Abstract

The control problem for the multivariable and nonlinear dynamics of unmanned rotorcrafts is treated with the use of a flatness-based control approach which is implemented in successive loops. The state-space model of 6DOF autonomous quadrotors is separated into two subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. The state variables of the second subsystem become virtual control inputs for the first subsystem. In turn, exogenous control inputs are applied to the second subsystem. The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis. The validity of the control method is further confirmed through simulation experiments showing precise tracking of 3D flight paths by the 6DOF quadrotor.

References

1.
Rigatos
,
G.
,
2016
,
Nonlinear Control and Filtering Using Differential Flatnesss Theory Approaches: Applications to Electromechanical Systems
,
Springer
,
Cham, Switzerland
.
2.
Rigatos
,
G.
, and
Busawon
,
K.
,
2018
,
Robotic Manipulators and Vehicles: Control, Estimation and Filtering
,
Springer
,
Cham, Switzerland
.
3.
Rigatos
,
G.
,
Abbaszadeh
,
M.
, and
Siano
,
P.
,
2022
,
Control and Estimation of Dynamical Nonlinear and Partial Differential Equation Systems: Theory and Applications
,
IET Publications
,
London, UK
.
4.
Rigatos
,
G.
, and
Karapanou
,
E.
,
2020
,
Advances in Applied Nonlinear Optimal Control
,
Cambridge Scholars Publishers
,
Newcastle, UK
.
5.
Levine
,
J.
,
2009
,
Analysis and Control of Nonlinear Systems: A Flatness-Based Approach
,
Springer
,
Berlin/Heidelberg
.
6.
Riachy
,
S.
,
Fliess
,
M.
,
Join
,
C.
, and
Barbot
,
J. P.
,
2010
, “
Vers Une Simplification de la Commande Non Linéaire: L'exemple d'un Avion à Décollage Vertical
,”
Sixième Conférence Internationale Francophone D'Automatique, CIFA 2010
, Nancy, France, June.
7.
Fliess
,
M.
, and
Mounier
,
H.
,
1999
, “
Tracking Control and π-Freeness of Infinite Dimensional Linear Systems
,”
Dynamical Systems, Control, Coding and Computer Vision
, Vol.
258
,
G.
Picci
, and
D. S.
Gilliam
eds.,
Birkhaüser
,
Basel, Switzerland
, pp.
41
68
.
8.
Villagra
,
J.
,
d'Andrea-Novel
,
B.
,
Mounier
,
H.
, and
Pengov
,
M.
,
2007
, “
Flatness-Based Vehicle Steering Control Strategy With SDRE Feedback Gains Tuned Via a Sensitivity Approach
,”
IEEE Trans. Control Syst. Technol.
,
15
(
3
), pp.
554
565
.10.1109/TCST.2007.894651
9.
Bououden
,
S.
,
Boutat
,
D.
,
Zheng
,
G.
,
Barbot
,
J. P.
, and
Kratz
,
F.
,
2011
, “
A Triangular Canonical Form for a Class of 0-Flat Nonlinear Systems
,”
Int. J. Control
,
84
(
2
), pp.
261
269
.10.1080/00207179.2010.549844
10.
Menhour
,
L.
,
d'Andréa-Novel
,
B.
,
Fliess
,
M.
, and
Mounier
,
H.
,
2014
, “
Coupled Nonlinear Vehicle Control: Flatness-Based Setting With Algebraic Estimation Techniques
,”
Control Eng. Pract.
,
22
, pp.
135
146
.10.1016/j.conengprac.2013.09.013
11.
Nicolau
,
F.
,
Respondek
,
W.
, and
Barbot
,
J. P.
,
2021
, “
How to Minimally Modify a Dynamical System When Constructing Flat Inputs
,”
Int. J. Robust Nonlinear Control
,
31
(
18
), pp.
9538
9561
.10.1002/rnc.5790
12.
Letelier
,
C.
, and
Barbot
,
J. P.
,
2021
, “
Optimal Flatness Placement of Sensors and Actuators for Controlling Chaotic Systems
,”
Chaos
,
31
(
10
), p.
103114
.10.1063/5.0055895
13.
Sira-Ramirez
,
H.
, and
Agrawal
,
S.
,
2004
,
Differentially Flat Systems
,
Marcel Dekker
,
New York
.
14.
Lévine
,
J.
,
2011
, “
On Necessary and Sufficient Conditions for Differential Flatness
,”
Applicable Algebra Eng., Commun. Comput.
