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Int. J. Vehicle Autonomous Systems, Vol. 11, No. 4, 2013
A robust longitudinal sliding-mode controller design for autonomous ground vehicle based on fuzzy logic Ping Hu, Jinghua Guo and Linhui Li* State Key Laboratory of Structural Analysis for Industrial Equipment, School of Automotive Engineering, Dalian University of Technology, Dalian 116024, China E-mail:
[email protected] E-mail:
[email protected] E-mail:
[email protected] *Corresponding author
Rongben Wang College of Traffic, Jilin University, Changchun 130012, China E-mail:
[email protected] Abstract: This paper describes the development of a robust longitudinal controller for autonomous ground vehicle with inherent unknown nonlinearities and parametric uncertainties. The longitudinal controller is designed using Sliding-Mode Control (SMC) strategy based on fuzzy logic, which works through switching between the throttle actuator and brake actuator according to a predetermined criterion. The proposed longitudinal controller not only eliminates the chattering phenomenon in the Sliding-Mode Control (SMC) but also copes with the system uncertainties and external disturbances. Additionally, the convergence of closed-loop longitudinal control system is proved by the Lyapunov stability theory. Finally, simulation and experimental results indicate the strong robustness and commendable tracking performance of proposed controller. Keywords: autonomous ground vehicle; longitudinal control; fuzzy logic; SMC; sliding-mode control; disturbance. Reference to this paper should be made as follows: Hu, P., Guo, J., Li, L. and Wang, R. (2013) ‘A robust longitudinal sliding-mode controller design for autonomous ground vehicle based on fuzzy logic’, Int. J. Vehicle Autonomous Systems, Vol. 11, No. 4, pp.368–383. Biographical notes: Ping Hu received his BE, ME and PhD from Jilin University of Technology, China, in 1982, 1984 and 1993, respectively. He is currently a full Professor in State Key Laboratory of Structural Analysis for Industrial Equipment and the Dean of School of Automotive Engineering, Dalian University of Technology, China. He has following honours to his credit: Gainers of National Outstanding Youth Fund in China, Special Copyright © 2013 Inderscience Enterprises Ltd.
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Allowance of State Department and Elitist Fund of Ministry of Education. His research interests include vehicle design and manufacturing and solid mechanics. Jinghua Guo is currently a PhD candidate in State Key Laboratory of Structural Analysis for Industrial Equipment, School of Automotive Engineering, Dalian University of Technology, China. His research interests include autonomous ground vehicles, non-linear control of mechanical systems. Linhui Li received his PhD from Jilin University, China, in 2008. He is currently an Assistant Professor in State Key Laboratory of Structural Analysis for Industrial Equipment, School of Automotive Engineering, Dalian University of Technology, China. His research interests include automatic-guided vehicles, image processing, pattern recognition and behaviour control. Rongben Wang received his BE, ME and PhD from Jilin University of Technology, China, in 1970, 1991 and 1995, respectively. He is currently a Professor in College of Traffic, Jilin University, China. His research interests include automatic-guided vehicles, computer vision systems and image processing.
1
Introduction
Autonomous ground vehicles have drawn much attention from numerous researchers for many years since they have substantial potential applications such as in construction, agriculture or planetary exploration. Automated longitudinal control is one of the fundamental functions for autonomous ground vehicle and exerts important influences on the navigation performances. Recently, much effort has been spent on various longitudinal control laws for on-highway vehicles. Sliding-mode control (SMC) scheme has been proposed based on non-linear vehicle models by Gerdes and Hedrick (1997), but their results did not include non-systematic input delay throttle and brake control. A modified sliding with variable control parameter was introduced to reduce the large change of pressure feedback in the brake control of highway vehicles by Liang and Chong, (2003). Longitudinal fuzzy controller with pole placement in Linear Matrix Inequation region, which is only considering throttle control, is given by Toulotte et al. (2008). In Fritz (1996), a neural-network automotive speed controller is presented, which could be used for autonomous intelligent cruise control including stop-and-go traffic situations. Longitudinal controller designed by means of second-order sliding mode technique is validated by experimental prototype vehicle in Nouveliere and Mammar (2007). Longitudinal controller design for autonomous ground vehicle differs from on-highway vehicle due to the differences in operation conditions. Ground vehicles often operate on unprepared, changing, and unpredictable off-road terrain, ranging from paved highways to spongy topsoil. Therefore, longitudinal controller for ground vehicles should provide an appropriate velocity response and must be able to quickly handle uncertainties and parameter variations caused by varying operating conditions.
