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

Figure 1. Definition of mission grid.

Figure 2. Definition of flight directions of UAV.

targets move freely in and perceive and evade the UAVs that are searching for them. Based on this definition,
a cooperative search task requires UAVs to discover and track all targets using a cooperative search method [24] .

2.1. Motion model of UAVs
Mission area is divided into × grid cells with as the side length of a single cell, which are used as
mission grid or UAV motion grid and denoted as Ω . It is agreed that the UAV has limited movement between

mission grid cells, where the cell with m-th row and n-th column in Ω is marked as . Figure 1 shows the

specific representation of the mission grid.

Based on this definition, the multi-UAV system executing cooperative search tasks can be considered as a com-
plete control system. The state variables of the UAVs at time can be represented as ( ) = { 1 ( ), 2 ( ),
( )}, where ( ), = 1, 2, , represents the position at time in Ω of i-th UAV. Each UAV

, ( ), ,
can move to the adjacent cells or stay in the current cell every motion cycle of Δ time. Figure 2 shows the
definition of flight directions of UAVs.

The control input of i-th UAV at time can be represented as ( ) ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}, where =
1, 2, , ; flight direction ”9” represents staying in the current cell, and flight directions 1-8 represent moving
one step towards adjacent cells. Therefore, the control input of the multi-UAV system at time can be repre-
( )}, and the state model of the multi-UAV system can be recorded as
sented as ( ) = { 1 ( ), 2 ( ), ,
( +1 ) = F( ( ), ( )), where F(·) is the state transition function of the system.