CFPSO versus PSO 171 0 7。63E—6 CFPSO versus CPSO 171 0 7。63E—6

CFPSO  versus WUI-45 171 0 7。63E—6 CFPSO versus WUII 171 0 7。63E—6

CFPSO versus PSO-IM 171 0 7。63E—6 CFPSO versus LPSO 171 0 7。63E—6

a    Rþ: The sum of ranks for the cases in which the first algorithm outperforms the second one。

b    R— :  The sum of ranks for the  cases in which the  second  algorithm outperforms the first   one。

CFPSO    PSO    CPSO   WUI− 45   WUII  PPSO− IM LPSO

CFPSO    PSO    CPSO   WUI− 45   WUII  PPSO− IM LPSO

CFPSO    PSO    CPSO   WUI− 45   WUII  PPSO− IM LPSO CFPSO    PSO    CPSO   WUI− 45   WUII  PPSO− IM LPSO

Fig。 14。 The consumed energy in case 1, case 2, case 3, case 4, case 5, and case 6 based on 3 robots with 50 runs。

obtained by using wind information and concentration information, and the parameter ‘‘sampling time’’ refers to discrete decision-making time。 The parameters j and k are used to control the quality of data received and the search region, respec- tively。 The reader can understand the parameters used in Table 7 by referring to [23,24]。 The parameters b; c; a; a and x given in Table 8 are used to guarantee the finite-time convergence of the motion control while the parameters vmax and xmax are utilized to limit the maximum linear velocity and angular velocity of robots。

It is worth mentioning that the robot group will search for the odor clues along the direction of y axis from the initial positions (right-up corner) to the target positions (right-down corner) in the initial stage。 Once the odor clues are detected by any robot, the proposed CFPSO algorithm will start to run。 Moreover, we use a circle where the real position of the odor source is regarded as a center with a predefined radius 1 m as one of termination conditions, which means that the search task is terminated if any robot enters the circle。 The maximal search time 1500 s is used as another termination condition。 As an example, the motion process of the robot group controlled by the proposed CFPSO algorithm is illustrated in Fig。 12。

In Fig。 12(a), the initial positions  of  the  robot  group  are  set  at  the  right-up  corner  in  the  search  region。  In  Fig。  12(b),  and Fig。 12(c), the robot group controlled by ui ðtÞ traces the plume and moves along the plume according to the probable posi- tions of the odor source hi ðkÞ。 In Fig。 12(d), the robot group finds the real odor source。 From 0 s to about 40 s, the robots keep the predefined position (80 m, 0 m) of the odor source。 After about 40 s, the robot group  detects  the  odor  clues,  and  then  the proposed CFPSO algorithm starts to run。 Correspondingly, the prediction  errors  and  average  prediction  errors  based  on  50 runs  of  five   robots  for  the  position  of  the   odor  source  are   shown  in   Fig。  13   where  the   real  position  of   the  odor  source      is