators; task and movement workload also become more concentrated.

A. Objective-Specific Bundle Depth

  • B = 12 is the lowest-mean MinSum setting and B = 1 the lowest-mean MinMax setting for all three allocators; evaluating MinSum references raises MinMax cost by 45.6% for ACBBA, 67.6% for HIPC, and 94.3% for PI.After excluding B = 1, the full-sample MinMax penalties remain 42.7%, 59.6%, and 75.0%, respectively.Source: A. Objective-Specific Bundle Depth · p. 3
  • From B = 1 to B = 12, MinSum effort falls 19.0% for ACBBA, 23.0% for PI, and 31.8% for HIPC, while MinMax makespan rises 45.6%, 94.3%, and 67.6%, respectively.The response curves show this deeper-bundle tradeoff across the three allocators.Source: Figure 1 · p. 3, A. Objective-Specific Bundle Depth · p. 3
  • From B = 1 to B = 12, target-workload Gini rises from 0.23 to 0.39 for ACBBA, 0.23 to 0.56 for HIPC, and 0.21 to 0.58 for PI, consistent with the MinSum–MinMax separation.Movement-workload Gini rises over the same range for all three allocators.Source: A. Objective-Specific Bundle Depth · pp. 3–4

B. Effects of Packet Loss

Under packet loss, ACBBA and PI shift their lowest-mean MinSum setting to shallow bundles, while HIPC continues to favor deep bundles; held-out transfer confirms costs for retaining ideal-network settings.

B. Effects of Packet Loss

  • Under loss, ACBBA and PI reach their lowest-mean MinSum at B = 2 rather than B = 12, while HIPC continues to favor the deep-bundle region.For ACBBA, effort degradation relative to ideal communication rises from 19.7% at B = 1 to 64.7% at B = 12; for PI it rises from 32.7% to 78.1%.Source: B. Effects of Packet Loss · p. 4
  • Retaining the ideal MinSum reference under loss incurs held-out MinSum penalties of 14.4% for ACBBA and 7.2% for PI, and raises MinMax cost by 30.0% and 41.8%, respectively, relative to B = 2.Cross-fitting selected (Bideal, Bloss) = (12, 2) in 498 of 500 ACBBA folds and all 500 PI folds.Source: B. Effects of Packet Loss · p. 4
  • HIPC’s loss surface is nearly flat from B = 8 to B = 12, and MinMax-specific references remain B = 1 in both network conditions for every allocator.For HIPC, training-fold selection alternates between B = 8 and B = 12 without held-out benefit from retuning.Source: B. Effects of Packet Loss · p. 4

C. Sensitivity to Target Load

Additional five- and twenty-target experiments largely preserve the ideal-communication objective response and reproduce the ACBBA and PI MinSum shift under packet loss.

C. Sensitivity to Target Load

  • At five and twenty targets, all three allocators continue to favor deep bundles for MinSum and shallow bundles for MinMax under ideal communication, with only negligible changes in exact lowest-mean settings.At twenty targets, PI’s MinSum means are nearly identical at B = 8 and B = 12, while ACBBA’s MinMax reference shifts by only 0.32 steps.Source: C. Sensitivity to Target Load · p. 4
  • At five, ten, and twenty targets, packet loss moves ACBBA and PI toward shallow MinSum bundles, while HIPC remains in the deep-bundle region.MinMax remains stable at five and ten targets; at twenty, ACBBA shifts from B = 3 to B = 2, while PI’s 0.2-step difference is effectively a tie.Source: C. Sensitivity to Target Load · p. 4

A. Interpretation of the Bundle-Length Response

Bundle length creates an objective trade-off: deeper bundles support aggregate route efficiency but can concentrate work, while packet loss changes the preferred MinSum operating region for ACBBA and PI. HIPC retains a deep MinSum region, and degraded-communication evaluations should distinguish fixed-configuration robustness from condition-specific performance.

A. Interpretation of the Bundle-Length Response

  • Increasing B permits longer, spatially coherent routes that reduce aggregate movement while concentrating tasks and travel on fewer robots, with workload Gini supporting this interpretation.MinSum and MinMax favor systematically different operating regions.Source: A. Interpretation of the Bundle-Length… · p. 4
  • With packet loss, ACBBA and PI reach their lowest mean MinSum costs at B = 2, consistent with deeper bundles leaving more stale commitments unresolved after dropped messages.Both allocators use exchanged bid or significance information to resolve competing assignments.Source: A. Interpretation of the Bundle-Length… · p. 4
  • Under packet loss, HIPC retains a nearly flat MinSum operating region from B = 8 to B = 12, although its absolute effort increases.Its local team prediction and plan consensus may reduce dependence on every explicit bundle exchange.Source: A. Interpretation of the Bundle-Length… · p. 5

B. Implications for Communication-Robust Evaluation

  • For ACBBA and PI under MinSum, the ideal-network reference is dominated under the tested channel, while HIPC and primary-experiment MinMax preferred regions transfer despite absolute degradation.A fixed-B experiment measures robustness of a nominal configuration, not best performance attainable under degradation.Source: B. Implications for… · p. 5
  • Degraded-network benchmarks should distinguish nominal-configuration transfer from condition-specific performance and report the tested bundle range, objective, selection condition, and response.Condition-specific best-performance claims should use separate selection data from the relevant communication regime or demonstrate transfer of the nominal response.Source: B. Implications for… · p. 5

C. Limitations

Communication degradation changes the bundle-length relationship: ACBBA and PI incur held-out MinSum penalties when retaining ideal-network settings, while HIPC retains a deep MinSum region. The study’s conclusions are bounded by its grid-based simulation setting and exploratory target-load extensions.

C. Limitations

  • The study is limited to grid-based simulation with four homogeneous robots, static known targets, three allocators, six bundle lengths, and one independent packet-loss level.The 5- and 20-target extensions use 25 scenarios per condition and provide exploratory rather than confirmatory evidence.Source: C. Limitations · p. 5

V. CONCLUSION

  • Under ideal communication, increasing B from 1 to 12 reduces MinSum cost by 19.0% for ACBBA, 31.8% for HIPC, and 23.0% for PI, while increasing MinMax cost by 45.6%, 67.6%, and 94.3%, respectively.Workload concentration is consistent with longer, consolidated routes linking these responses.Source: §V · p. 5
  • Under 25% packet loss, retaining the ideal-network setting incurs held-out MinSum penalties of 14.4% for ACBBA and 7.2% for PI; HIPC retains a deep MinSum region, and ACBBA and PI shifts recur at two additional target loads.Absolute HIPC performance still degrades, and the affected objectives and practical magnitudes vary across target loads.Source: §V · p. 5
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