Citation: Yih, C.-C.; Wu, S.-J. Sliding
Mode Path following and Control
Allocation of a Tilt-Rotor Quadcopter.
Appl. Sci. 2022, 12, 11088. https://
doi.org/10.3390/app122111088
Academic Editors: Jaroslaw Pytka,
Andrzej Łukaszewicz, Zbigniew
Kulesza, Wojciech Giernacki and
Andriy Holovatyy
Received: 27 September 2022
Accepted: 30 October 2022
Published: 1 November 2022
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Article
Sliding Mode Path following and Control Allocation of a
Tilt-Rotor Quadcopter
Chih-Chen Yih * and Shih-Jeh Wu
Department of Mechanical & Automation Engineering, I-Shou University, Kaohsiung 84001, Taiwan
* Correspondence: ccyih@isu.edu.tw; Tel.: +886-7-657-7711 (ext. 3229)
Abstract:
A tilt-rotor quadcopter (TRQ) equipped with four tilt-rotors is more agile than its under-
actuated counterpart and can fly at any path while maintaining the desired attitude. To take advantage
of this additional control capability and enhance the quadrotor system’s robustness and capability, we
designed two sliding mode controls (SMCs): the typical SMC exploits the properties of the rotational
dynamics, and the modified SMC avoids undesired chattering. Our simulation studies show that
the proposed SMC scheme can follow the planned flight path and keep the desired attitude in the
presence of variable deviations and external perturbations. We demonstrate from the Lyapunov
stability theorem that the proposed control scheme can guarantee the asymptotic stability of the TRQ
in terms of position and attitude following via control allocation.
Keywords: tilt-rotor quadcopter (TRQ); sliding mode control (SMC); control allocation; path following
1. Introduction
Due to advancements in microprocessors and sensors, quadrotors have recently received
much attention, playing an increasingly important role in unmanned aerial vehicles (UAVs).
Now, quadrotors can easily hover indoors or outdoors and fly fast with global positioning
system (GPS) devices or tiny cameras. Generally, changing the velocities of rotors [
1
,
2
] can
generate lift and steering torque to control the attitude and position of the quadcopter.
Scholars and engineers have proposed several methods to solve the control problem
for a quadrotor. These methods can be divided into: PID control [
3
–
5
], feedback lineariza-
tion [
6
], optimal control [
7
], back-stepping [
8
,
9
], SMC [
10
–
13
], robust control [
14
], neural
control [
15
,
16
], and nonlinear control [
17
]. To handle uncertainty systematically, researchers
have extensively applied SMCs to address the robust control problem of quadrotors.
The super-twist control algorithm [
18
–
20
], a second-order SMC, has been studied to
alleviate harmful chattering and maintain the robust capability of first-order SMCs. The
studies in [
21
–
23
] demonstrate the stability and finite-time convergence of the super-twist
control algorithm for single-variable systems through a Lyapunov stability analysis. For
instance, Xu et al. [
11
] studied an adaptive terminal sliding mode for a quadrotor attitude
control with specified capability and input saturation. In addition, Besnard et al. [
12
]
proposed an observer-based SMC to address model uncertainty and wind perturbation.
The recent work in [
24
,
25
] introduced the perturbation observer incorporating enhanced
SMC for application in quadrotor UAV control.
Recently, several control methods have been proposed to solve the localization or
following problem of under-actuated quadrotors, but these methods are still insufficient
and have many shortcomings. For example, if the actuator fails or the rotor is damaged,
the quadrotor will crash due to a lack of actuator redundancy to restore attitude and
position. Tilt-rotor quadrotors [
26
] can increase the degree of control freedom and provide
control redundancy. Compared with under-actuated quadrotors, full-drive quadrotors
have more flexibility than under-actuated quadrotors and have recently attracted the
research community’s attention. Ryll et al. [
27
] proposed a modeling approach for an
Appl. Sci. 2022, 12, 11088. https://doi.org/10.3390/app122111088 https://www.mdpi.com/journal/applsci