,
22
(
1
), pp.
47
90
.10.1007/s00200-010-0137-x
15.
Nicolau
,
F.
,
Respondek
,
W.
, and
Barbot
,
J. P.
,
2021
, “
Construction of Flat Inputs for Mechanical Systems
,”
Seventh IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
,
Berlin, Germany
, Oct.
16.
Limaverde Filho
,
J. O.
,
Fortaleza
,
E. C. R.
, and
Campos
,
M. C. M.
,
2022
, “
A Derivative-Free Nonlinear Kalman Filtering Approach Using Flat Inputs
,”
Int. J. Control
,
95
(
11
), pp.
2900
2910
.10.1080/00207179.2021.1941264
17.
Barbot
,
J. P.
,
Fliess
,
M.
, and
Floquet
,
T.
,
2007
, “
An Algebraic Framework for the Design of Nonlinear Observers With Uknown Inputs
,”
IEEE 46th International Conference on Decision and Control
,
New Orleans, LA
, Dec.
12
14
.10.1109/CDC.2007.4434695
18.
Khalil
,
H.
,
1996
,
Nonlinear Systems
,
Prentice Hall
,
Upper Saddle River, NJ
.
19.
Rigatos
,
G. G.
, and
Tzafestas
,
S. G.
,
2007
, “
Extended Kalman Filtering for Fuzzy Modelling and Multi-Sensor Fusion
,”
Math. Comput. Modell. Dyn. Syst.
,
13
(
3
), pp.
251
266
.10.1080/01443610500212468
20.
Basseville
,
M.
, and
Nikiforov
,
I.
,
1993
,
Detection of Abrupt Changes: Theory and Applications
,
Prentice Hall
,
Upper Saddle River, NJ
.
21.
Rigatos
,
G.
, and
Zhang
,
Q.
,
2009
, “
Fuzzy Model Validation Using the Local Statistical Approach
,”
Fuzzy Sets Syst.
,
160
(
7
), pp.
882
904
.10.1016/j.fss.2008.07.008
22.
Chamseddine
,
A.
,
Zhang
,
Y.
,
Rabbath
,
C. A.
,
Join
,
C.
, and
Theilliol
,
D.
,
2012
, “
Flatness-Based Trajecotry Planning/Replanning for a Quadrotor Unmanned Aerial Vehicle
,”
IEEE Trans. Aerosp. Electron. Syst.
,
48
(
4
), pp.
2832
2848
.10.1109/TAES.2012.6324664
23.
Lee
,
T.
,
2018
, “
Geometric Control of Quadrotor UAVs Transporting a Cable-Suspended Rigid Body
,”
IEEE Trans. Control Syst. Technol.
,
26
(
1
), pp.
255
264
.10.1109/TCST.2017.2656060
24.
Yu
,
X.
,
Zhou
,
X.
,
Guo
,
K.
,
Jia
,
J.
,
Guo
,
L.
, and
Zhang
,
Y.
,
2022
, “
Safety Flight Control For a Quadrotor UAV Using Differential Flatness and Dual-Loop Observers
,”
IEEE Trans. Ind. Electron.
,
69
(
12
), pp.
13326
13336
.10.1109/TIE.2021.3135640
25.
Tognon
,
M.
,
Dash
,
S. S.
, and
Franchi
,
A.
,
2016
, “
Observer-Based Control of Position and Tension for an Aerial Robot Tethered To a Moving Platform
,”
IEEE Rob. Autom. Lett.
,
1
(
2
), pp.
732
737
.10.1109/LRA.2016.2523599
26.
Chamseddine
,
A.
,
Theilliol
,
D.
,
Zhang
,
Y. M.
,
Join
,
C.
, and
Rabbath
,
C. A.
,
2015
, “
Active Fault Tolerant Control System Design With Trajectory Re-Planning Against Actuator Fault and Saturation: Application to a Quadrotor Command Aerial Vehicle
,”
Int. J. Adapt. Control Signal Process
,
29
(
1
), pp.
1
23
.10.1002/acs.2451
27.
Ogunbodede
,
O.
,
Nandi
,
S.
, and
Signh
,
T.
,
2019
, “
Periodic Control of Unmanned Aerial Vehicles Based on Differential Flatness
,”
ASME J. Dyn. Syst. Meas. Control
,
141
(
7
), p.
071003
.10.1115/1.4043114
28.
Abadi
,
A.
