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Page 10 of 27 Wang et al. Intell Robot 2023;3(4):538-64 I http://dx.doi.org/10.20517/ir.2023.30

response map varies with the UAVs’ detection results. Denote the grid of detection response map as Ω , in

which the cell with m-th row and n-th column is denoted as and the corresponding response value is
denoted as . The update of the detection response map after time can be classified into the following
three situations based on the detection results of every UAV:

(i) i-thUAVfindsatargetin ( +1 ) withthesituationthat hasthesameregionaldefinitionas ( +1 )

in Ω ( +1 ):

1 (16)
( +1 ) = ( ) + ( ) · [1 − ( )]

where 1 ∈ (0, 1) is the sensitivity coefficient of detection response. In order to avoid missed detections,
the response value is sensitive to detected targets and insensitive to undetected targets. The increase in
response value is related to the detection probability of UAVs.

(ii) i-th UAV finds nothing in ( +1 ) with the same situation above:

[ 1 ]

( +1 ) = 1 − ( ) 1 · ( ) (17)

(iii) is outside the area of the detection range of any UAV:

( +1 ) = 2 · ( ) (18)
where 2 ∈ (0, 1) is the attenuation coefficient of response value.

4. COOPERATIVE SEARCH PATH PLANNING
In order to improve the path planning efficiency of the search problem, a cooperative search method CSMTPE
based on MPC is designed with the basic idea of time-domain rolling optimization, which transforms the
large time-domain search problem into a continuous short-term path planning problem and guides the UAVs
to search and track targets faster and more effectively [26] .

4.1. MPC method
According to the idea of MPC, by predicting and evaluating the search behavior in a limited period of time un-
der different search decisions, the control input required by the current UAV swarm can be determined based
on the current environment information. Figure 7 shows the cooperative search decision-making process for
multi-UAV systems based on the idea of MPC.

Itisassumedthatanoptimizationprocesswillconsiderthecooperativesearchprocessof stepsinfutureand
evaluate the search benefits associated with different control inputs. Denote the search decision set of certain
( | )},
controlinputsinfutureformulti-UAVsystemsattime as U( | ) = {U 1 ( | ), U 2 ( | ), , U ( | ), , U
1≤ ≤ , in which U ( | ) = { ( | ), ( +1 | ), , ( + −1 | )} is the set of the control input sequence
in future for i-th UAV and ( + | ) is the corresponding control input at time + .

Obviously, the quantitative search effectiveness of the search path can be uniquely obtained through an objec-
tive function J(·), which is based on the state ( ) and search decision set U( | ) of the multi-UAV system
at time , and the prediction evaluation process of the search can be achieved. Finally, the optimal search
decision set U ( | ) can be obtained by the optimization model of MPC as follows:
∗