Page 39 - Read Online

Page 6 of 27 Wang et al. Intell Robot 2023;3(4):538-64 I http://dx.doi.org/10.20517/ir.2023.30

( )
 3 3
 − + 2 ·e ,
 1 e e > 0
F = (2)

0, e e ≤ 0


where e is the unit direction vector of the flight direction of i-th UAV, e is the unit direction vector pointing
vertically to the target from the direction of e , is the response amplitude of virtual evasive force B, and
1 and 2 represent the corresponding response distances in straight and vertical directions, respectively.
This assumption reasonably estimates the target’s evasive behavior toward the UAV’s pursuit. The final evasive
virtual force of the moving target can be represented as:

[ ]
∑ ∑

F = = F = F + F (3)

=1 =1
In summary, based on the Gauss-Markov motion model, it is assumed that the motions in the x and y axes are
independent of each other, the transition probability density function of the target from the position ( , )
to the position ( +1 , +1 ) after one motion cycle Δ can be represented as:

2
2
1
1 − 2 2 [( +1 − ) +( +1 − ) ]
{( +1 , +1 )|( , )} = (4)
2
2
In order to appropriately allocate the proportion of random movement and the directional evasive movement,
the hyperbolic tangent (tanh) function is used to saturate the virtual evasive force of the target in this paper.
Therefore, the means of and and variance of can be defined as:
2

= tanh(∥F∥)

= + ·
∥F∥
(5)

= + ·
∥F∥
3 = (1 − )·

where ∈ [0, 1] is the saturated partition coefficient of evasive movement. According to the common defi-
nitionofthe 3 rule, isappropriatelyallocatedbytheguidanceofvirtualevasiveforce, andconsequently,
the evasive maneuver of targets can be realized.

2.3. Detection model of UAV
The UAV detection range is defined as a square area with a side length of centered on the UAV’s current
position, which can be represented as the mission grid cell and its adjacent cells where the UAV is located.

Considering the real-time changes in UAV position, denote the detection grid of i-th UAV as Ω , which can
be regarded as a certain range in Ω , and its side length is times that of a single mission grid cell. Same as

above, the detection grid cell of i-th UAV with m-th row and n-th column is marked as . Figure 5 shows

the specific representation of the detection grid of i-th UAV.

The i-th UAV can only detect the area within Ω . The detection is carried out in every single detection grid

cell, and the detection probability corresponding to is , which can be defined as a general form [25] as: