Article
Nonlinear Model Predictive Control for Unmanned
Aerial Vehicles
†
Pengkai Ru
‡
and Kamesh Subbarao *
,‡
Department of Mechanical & Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019,
USA; pengkai.ru@mavs.uta.edu
* Correspondence: subbarao@uta.edu; Tel.: +1-817-272-7467
† This paper is an extended version of our paper published in the Proceedings of the AIAA Atmospheric
Flight Mechanics Conference, AIAA Aviation Forum, Dallas, TX, USA, 22–25 June 2015; Kamesh Subbarao,
Carlos Tule and Pengkai Ru, Nonlinear Model Predictive Control Applied to Trajectory Tracking for
Unmanned Aerial Vehicles, No. AIAA 2015-2857.
‡ These authors contributed equally to this work.
Academic Editor: David Anderson
Received: 26 April 2017; Accepted: 12 June 2017; Published: 17 June 2017
Abstract:
This paper discusses the derivation and implementation of a nonlinear model predictive
control law for tracking reference trajectories and constrained control of a quadrotor platform.
The approach uses the state-dependent coefficient form to capture the system nonlinearities into a
pseudo-linear system matrix. The state-dependent coefficient form is derived following a rigorous
analysis of aerial vehicle dynamics that systematically accounts for the peculiarities of such systems.
The same state-dependent coefficient form is exploited for obtaining a nonlinear equivalent of the
model predictive control. The nonlinear model predictive control law is derived by first transforming
the continuous system into a sampled-data form and and then using a sequential quadratic
programming solver while accounting for input, output and state constraints. The boundedness of
the tracking errors using the sampled-data implementation is shown explicitly. The performance of
the nonlinear controller is illustrated through representative simulations showing the tracking of
several aggressive reference trajectories with and without disturbances.
Keywords: nonlinear; model predictive control; constraints; trajectory tracking; stability
1. Introduction
A quadrotor helicopter platform (often just called a quadrotor) is an under-actuated helicopter
with two pairs of rotors in a cross-configuration capable of spinning at different angular velocities in
order to achieve translational and rotational motion. Rotor pair
(
1, 3
)
spins in one direction, while the
pair (2, 4) spins in the opposite (see Figure 1).
The different motions the quadrotor can perform are: (a) vertical motion: simultaneous change in
rotor speed; (b) roll motion: imbalance in the rotor speed of pair
(
2, 4
)
; (c) pitch motion: imbalance in
the rotor speed of pair (1, 3); (d) yaw motion: imbalance between all rotors.
Quadrotors have gained popularity as research platforms because of their simplicity of design
and low cost of manufacturing. Because they are challenging vehicles to control, wherever operated
in an indoor environment or in the open field, they serve as great platforms for research. They also
possess many advantages over standard helicopters in terms of safety and efficiency at small sizes [
1
].
There are many applications for a quadrotor platform, both in the military and the civil sectors, which
are summarized quite extensively in [2–6].
Aerospace 2017, 4, 31; doi:10.3390/aerospace4020031 www.mdpi.com/journal/aerospace
