Multi-articulated and redundantly actuated virtual track trains (VTTs) are inevitably exposed to unknown exogenous disturbances and various operating conditions. To address the complex over-actuated tracking-control problem, this study proposes a decoupling control scheme for an all-wheel independent drive and all-wheel active steering VTT composed of multiple modules, wherein the adaptive robust path-tracking and longitudinal speed control algorithms of the VTT are decoupled. An appropriate control-oriented nonlinear dynamic model for VTT path-tracking control is formulated using Lagrange’s equations. To compensate for the model uncertainties and environmental disturbances without priors and parameter estimations, a robust control algorithm using radial basis function neural network and sliding mode is proposed. The asymptotic stability of the algorithm is proved, and its adaptation law is derived using the Lyapunov theory. Moreover, a novel traction/braking control algorithm based on the wheel speed distribution model and double closed-loop control algorithm is suggested. Using a multi-body dynamic model of the VTT with seven modules, simulations are performed to evaluate the effectiveness and superiority of the proposed path-tracking algorithm. The obtained results indicate that the proposed algorithm could realise the expectable performance of the VTT path tracking and longitudinal speed control. Moreover, the proposed control algorithm has good scalability for multi-articulated and redundantly actuated VTT.
ZhangYKhajepourAAtaeiM.A universal and reconfigurable stability control methodology for articulated vehicles with any configurations. IEEE Trans Veh Technol2020; 69(4): 3748–3759.
2.
LengHRenLJiY.Analysis methodology of compatibility between motion control and mechanical architecture of a newly designed gantry virtual track train and the path-tracking control strategy. Proc IMechE, Part C: J Mechanical Engineering Science2022; 236(13): 6985–7005.
3.
YinZZhangJSuiH.Stochastic responses characteristics of a virtual track train excited by road irregularities. IEEE Trans Veh Technol2022; 71: 8152–8163.
4.
LengHRenLJiY.Cascade modular path following control strategy for gantry virtual track train: time-delay stability and forward predictive model. IEEE Trans Veh Technol2022; 71(7): 6969–6983.
5.
YinZZhangJLuH, et al. Dynamics modeling and analysis of a four-wheel independent motor-drive virtual-track train. Proc IMechE, Part K: J Multi-body Dynamics2021; 235(1): 134–149.
6.
KuralKHatzidimitrisPvan de WouwN, et al. Active trailer steering control for high-capacity vehicle combinations. IEEE Trans Intell Vehicles2017; 2(4): 251–265.
7.
LiuXMadhusudhananAKCebonD.Minimum swept-path control for autonomous reversing of a tractor semi-trailer. IEEE Trans Veh Technol2019; 68(5): 4367–4376.
8.
SorgeF.On the sway stability improvement of car–caravan systems by articulated connections. Veh Syst Dyn2015; 53(9): 1349–1372.
9.
WangQHeY.A study on single lane-change manoeuvres for determining rearward amplification of multi-trailer articulated heavy vehicles with active trailer steering systems. Veh Syst Dyn2016; 54(1): 102–123.
10.
JujnovichBACebonD.Path-following steering control for articulated vehicles. J Dyn Syst Meas Control2013; 135(3): 1–15.
11.
Keymasi KhalajiARahimi BidgoliMMoosavianSAA. Non-model-based control for a wheeled mobile robot towing two trailers. Proc IMechE, Part K: J Multi-body Dynamics2015; 229(1): 97–108.
12.
KhalajiAK.PID-based target tracking control of a tractor-trailer mobile robot. Proc IMechE, Part C: J Mechanical Engineering Science2019; 233(13): 4776–4787.
13.
YinZZhangJLuH.Establishment and comparison of a spatial dynamics model for virtual track train with different steering modes. Proc IMechE, Part K: J Multi-body Dynamics2021; 235(3): 481–498.
14.
LvKWangJChengH, et al. Modeling of hydro-pneumatic suspension system with fractional order terms and simulation analysis of road friendliness. Proc IMechE, Part D: J Automobile Engineering. Epub ahead of print 12 July 2022. DOI: 10.1177/09544070221110073.
15.
FangPCaiYChenL, et al. A high-performance neural network vehicle dynamics model for trajectory tracking control. Proc IMechE, Part D: J Automobile Engineering2023; 237: 1695–1709.
16.
NiuZJinSWangR, et al. Geometry optimization of a planar double wishbone suspension based on whole-range nonlinear dynamic model. Proc IMechE, Part D: J Automobile Engineering2022; 236(4): 569–581.
17.
AstolfiABolzernPLocatelliA.Path-tracking of a tractor-trailer vehicle along rectilinear and circular paths: a Lyapunov-based approach. IEEE Trans Robot Autom2004; 20(1): 154–160.
18.
BolzernPDeSantisRMLocatelliA.An input-output linearization approach to the control of an n-body articulated vehicle. J Dyn Syst Meas Control2001; 123(3): 309–316.
19.
BolzernPDeSantisRMLocatelliA, et al. Path-tracking for articulated vehicles with off-axle hitching. IEEE Trans Control Syst Technol1998; 6(4): 515–523.
20.
MichalekMMPatkowskiBGawronT.Modular kinematic modelling of articulated buses. IEEE Trans Veh Technol2020; 69(8): 8381–8394.
