Digitization Can Stall Swarm Transport: Commensurability Locking in Quantized-Sensing Chains
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arXiv
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| Autori principali: | , , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915702782296064 |
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| author | Cappetto, Caroline N. Messinger, Penelope Yasumura, Kaitlyn S. Rothman, Miro Do, Tuan K. Wang, Gao Liu, Liyu Austin, Robert H. Li, Shengkai Phan, Trung V. |
| author_facet | Cappetto, Caroline N. Messinger, Penelope Yasumura, Kaitlyn S. Rothman, Miro Do, Tuan K. Wang, Gao Liu, Liyu Austin, Robert H. Li, Shengkai Phan, Trung V. |
| contents | We present a minimal model for autonomous robotic swarms in one- and higher-dimensional spaces, where identical, field-driven agents interact pairwise to self-organize spacing and independently follow local gradients sensed through quantized digital sensors. We show that the collective response of a multi-agent train amplifies sensitivity to weak gradients beyond what is achievable by a single agent. We discover a fractional transport phenomenon in which, under a uniform gradient, collective motion freezes abruptly whenever the ratio of intra-agent sensor separation to inter-agent spacing satisfies a number-theoretic commensurability condition. This commensurability locking persists even as the number of agents tends to infinity. We find that this condition is exactly solvable on the rationals -- a dense subset of real numbers -- providing analytic, testable predictions for when transport stalls. Our findings establish a surprising bridge between number theory and emergent transport in swarm robotics, informing design principles with implications for collective migration, analog computation, and even the exploration of number-theoretic structure via physical experimentation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Digitization Can Stall Swarm Transport: Commensurability Locking in Quantized-Sensing Chains Cappetto, Caroline N. Messinger, Penelope Yasumura, Kaitlyn S. Rothman, Miro Do, Tuan K. Wang, Gao Liu, Liyu Austin, Robert H. Li, Shengkai Phan, Trung V. Soft Condensed Matter We present a minimal model for autonomous robotic swarms in one- and higher-dimensional spaces, where identical, field-driven agents interact pairwise to self-organize spacing and independently follow local gradients sensed through quantized digital sensors. We show that the collective response of a multi-agent train amplifies sensitivity to weak gradients beyond what is achievable by a single agent. We discover a fractional transport phenomenon in which, under a uniform gradient, collective motion freezes abruptly whenever the ratio of intra-agent sensor separation to inter-agent spacing satisfies a number-theoretic commensurability condition. This commensurability locking persists even as the number of agents tends to infinity. We find that this condition is exactly solvable on the rationals -- a dense subset of real numbers -- providing analytic, testable predictions for when transport stalls. Our findings establish a surprising bridge between number theory and emergent transport in swarm robotics, informing design principles with implications for collective migration, analog computation, and even the exploration of number-theoretic structure via physical experimentation. |
| title | Digitization Can Stall Swarm Transport: Commensurability Locking in Quantized-Sensing Chains |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2510.17117 |