UAV Circular Flight

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Part of project 'System Dynamics'
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Simulation model of an Unmanned Aerial Vehicle in a circular flight around a target, at constant height, using system dynamics and agent-based technologies. The simulation was used as classroom material for the Mathematics I lectures taught by the author at the Bachelor in Aeronautical Management ( at Lusophone University of Humanities and Technologies’s “School of the Economic Sciences and Organizations”.

The full lecture materials, including webinars (in Portuguese) are available at:


The UAV turns and moves in the direction of motion, the motion is determined by the three coordinates x, y and z, the third coordinate is constant and equal to the height which is user defined by manipulating the height slider.

In the agent section the algorithm sets the heading to the computed value of x and y and moves the agent in that direction, the values of the x and y coordinates are obtained in the system dynamics modeling tab. The angular velocity is set to v, which is also controlled by the user as a slider, the user also controls the radius of the motion, which is the r slider.

The angle is the integral of the angular velocity, so that we get the following dynamics for the UAV's coordinates:

x(t) = r * cos(angle(t))

y(t) = r * sin(angle(t))

z(t) = height

The whole model serves as a classroom example of a drone flying in a circular path around a target at constant angular velocity.

In this case, assuming the initial value for the angle to be zero, the numeric integration approximates the equation:

angle(t) = v*t

Which leads to the equations of motion:

x(t) = r * cos(v*t)

y(t) = r * sin(v*t)

z(t) = height

The user can define the angular velocity to be positive or negative, this provides for a discussion point in class on angular velocity and the motion of the UAV.


The model uses Netlogo’s system dynamics modeler in conjunction with agent-based modeling showing how system dynamics and agent-based technologies can be used in conjunction for basic robotics simulations in Netlogo.


The model is the second in a series of system dynamics applied to robotics used in the author's classes on Mathematics for Aeronautical Management, the first model is:

Carlos Pedro Gonçalves, All Rights Reserved, 2021, Drone - Circular Motion, Lusophone University of Humanities and Technologies.


Carlos Pedro Gonçalves, All Rights Reserved, 2021, UAV Circular Flight, Lusophone University of Humanities and Technologies.

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Click to Run Model

;; system-dynamics-setup, system-dynamics-do-plot, and system-dynamics-go are automatically
;; generated by the System Dynamics Modeler.  The code can be viewed in the
;; Code Tab of the System Dynamics Modeler.

to setup
  crt 1
  ask turtles[setxyz r 0 height
              set color 45
              set size 8]
  ask turtles[facexy x y
              setxy x y]

to go
  ask turtles[facexy x y
              setxy x y]

There is only one version of this model, created about 1 year ago by Carlos Pedro S. Gonçalves.

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