TY - JOUR

T1 - On the Throughput of the Common Target Area for Robotic Swarm Strategies

AU - Passos, Yuri Tavares

AU - Duquesne, Xavier

AU - Soriano Marcolino, Leandro

PY - 2022/7/16

Y1 - 2022/7/16

N2 - A robotic swarm may encounter traffic congestion when many robots simultaneously attempt to reach the same area. This work proposes two measures for evaluating the access efficiency of a common target area as the number of robots in the swarm rises: the maximum target area throughput and its maximum asymptotic throughput. Both are always finite as the number of robots grows, in contrast to the arrival time at the target per number of robots that tends to infinity. Using them, one can analytically compare the effectiveness of different algorithms. In particular, three different theoretical strategies proposed and formally evaluated for reaching a circular target area: (i) forming parallel queues towards the target area, (ii) forming a hexagonal packing through a corridor going to the target, and (iii) making multiple curved trajectories towards the boundary of the target area. The maximum throughput and the maximum asymptotic throughput (or bounds for it) for these strategies are calculated, and these results are corroborated by simulations. The key contribution is not the proposal of new algorithms to alleviate congestion but a fundamental theoretical study of the congestion problem in swarm robotics when the target area is shared.

AB - A robotic swarm may encounter traffic congestion when many robots simultaneously attempt to reach the same area. This work proposes two measures for evaluating the access efficiency of a common target area as the number of robots in the swarm rises: the maximum target area throughput and its maximum asymptotic throughput. Both are always finite as the number of robots grows, in contrast to the arrival time at the target per number of robots that tends to infinity. Using them, one can analytically compare the effectiveness of different algorithms. In particular, three different theoretical strategies proposed and formally evaluated for reaching a circular target area: (i) forming parallel queues towards the target area, (ii) forming a hexagonal packing through a corridor going to the target, and (iii) making multiple curved trajectories towards the boundary of the target area. The maximum throughput and the maximum asymptotic throughput (or bounds for it) for these strategies are calculated, and these results are corroborated by simulations. The key contribution is not the proposal of new algorithms to alleviate congestion but a fundamental theoretical study of the congestion problem in swarm robotics when the target area is shared.

KW - robotic swarm

KW - common target

KW - throughput

KW - congestion

KW - traffic control

U2 - 10.3390/math10142482

DO - 10.3390/math10142482

M3 - Journal article

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 14

M1 - 2482

ER -