21.
EsmaeiliNKazemiRTabatabaei OrehSH.An adaptive sliding mode controller for the lateral control of articulated long vehicles. Proc IMechE, Part K: J Multi-body Dynamics2019; 233(3): 487–515.
22.
NiZHeY.Design and validation of a robust active trailer steering system for multi-trailer articulated heavy vehicles. Veh Syst Dyn2019; 57(10): 1545–1571.
23.
KayacanERamonHSaeysW.Robust trajectory tracking error model-based predictive control for unmanned ground vehicles. IEEE ASME Trans Mechatron2016; 21(2): 806–814.
24.
KayacanESaeysWRamonH, et al. Experimental validation of linear and nonlinear MPC on an articulated unmanned ground vehicle. IEEE ASME Trans Mechatron2018; 23(5): 2023–2030.
25.
ZhangYKhajepourAHashemiE, et al. Reconfigurable model predictive control for articulated vehicle stability with experimental validation. IEEE Trans Transp Electrification2020; 6(1): 308–317.
26.
ZhaoHZhouSChenW, et al. Modeling and motion control of industrial tractor–trailers vehicles using force compensation. IEEE ASME Trans Mechatron2021; 26(2): 645–656.
27.
ZhouSZhaoHChenW, et al. Dynamic state estimation and control of a heavy tractor–trailers vehicle. IEEE ASME Trans Mechatron2021; 26(3): 1467–1478.
28.
LatifAChalhoubNPilipchukV.Control of the nonlinear dynamics of a truck and trailer combination. Nonlinear Dyn2020; 99(4): 2505–2526.
29.
YuanJSunFHuangY.Trajectory generation and tracking control for double-steering tractor–trailer mobile robots with on-axle hitching. IEEE Trans Ind Electron2015; 62(12): 7665–7677.
30.
ZhouSZhaoHChenW, et al. Robust path following of the tractor-trailers system in GPS-denied environments. IEEE Robot Autom Lett2020; 5(2): 500–507.
31.
HuCWangZTaghavifarH, et al. MME-EKF-based path-tracking control of autonomous vehicles considering input saturation. IEEE Trans Veh Technol2019; 68(6): 5246–5259.
32.
JiXHeXLvC, et al. Adaptive-neural-network-based robust lateral motion control for autonomous vehicle at driving limits. Control Eng Pract2018; 76: 41–53.
33.
WagnerSNitzscheGHuberR. Advanced automatic steering systems for multiple articulated road vehicles. In: ASME 2013 international mechanical engineering congress and exposition (IMECE), San Diego, CA, USA, 15–21 November2013, pp.1–11. New York: ASME.
34.
WagnerSZipserSBartholomaeusR, et al. A novel two DOF control for train-like guidance of multiple articulated vehicles. In: ASME 2009 international design engineering technical conferences and computers and information in engineering conference (IDETC-CIE), San Diego, CA, USA, 30 August–2 September2009, pp.1989–1997. New York: ASME.
35.
BruinDDBoschPPJVD. Modelling and control of a double articulated vehicle with four steerable axles. In: Proceedings of the 1999 American control conference (ACC), San Diego, CA, USA, 2–4 June1999, pp.3250–3254. New York: IEEE.
36.
JouilaANouriK.An adaptive robust nonsingular fast terminal sliding mode controller based on wavelet neural network for a 2-DOF robotic arm. J Franklin Inst2020; 357(18): 13259–13282.
37.
HanZZhangKYangT, et al. Spacecraft fault-tolerant control using adaptive non-singular fast terminal sliding mode. IET Control Theory Appl2016; 10(16): 1991–1999.
38.
QiaoLZhangW.Double-loop integral terminal sliding mode tracking control for UUVs with adaptive dynamic compensation of uncertainties and disturbances. IEEE J Oceanic Eng2019; 44(1): 29–53.
39.
RianiAMadaniTBenallegueA, et al. Adaptive integral terminal sliding mode control for upper-limb rehabilitation exoskeleton. Control Eng Pract2018; 75: 108–117.
40.
QiaoLZhangW.Adaptive second-order fast nonsingular terminal sliding mode tracking control for fully actuated autonomous underwater vehicles. IEEE J Oceanic Eng2019; 44(2): 363–385.
41.
ShtesselYPlestanFTalebM.Lyapunov design of adaptive super-twisting controller applied to a pneumatic actuator. IFAC Proc Volumes2011; 44(1): 3051–3056.
FengG.A compensating scheme for robot tracking based on neural networks. Robot Auton Syst1995; 15(3): 199–206.
44.
LewisFLLiuKYesildirekA.Neural net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw1995; 6(3): 703–715.
45.
GhellabMZZeghlacheSDjeriouiA, et al. Experimental validation of adaptive RBFNN global fast dynamic terminal sliding mode control for twin rotor MIMO system against wind effects. Measurement2021; 168: 108472.
46.
RajamaniR.Vehicle dynamics and control. New York, NY: Springer, 2011.
47.
DarbaADe BelieFD’haeseP, et al. Improved dynamic behavior in BLDC drives using model predictive speed and current control. IEEE Trans Ind Electron2016; 63(2): 728–740.
