The current work exploits the effects of time-delays on the stability of unmanned aerial vehicles s). In this regard, the main contribution is a symbolic/numeric application of the multiplicity-induced-dominancy property in the control of unmanned aerial vehicles rotorcrafts featuring time-delays. The multiplicity-induced-dominancy property is considered to address two of the most representative aerial robotic platforms: a classical quadrotor vehicle and a quadrotor vehicle endowed with tilting rotors. The aforementioned property leads to an effective delayed feedback control design (multiplicity-induced-dominancy tuning criteria), allowing the system to meet prescribed behavior conditions based on the placement of the rightmost root of the corresponding closed-loop characteristic function/quasipolynomial. Lastly, the results of detailed numerical simulations, including the linear and non-linear dynamics of the vehicle, are presented and discussed to validate the proposal.
Al-AliIZweiriYAMoosaN, et al. (2020) State of the art in tilt-quadrotors, modelling, control and fault recovery. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science234(2): 474–486.
2.
Alvarez-MunozJMarchandNGuerrero-CastellanosJF, et al. (2018) Rotorcraft with a 3DOF rigid manipulator: quaternion-based modeling and real-time control tolerant to multi-body couplings. International Journal of Automation and Computing15(5): 547–558.
3.
Alvarez-MuñozJUCastillo-ZamoraJJEscarenoJ, et al. (2019 June) Time-delay control of a multi-rotor VTOL multi-agent system towards transport operations. In: 2019 International Conference on Unmanned Aircraft Systems (ICUAS), Atlanta, GA, USA, 11-14 June 2019. IEEE, 276–283.
4.
BaloghTInspergerTBoussaadaI, et al. (2020) Towards an MID-based delayed design for arbitrary-order dynamical systems with a mechanical application. IFAC-PapersOnLine53(2): 4375–4380.
5.
BaloghTBoussaadaIInspergerT, et al. (2021) Conditions for stabilizability of time‐delay systems with real‐rooted plant. International Journal of Robust and Nonlinear Control32: 3206–3224.
6.
BenarabABoussaadaITrabelsiK, et al. (2020 October) The MID property for a second-order neutral time-delay differential equation. In: 2020 24th International Conference on System Theory, Control and Computing (ICSTCC), Sinaia, Romania, 8-10 October 2020. IEEE, 7–12
7.
BoussaadaINiculescuSI (2015) Tracking the algebraic multiplicity of crossing imaginary roots for generic quasipolynomials: a Vandermonde-based approach. IEEE Transactions on Automatic Control61(6): 1601–1606.
8.
BoussaadaINiculescuS-I (2016) Characterizing the codimension of zero singularities for time-delay systems. Acta Applicandae Mathematicae145(1): 47–88.
9.
BoussaadaIUnalHUNiculescuSI (2016 July). Multiplicity and stable varieties of time-delay systems: a missing link. In: 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS), Minneapolis, MN, USA, July 12th-15th.
10.
BoussaadaITlibaSNiculescuS-I, et al. (2018) Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system. Linear Algebra and Its Applications542: 589–604.
11.
BoussaadaINiculescuS-IEl-AtiA, et al. (2020a) Multiplicity-induced-dominancy in parametric second-order delay differential equations: analysis and application in control design. ESAIM: Control, Optimisation and Calculus of Variations26: 57.
12.
BoussaadaIMazantiGNiculescuSI, et al. (2020b) Partial pole placement via delay action: a Python software for delayed feedback stabilizing design. In: 2020 24th International Conference on System Theory, Control and Computing (ICSTCC), Sinaia, Romania, 8-10 October 2020, IEEE, 196–201.
13.
CabreiraTBrisolaraLFerreiraPRJr (2019) Survey on coverage path planning with unmanned aerial vehicles. Drones3(1): 4.
14.
CaoXShiPLiZ, et al. (2018) Neural-network-based adaptive backstepping control with application to spacecraft attitude regulation. IEEE Transactions on Neural Networks and Learning Systems29(9): 4303–4313.
15.
Castillo-ZamoraJJCamarillo-GómezKAPérez-SotoGI, et al. (2018) Comparison of PD, PID and sliding-mode position controllers for V-tail quadcopter stability. IEEE Access6: 38086–38096.
16.
