ð45Þ

pyiðkÞ¼ hyiðkÞþ signðwyÞ· j

2 · wx

where pxi ðkÞ and pyi ðkÞ are the coordinates of pi ðkÞ at the x and y axis, respectively。

In addition, if the search time of the robot group failing to detect the plume is over 20s, the robot group will explore the area around the estimated position hi ðkÞ, which can be described by

pi ðkÞ¼ hi ðkÞþ randðÞ · 2k — k ð46Þ

Table 10

The statistical results of search time for 3 robots based on 50   runs。

Cases Index CFPSO PSO CPSO WUI-45 WUII PSO-IM LPSO

Case 1 success%a 100 4 6 2 34 80 100

mean_timeb 162。51 991。53 990。29 995。90 837。40 602。15 289。79

std_timec 18。76 43。99 42。04 29。01 265。65 264。16 71。55

p timed – 6。63E—20⁄  f 9。12E—20⁄ 4。73E—20⁄ 1。74E—18⁄ 6。80E—18⁄ 1。95E—17⁄

rank e 1 6 5 7 4 3 2

Case 2 success% 98 54 32 32 20 86 94

mean_time 201。82 860。28 894。94 917。18 894。69 398。28 348。87

std_time 158。12 176。30 187。32 149。54 243。62 324。99 216。94

p time – 1。08E—16⁄ 2。53E—17⁄