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This research exposes a critical flaw in multi-robot coordination algorithms where standard pairwise approximation methods frequently select suboptimal exploration plans compared to exact evaluations. The study demonstrates that minimizing reconstruction error does not guarantee better plan selection, revealing significant performance gaps when higher-order robot interactions are ignored. These findings are vital for developers of autonomous systems aiming to optimize coverage and efficiency without incurring the computational cost of full joint evaluations.
Pairwise Approximation Can Select the Wrong Multi-Robot Plan
arXiv:2609.29929v1 Announce Type: new Abstract: Multi-robot coordination methods often score a joint plan from singleton and pairwise terms, leaving out the terms that involve three or more robots. We measure the plan-selection regret of two pairwise approximations to delivered coverage using frozen multi-robot trajectories. For each four-robot plan on an indoor exploration benchmark, replaying all 16 robot subsets gives the exact delivered-coverage set function $F$. From the same subset values we compute two pairwise scores: the exact order-2 M\"obius truncation $F_2$, which depends only on the singleton and pair values, and an equal-weight least-squares two-additive fit $G$. Ranking by $F_2$ instead of $F$ changes the selected plan on six of seven maps at the 15 m candidate-generation range in each of two candidate families, with regret up to 0.337 of map coverage. Switching to $G$ reduces the regret but still changes the selection on three of seven maps in each family. The additive score $F_1$, which keeps only the singleton terms, selects the exact winner on six of seven maps in one family and four of seven in the other, against one of seven for $F_2$. We also find that lower average reconstruction error does not guarantee lower selection regret.
Abstract:Multi-robot coordination methods often score a joint plan from singleton and pairwise terms, leaving out the terms that involve three or more robots. We measure the plan-selection regret of two pairwise approximations to delivered coverage using frozen multi-robot trajectories. For each four-robot plan on an indoor exploration benchmark, replaying all 16 robot subsets gives the exact delivered-coverage set function $F$. From the same subset values we compute two pairwise scores: the exact order-2 Möbius truncation $F_2$, which depends only on the singleton and pair values, and an equal-weight least-squares two-additive fit $G$. Ranking by $F_2$ instead of $F$ changes the selected plan on six of seven maps at the 15 m candidate-generation range in each of two candidate families, with regret up to 0.337 of map coverage. Switching to $G$ reduces the regret but still changes the selection on three of seven maps in each family. The additive score $F_1$, which keeps only the singleton terms, selects the exact winner on six of seven maps in one family and four of seven in the other, against one of seven for $F_2$. We also find that lower average reconstruction error does not guarantee lower selection regret.
6 pages, 4 figures, 1 table. Accepted at the IROS 2026 Workshop on Intelligent Information Gathering. Code: this https URL
Robotics (cs.RO); Multiagent Systems (cs.MA)
arXiv:2609.29929 [cs.RO]
(or arXiv:2609.29929v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.29929 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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