Cooperative Behaviours with Swarm Intelligence in Multirobot Systems for Safety Inspections in Underground Terrains

Table 7

QLACS Example I navigational analytical solution.

Starting state: 𝐹; Potential states: 𝐷, 𝐸, 𝐺; (1) Use (2), 𝜂𝐹,𝐷=1, 𝜂𝐹,𝐸 = 1, 𝜂,𝐺 = 1; (2) Use (3), 𝐿𝑘 = 1, Δ𝜏^𝑘(𝐹,𝐷)=2/1=2, Δ𝜏^𝑘(𝐹,𝐸)=2, Δ𝜏^𝑘(𝐹,𝐺)=2; (3) Use (4), 𝜏𝐹,𝐷=(1−0.01)∗0.01+2=2.0099=2.01, 𝜏𝐹,𝐸=2.01, 𝜏𝐹,𝐺=2.01; First pheromone update; 𝐹𝐺𝐸𝐶0.012.012.01𝐷𝐴𝐵2.010.010.010.01; (4) Use (5) 𝑤(𝐹,𝐷)= [𝜏𝐹,𝐷]^𝛼[𝜂𝐹,𝐷]^𝛽=(2.01)^3=8.12, 𝑤(𝐹,𝐸)=8.12, 𝑤(𝐹,𝐺)=8.12; Sum = 𝑤(𝐹,𝐷)+𝑤(𝐹,𝐸)+𝑤(𝐹,𝐺)=24.36; 𝑃𝑟()=𝑤𝐹,𝐷=sum8.1224.36=0.33, 𝑃𝑟(𝐹,𝐸)=0.33, 𝑃𝑟(𝐹,𝐺)=0.33; Probabilities; 𝐶0𝐹𝐺𝐸00.330.33𝐷𝐴𝐵0.3300; (5) Use (6); 𝐻0𝐶0𝐹𝐺𝐸00.330.33𝐷𝐴𝐵0.3300; Call Rand; Rand = 0.07, Rand falls in state 𝐸. Roulette wheel selects 𝐸 as the next state, end of roulette wheel.; (6) Update trail: 𝐹, 𝐸

Current state: 𝐸; Potential states: 𝐵, 𝐷, 𝐺; (1) Use (2), 𝜂𝐸,𝐵=1/2, 𝜂𝐸,𝐷=1/2, 𝜂𝐸,𝐺=1; (2) Use (3), 𝐿𝑘=(𝐹−𝐸−𝐷)=1+2=3, 𝐿𝑘=(𝐹−𝐸−𝐵)=1+2=3, 𝐿𝑘=(𝐹−𝐸−𝐺)=1+2=3; Δ𝜏^𝑘=23=0.67; (3) Use (4), 𝜏𝐸,𝐵=(1−0.01)∗2.01+0.67=2.66, 𝜏𝐸,𝐷=2.66, 𝜏𝐸,𝐺=2.66; Second pheromone update; 𝐹𝐺𝐸𝐶0.012.662.01𝐷𝐴𝐵2.660.012.660.01; (4) Use (5) 𝑤(𝐸,𝐵)= (2.66)^3∗(1/2)^2=4.71, 𝑤(𝐸,𝐷)=4.71, 𝑤(𝐸,𝐺)=(2.66)^3∗(1)^2=18.82; Sum = 4.71+4.71+18.82=28.24; 𝑃𝑟()=𝑤𝐸,𝐵=sum4.7128.24=0.17, 𝑃𝑟(𝐸,𝐷)=4.7128.24=0.17, 𝑃𝑟(𝐸,𝐺)=18.8228.24=0.67; Probabilities; 𝐶0𝐹𝐺𝐸00.670𝐷𝐴𝐵0.1700.17; (5) Use (6); 𝐻0𝐶0𝐹𝐺𝐸00.670𝐷𝐴𝐵0.1700.17; Call Rand; Rand = 0.9, Rand falls in state 𝐷. Roulette wheel selects 𝐷 as the next state, end of roulette wheel.; (6) Update trail: 𝐹, 𝐸, 𝐷