,
El-Amraoui
,
A.
,
Mekki
,
H.
, and
Ramdani
,
N.
,
2020
, “
Robust Tracking Control of Quadrotor Based on Flatness and Active Disturbance Rejection Control
,”
IET Control Theory Appl.
,
14
(
8
), pp.
1057
1068
.10.1049/iet-cta.2019.1363
29.
Rigatos
,
G.
,
Siano
,
P.
, and
Zervos
,
N.
,
2015
, “
A New Concept of Flatness-Based Control of Nonlinear Dynamical Systems
,” 13th IEEE International Conference on Industrial Informatics (
INDIN
),
Cambridge, UK
, July
22
24
.10.1109/INDIN.2015.7281897
30.
Rigatos
,
G.
,
Siano
,
P.
,
Ademi
,
S.
, and
Wira
,
P.
,
2018
, “
Flatness-Based Control of DC-DC Converters Implemented in Successive Loops
,”
Electric Power Compon. Syst.
,
46
(
6
), pp.
673
687
.10.1080/15325008.2018.1464612
31.
Zhang
,
Y. M.
,
Chamseddine
,
A.
,
Rabbath
,
C. A.
,
Gordon
,
B. W.
,
Su
,
C.-Y.
,
Rakheja
,
S.
,
Fulford
,
C.
,
Apkarian
,
J.
, and
Gosselin
,
P.
,
2013
, “
Development of Advanced FDD and FTC Techniques With Application to an Unmanned Quadrotor Helicopter Testbed
,”
J. Franklin Inst.
,
350
(
9
), pp.
2396
2422
.10.1016/j.jfranklin.2013.01.009
32.
Martins
,
L.
,
Cardeira
,
C.
, and
Oliveira
,
P.
,
2021
, “
Feedback Linearization With Zero Dynamics Stabilization for Quadrotor Control
,”
J. Intell. Rob. Syst.
,
101
(
1
), pp.
1
17
: 10.1007/s10846-020-01265-2
33.
Sheng
,
Y.
, and
Tao
,
G.
,
2021
, “
System Characterization and Adaptive Tracking Control of Quadrotors Under Multiple Operating Conditions
,”
J. Guid., Navig. Control
,
01
(
02
), pp.
2150006
2150045
.10.1142/S2737480721500060
34.
Ghandour
,
J.
,
Aberkan
,
S.
, and
Ponsart
,
J. C.
,
2014
, “
Feedback Linearization Approach for Standard and Fault Tolerant Control: Application to a Quadrotor UAV Testbed
,”
J. Phys.: Conf. Ser.
,
570
, p.
082003
.10.1088/1742-6596/570/8/082003
35.
Dalwadi
,
N.
,
Deb
,
D.
, and
Muyeen
,
S. M.
,
2022
, “
Adaptive Backstepping Controller Design of Quadrotor Biplane for Payload Delivery
,”
IET Intell. Transportation Syst.
,
16
(
12
), pp.
1738
1752
.10.1049/itr2.12171
36.
Mochida
,
S.
,
Matsuda
,
R.
,
Ibuki
,
T.
, and
Sampei
,
M.
,
2021
, “
A Geometric Control of Hoverability Analysis for Multirotor UAVs With Upward Oriented Rows
,”
IEEE Trans. Rob.
,
37
(
5
), pp.
1765
1779
.10.1109/TRO.2021.3064101
37.
Diaz-Mendez
,
Y.
,
de Jesus
,
L. D.
,
de Sousa
,
M. S.
,
Counha
,
S. S.
, and
Ramos
,
A. B.
,
2021
, “
Conditional Integrator Sliding-Mode Controller of an Unmanned Quadrotor Helicopter
,”
Proc. IMechE - Part I: J. Syst. Control Eng.
,
236
(
3
), pp.
458
472
.10.1177/09596518211049861
38.
Ofodile
,
N. A.
, and
Turner
,
M. C.
,
2016
, “
Decentralized Approaches to Antiwind-Up Design With Appplication to Quadrotor Unmanned Aerial Vehicle
,”
IEEE Trans. Control Syst. Technol.
,
24
(
6
), pp.
1980
1992
.10.1109/TCST.2016.2521799
39.
Jin
,
X.
,
Tang
,
Y.
,
Shi
,
Y.
,
Zhang
,
W.
, and
Du
,
W.
