Page 116 - Read Online

Page 64 Guan et al. Intell Robot 2024;4(1):61-73 I http://dx.doi.org/10.20517/ir.2024.04

Based on the relative position of the follower and leader in Figure 1A and B, we can formulate the position of
the leader UAV as follows:

= + cos cos − sin + cos sin ,
= + sin cos + cos + sin sin , (3)
= + sin + cos .

In the reference coordinate system, where , ,and are, the representation can be depicted as follows:

   − 
   
  = −1   (4)
   − 
   
   − 

where the matrix is:

 cos cos − sin cos sin 
 
=  sin cos cos  (5)
 sin sin 
 sin 0 cos 
 
By considering the position of the leader UAV and the desired inter-drone distance, we can compute the ex-
pected position of the follower UAV in the inertial coordinate system. The relative expected position of the
follower is denoted by , and . The error between the current position of the follower and the desired
ˆ
ˆ
ˆ
position is defined as:

ˆ
 −   − 
   
=   =  ˆ  (6)
 −   − 
   ˆ 
 −   − 
ˆ
 1   1   −   − 
       
  =   =   =  ˆ  (7)
 2   2   −   − 
       ˆ 
 3   3   −   − 
Assume that each following drone is equipped with three PID controllers to control its speed , heading angle
and pitch angle . Thes econtrollers can generate the control inputs , , and of the following
drone based on the errors , and . The formula is as follows:

∫

= + + ,

∫

= + + , (8)

∫

= + + .