rank 1 6 5 7 4 3 2

Average rank 1。11 5。22 5。22 6。88 4。55 3 1。88

a   success%: The value denotes the success rate among 50 runs。

b   mean_time: The value is the mean of search time among 50   runs。

c   std_time: The value is the standard error of search time among 50 runs。

d p time: The value is a p value of a two-sample Wilcoxon rank sum test for search time between  the  CFPSO  algorithm  and  the  other comparison algorithms in the corresponding column。 The p value being smaller means that the results obtained by the CFPSO algorithm are significant compared with the results achieved by the other    algorithms。

e   rank: Composite ranking is applied to all of algorithms, which is evaluated by the descending order of success rate and the ascending order of search

time。

f

m:  The  difference  between  two  samples  is  significant  at  a  level  a ¼ 0:05。

where randðÞ is a random number on the internal ½0; 1]; k is a parameter that can adjust the search range。 Once the robot group detects the chemical concentration, a new pi ðkÞ will be calculated in the light of   (45)。

5。2。Motion process of a group of    robots

In this subsection, we will adopt the Farrell’s odor model to build a simulation environment whose parameters are shown in Table 6, and test the search efficiency of a multi-robot system coordinated by the proposed continuous-time FPSO algo- rithm (CFPSO)。 In Table 7, it should be pointed out that the parameters c1   and c2   are to weight the probable positions

Table 11

The statistical results of search time for 5 robots based on 50   runs。

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

Case 1 success%a 100 10 4 8 72 90 100

mean_timeb 165。06 983。61 993。15 975。72 718。74 616。85 267。54

std_timec 24。55 53。38 37。68 85。26 256。87 206。78 53。14

p timed