,
2022
, “
Event-Triggered Formation Control for a Class of Uncertain Euler-Lagrange SystemsL Theory and Experiment
,”
IEEE Trans. Control Syst. Technol.
,
30
(
1
), pp.
336
343
.10.1109/TCST.2021.3055370
40.
Rigatos, G., Siano, P., Abbaszadeh, M., and Monteriu A., “A Nonlinear Optimal Control Approach for the Autonomous Octorotor,”
Advanced Control for Applications
, 2(3), p. e50.10.1002/adc2.50
41.
Ai
,
X.
, and
Yu
,
J.
,
2019
, “
Fixed-Time Trajectory Tracking for a Quadrotor With External Disturbances: A Flatness-Based Sliding-Mode Control Approach
,”
Aerospace Science and Technology
, Vol.
89
,
Elsevier
,
Amsterdam, The Netherlands
, pp.
58
76
.
42.
Ma
,
D.
,
Xia
,
Y.
,
Shen
,
G.
,
Jia
,
Z.
, and
Li
,
T.
,
2018
, “
Flatness-Based Adaptive Sliding-Mode Tracking Control for a Quadrotor With Disturbances
,”
J. Franklin Inst.
,
355
(
14
), pp.
6300
6322
.10.1016/j.jfranklin.2018.06.018
43.
Baldini
,
A.
,
Felicetti
,
R.
,
Freddi
,
A.
,
Longhi
,
S.
,
Monteriu
,
A.
, and
Rigatos
,
G.
,
2019
, “
Actuator Fault Tolerant Position Control of a Quadrotor Unmanned Aerial Vehicle
,”
IEEE Systol 2019, Fourth IEEE Conference on Control and Fault Tolerant Systems
,
Casablanca, Morocco
, Sept.
18
20
.10.1109/SYSTOL.2019.8864785
44.
Wang
,
J.
,
Boussaada
,
I.
,
Cela
,
A.
,
Mounier
,
H.
, and
Niculescu
,
S. I.
,
2012
, “
Analysis and Control of Quadrotor Via a Normal Form Approach
,”
IEEE International Symposium on Mathematical Theory of Networks and Systems
,
Melbourne, Australia
, Aug.
45.
Freddi
,
A.
,
Lanzon
,
A.
, and
Longhi
,
S.
,
2011
, “
A Feedback Linearization Approach to Fault Tolerance in Quadrotor Vehicles
,”
18th IFAC World Congress
,
Milan, Italy
, Aug., pp.
5413
5418
.
46.
Rigatos
,
G.
, and
Siano
,
P.
,
2015
, “A New Nonlinear H-infinity Feedback Control Approach to the Problem of Autonomous Robot Navigation”,
J. Intell. Ind. Syst.
,
1
(
3
), pp.
179
186
.10.1007/s40903-015-0021-x
47.
Raffo
,
G. V.
,
Ortega
,
M. G.
, and
Rubio
,
F. R.
,
2010
, “
An Integral Predictive/Nonlinear H Control Structure for a Quadrotor Helicopter
,”
Automatica
,
46
(
1
), pp.
29
39
.10.1016/j.automatica.2009.10.018
48.
Lendek
,
Z.
,
Berna
,
A.
,
Guzman-Gimenez
,
J.
,
Sala
,
A.
, and
Garcia
,
P.
,
2011
, “
Application of Takagi-Sugeno Observers for State Estimation in a Quadrotor
,”
50th IEEE Conference on Decision and Control and European Control Conference
,
Orlando, FL
, Dec.
12
15
.10.1109/CDC.2011.6160439
49.
Lee
,
T.
,
2012
, “
Robust Adaptive Attitude Tracking on SO(3) With an Application to a Quadrotor UAV
,”
IEEE Trans. Control Syst. Technol.
,
2
(
5
), pp.
1924
1930
.10.1109/TCST.2012.2209887
50.
Wang
,
Y.
,
Guan
,
Y.
, and
Li
,
H.
,
2023
, “
Spiking-Free Disturbance Observer-Based Sliding-Mode Control for Mismatched Uncertain System
,”
ASME J. Dyn. Syst., Meas. Control
,
145
(
12
), p.
121004
.10.1115/1.4063609
51.
He
,
Y.
,
Pei
,
H.
, and
Sun
,
T.
,
2014
, “
Robust Tracking Control of Helicopters Using Backstepping With Disturbance Observers
,”
Asian J. Control
,
16
(
5
), pp.
1387
1402
.10.1002/asjc.827
You do not currently have access to this content.