Article
Pareto Optimal PID Tuning for Px4-Based Unmanned
Aerial Vehicles by Using a Multi-Objective Particle
Swarm Optimization Algorithm
Victor Gomez
1
, Nicolas Gomez
1
, Jorge Rodas
1,
* , Enrique Paiva
1
, Maarouf Saad
2
and Raul Gregor
1
1
Laboratory of Power and Control Systems (LSPyC), Facultad de Ingeniería, Universidad Nacional
de Asunción, Luque 2060, Paraguay; sebasg7@gmail.com (V.G.); ni_co182@hotmail.com (N.G.);
enpaiva93@gmail.com (E.P.); rgregor@ing.una.py (R.G.)
2
Power Electronics and Industrial Control Research Group (GRÉPCI), École de Technologie Supérieure,
Montreal, QC H3C 1K3, Canada; maarouf.saad@etsmtl.ca
* Correspondence: jrodas@ing.una.py
Received: 20 April 2020; Accepted: 26 May 2020; Published: 4 June 2020
Abstract:
Unmanned aerial vehicles (UAVs) are affordable these days. For that reason, there are
currently examples of the use of UAVs in recreational, professional and research applications. Most
of the commercial UAVs use Px4 for their operating system. Even though Px4 allows one to change
the flight controller structure, the proportional-integral-derivative (PID) format is still by far the most
popular choice. A selection of the PID controller parameters is required before the UAV can be used.
Although there are guidelines for the design of PID parameters, they do not guarantee the stability of
the UAV, which in many cases, leads to collisions involving the UAV during the calibration process.
In this paper, an offline tuning procedure based on the multi-objective particle swarm optimization
(MOPSO) algorithm for the attitude and altitude control of a Px4-based UAV is proposed. A Pareto
dominance concept is used for the MOPSO to find values for the PID comparing parameters of step
responses (overshoot, rise time and root-mean-square). Experimental results are provided to validate
the proposed tuning procedure by using a quadrotor as a case study.
Keywords:
multi-objective particle swarm optimization; Pareto front; proportional-integral-derivative;
Px4; quadrotor; unmanned aerial vehicles
1. Introduction
1.1. Historical Perspective of UAVs
Unmanned aerial vehicles (UAVs), also known as drones, have been used for centuries. They were
initially used for military purposes. The first recorded use of a UAV dates back to 1849 when the
Austrians attacked Venice (Italy) using explosive-laden, unmanned balloons [
1
]. However, even
though these unmanned balloons are not considered UAV’s today, this was a technology that the
Austrians developed which led to further breakthroughs in the development of the UAV. Subsequently,
in 1915, the British Army used UAVs to photograph areas at the Battle of Neuve Chapelle [
2
]. Due
to the military advantage that this technology provided, they continued development until, during
the years 1930–1940, the navies of different countries began experimenting with radio-controlled
UAV’s [
3
]. As a consequence, many UAV concepts have been developed, including the United States’
Curtiss N2C-2 aircraft, 1937 [
4
], the British DH.82B Queen Bee aircraft, 1935 and the Radioplane OQ-2,
1941 [
5
]. The latter was the first mass-produced UAV product in the United States and marked a
Aerospace 2020, 7, 71; doi:10.3390/aerospace7060071 www.mdpi.com/journal/aerospace
