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Wang et al. Intell Robot 2023;3(4):538-64 I http://dx.doi.org/10.20517/ir.2023.30 Page 11 of 27

Figure 7. Cooperative search decision-making process for multi-UAV systems based on the idea of MPC.

∗
∗
U ( | ) = {U ( | ), U ( | ), , U ∗ ( | )}
∗
1 2
= arg min J( ( ), U( | ))
U( | )
. .
(19)
( )
 ( + +1 | ) = F ( + | ), ( + | )



  ( + | )}
( + | ) = { 1 ( + | ), 2 ( + | ), ,
 ( | ) = ( )


 = 0, 1, , − 1

where U ( | ) = { ( | ), ( +1 | ), , ( + −1 | )} istheoptimalsetofthecontrolinputsequenceinfu-
∗
∗
∗
∗

ture for i-th UAV, and ( + | ) is the corresponding optimal control input at time + . Finally, by using the
∗

∗
firsttermoftheoptimaldecisionsetasthesystemoptimalcontrolinput ( | ) = { ( | ), ( | ), , ∗ ( | )}
∗
∗
1
2
at time and guiding the UAV swarm to perform a one-step search, the cooperative search decision-making
process for the current step can be completed.
4.2. Objective function
Considering that no actual search actions occurred during the estimation of the search results in prediction,
the virtual search process of future steps is based on the premise that no targets are found in each step.
4.2.1. Index of search effectiveness
The index of search effectiveness reflects the focus on the grid cells with a high existence probability of the
target, which is defined as:
 


1 ∑ ∑  ∏ ∏ [ ] 
( ) = · 1 − − ( + | )· (20)

 

=1 =1  ∈Ω 
 ( + | ) ∈ 
where − ( + | ) is the estimation of target probability before the detection occurs at time + during the

virtual search process with the updating method, as shown in Equation (10).
In addition, ∈ (0, 1) is the influence coefficient of the step q in future. In order to balance search effec-