Castillo-ZamoraJJEscareñoJAlvarezJ, et al. (2019 April). Disturbances and coupling compensation for trajectory tracking of a multi-link aerial robot. In: 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), Paris, France, 23-26 April 2019, IEEE, 738–743.
17.
Castillo-ZamoraJJCamarillo-GómezKAPérez-SotoGI, et al. (2021a) Mini-AUV hydrodynamic parameters identification via CFD simulations and their application on control performance evaluation. Sensors21(3): 820.
18.
Castillo-ZamoraJJHernández-DíezJEBoussaadaI, et al. (2021b). A preliminary parametric analysis of PID delay-based controllers for quadrotor UAVs. In: 2021 International Conference on Unmanned Aircraft Systems (ICUAS), Athens, Greece, 15-18 June 2021, IEEE, 28–37.
19.
DingYWangYChenB (2021) A practical time-delay control scheme for aerial manipulators. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering235(3): 371–388.
20.
EscareñoJCastilloJAbassiW, et al. (2017 October). Navigation strategy in-flight retrieving and transportation operations for a rotorcraft mav. In:2017 Workshop on Research, Education and Development of Unmanned Aerial Systems (RED-UAS), ping, Sweden, 3-5 October 2017, IEEE, 7–12.
21.
FortmannTEHitzKL (1977) An Introduction to Linear Control Systems. New York, United States of America: CRC Press.
22.
GerberMJTsaoTC (2018) Twisting and tilting rotors for high-efficiency, thrust-vectored quadrotors. Journal of Mechanisms and Robotics10(6): 061013.
23.
GerhardJJeffreyDJMorozG (2010) A package for solving parametric polynomial systems. ACM Communications in Computer Algebra43(3/4): 61–72.
24.
GuKChenJKharitonovVL (2003) Stability of Time-Delay Systems. New York, United States of America: Springer Science & Business Media.
25.
HaleJKLunelSMV (2013) Introduction to functional differential equations. New York, United States of America: Springer Science & Business Media, Vol. 99.
26.
HayesND (1950) Roots of the transcendental equation associated with a certain difference-differential equation. Journal of the London Mathematical Societys1-25(3): 226–232.
27.
HehnMD’AndreaR (2011 May). A flying inverted pendulum. 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, 9-13 May 2011, IEEE, 763–770.
28.
JiaoRChouWRongY, et al. (2021) Anti-disturbance attitude control for quadrotor unmanned aerial vehicle manipulator via fuzzy adaptive sigmoid generalized super-twisting sliding mode observer. Journal of Vibration and ControlOnline, First Published on February 16, 2021. DOI: 10.1177/1077546321989495.
29.
KartalYSubbaraoKGansNR, et al. (2020) Distributed backstepping based control of multiple UAV formation flight subject to time delays. IET Control Theory & Applications14(12): 1628–1638.
30.
KolarPGamezNJamshidiM (2020) Impact of time delays on networked control of Autonomous systems. Studies in Computational Intelligence835: 151–178.
LazardD (2006) Computing with parameterized varieties. In: MohamedElkadiBernardMourrainRagniPiene.Algebraic geometry and geometric modeling. Berlin, Heidelberg: Springer, 53–69.
33.
LiSDuanNXuZ, et al. (2020a) Tracking control of quadrotor UAV with input delay. In: 2020 39th Chinese Control Conference (CCC), Shenyang, China, 27-29 July 2020, IEEE, 646–649.
34.
LiLWangMXueK, et al. (2020b) Delay optimization in multi-UAV edge caching networks: a robust mean field game. IEEE Transactions on Vehicular Technology70(1): 808–819.
35.
LiangSGerhardJJeffreyDJMorozG (2010) A package for solving parametric polynomial systems.ACM Communications in Computer Algebra43(3–4): 61–72.
36.
LiuMZhangLShiP, et al. (2018) Fault estimation sliding-mode observer with digital communication constraints. IEEE Transactions on Automatic Control63(10): 3434–3441.
37.
López-HerńandezJEscarenoJMéndez-BarriosCF, et al. (2019 April). A Comparative stability analysis of underactuated versus fully actuated rotorcrafts having time-delay feedback. In: 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), Paris, France, 23-26 April 2019, IEEE, 1640–1645.
38.
MaDBoussaadaIBonnetC, et al. (2020 July) Multiplicity-induced-dominancy extended to neutral delay equations: towards a systematic PID tuning based on rightmost root assignment. In: 2020 American Control Conference (ACC), Denver, CO, USA, 1-3 July 2020, IEEE, pp. 1690–1695.
39.
MazantiGBoussaadaINiculescuS-I (2020) On qualitative properties of single-delay linear retarded differential equations: characteristic roots of maximal multiplicity are necessarily dominant. IFAC-PapersOnLine53(2): 4345–4350.
40.
MazantiGBoussaadaINiculescuS-I (2021) Multiplicity-induced-dominancy for delay-differential equations of retarded type. Journal of Differential Equations286: 84–118.
41.
MichielsWNiculescuSI (eds) (2014) Stability, Control, And Computation For Time-Delay Systems: An Eigenvalue-Based Approach. Second Edition, United States of America: Society for Industrial and Applied Mathematics.
42.
MofidOMobayenSZhangC, et al. (2021) Desired tracking of delayed quadrotor UAV under model uncertainty and wind disturbance using adaptive super-twisting terminal sliding mode control. ISA Transactions123, April 2022: 455–471.
43.
MolnarCABaloghTBoussaadaI, et al. (2021) Calculation of the critical delay for the double inverted pendulum. Journal of Vibration and Control27(3-4): 356–364.
44.
MoralesJRodriguezGHuangG, et al. (2020) Toward uav control via cellular networks: Delay profiles, delay modeling, and a case study within the 5-mile range. IEEE Transactions on Aerospace and Electronic Systems56(5): 4132–4151.
45.
MorozG (2008) Sur la décomposition réelle et algébrique des systemes dépendant de parametresDoctoral dissertation, Université Pierre et Marie Curie-Paris VI, Paris, France.
46.
NiculescuS-IMichielsW (2004) Stabilizing a chain of integrators using multiple delays. IEEE Transactions on Automatic Control49(5): 802–807.
47.
RouillierF (1999) Solving zero-dimensional systems through the rational univariate representation. Applicable Algebra in Engineering, Communication and Computing9(5): 433–461
48.
RuggieroFLippielloVOlleroA.(2018) Aerial manipulation: a literature review. IEEE Robotics and Automation Letters3(3): 1957–1964.
49.
RyllMBülthoffHHGiordanoPR (2014) A novel overactuated quadrotor unmanned aerial vehicle: modeling, control, and experimental validation. IEEE Transactions on Control Systems Technology23(2): 540–556.
50.
SaifA-WAAliyuADhaifallahMA, et al. (2018) Decentralized backstepping control of a quadrotor with tilted-rotor under wind gusts. International Journal of Control, Automation and Systems16(5): 2458–2472.
51.
SchiffJL (1999) The Laplace Transform: Theory and Applications. Netherlands: Springer Science & Business Media.
52.
ShakhatrehHSawalmehAHAl-FuqahaA, et al. (2019) Unmanned aerial vehicles (UAVs): a survey on civil applications and key research challenges. IEEE Access7: 48572–48634.
53.
SharmaMKarI (2021) Control of a quadrotor with network induced time delay. ISA Transactions111: 132–143.
54.
ShiraiJYamaguchiTTakabaK (2017 September) Remote visual servo tracking control of drone taking account of time delays. In: 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), Kanazawa, Japan, 19-22 September 2017, IEEE, pp. 1589–1594.
55.
SipahiRNiculescuSIAbdallahCT, et al. (2011) Stability and stabilization of systems with time delay. IEEE Control Systems Magazine31(1): 38–65.
56.
SteedEQuesadaERodolfoL, et al. (2016) Algebraic dominant pole placement methodology for unmanned aircraft systems with time delay. IEEE Transactions on Aerospace and Electronic Systems52(3): 1108–1119.
57.
WangWNonamiKHirataM, et al. (2010) Autonomous control of micro flying robot. Journal of Vibration and Control16(4): 555–570.
58.
XuSLamJ (2008) A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Science39(12): 1095–1113.
59.
XuZXuMWuY, et al. (2020) Distributed hunting problem of multi-quadrotor systems via bearing constraint method subject to time delays. Journal of the Franklin Institute357(12): 7537–7555.
60.
ZamoraJJCEscarenoJBoussaadaI, et al. (2020) Nonlinear control of a multilink aerial system and ASEKF-based disturbances compensation. IEEE Transactions on Aerospace and Electronic Systems57(2): 907–918.