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SMC is known not only for its robustness to model uncertainty and to parameter variations but also for its good disturbance rejection properties. However, SMC has limited usage in practise since it requires fast switching on the control input, which may result in chattering phenomenon .To eliminate or alleviate this chattering phenomenon, a boundary layer approach is introduced in Slotine and Sastry (1983). Although chattering can be alleviated through a boundary layer, tracking performance and robustness are compromised. Fuzzy logic control has been widely developed after the introduction of fuzzy logic by Zadeh, (1965). The application of fuzzy logic technique to eliminate or alleviate the chattering is proven as an effective means (Meystel et al., 1993; Yagiz and Hacioglu, 2005; Noroozi et al., 2009; Tao and Taur, 2008). Meystel et al. (1993) designed the fuzzy logic using two input variables: •
absolute radial distances from the origin and the absolute angle deviation from the sliding surface
•
the chattering of the SMC was alleviated by changing the equivalent and discontinuous control forces according to the commanded fuzzy logic.
Yagiz and Hacioglu (2005) suggested a SMC with moving sliding surface, which is decided dynamically by a fuzzy logic rule base. Noroozi et al. (2009) proposed an adaptive tracking fuzzy SMC to eliminate the chattering without deteriorating the system robustness. In this paper, a robust longitudinal sliding-mode controller based on fuzzy logic is proposed, and the control gains of SMC are tuned online by fuzzy logic algorithm. The simulation and experimental results illustrate the tracking performance of the proposed control algorithm. The structure of this paper is organised as follows: Section 2 presents the single-state vehicle longitudinal motion model, engine model and brake model. Section 3 describes the development of a longitudinal fuzzy-sliding control algorithm for an autonomous ground vehicle. In Section 4, the results of simulation and experiment are presented to show the effectiveness of proposed control algorithm. Finally, main conclusions are given in Section 5.
2
Vehicle model
The prototype vehicle is a front-wheel-drive system, as shown in Figure 1. The vehicle longitudinal dynamic model is simplified as three degrees of freedom model under the following assumptions: •
the dynamic characteristic of engine is approximated as a first-order model
•
torque converter is locked
•
no torsion of the drive axle
•
the slip between the tyres and the road surface is negligible.
A robust longitudinal sliding-mode controller design Figure 1
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The prototype vehicle (see online version for colours)
2.1 Vehicle longitudinal model The vehicle longitudinal dynamic model is developed using the bicycle model, and the state equation for the longitudinal motion of the vehicle is described by: ( J wf + J wr ) Ts − Tb − M rr − Fa − mg sin(θ ) m+ v = 2 h h
(1)
where Jwf and Jwr denote the front and rear wheel inertias, respectively; h is the tyre radius, m is the vehicle mass, f is the rolling resistance coefficient, θ is the road slope angle, Ts is the driving torque, Tb denote the brake torques. Fa = cxv2 is the aerodynamic drag, and cx is aerodynamic drag coefficient. Mrr = mgf cos(θ) is the rolling resistance torque. With a non-slip assumption, vehicle speed v and engine speed ωe are related by: v = Rg hωe
(2)
where Rg is the gear ratio. According to the assumption (2), the engine torque Te and the driving torque Ts are related by: J eω e = Te − Ts Rg
(3)
where Je is the engine/transmission inertias. From equations (1)–(3), the state equation of longitudinal motion can then be written by reflecting all of the forces and torques on the vehicle to the engine:
Jv = Te − Rg Tb − Rg h( M rr + Fa + mg sin θ ) + ∆E (t )
(4)
where J=
( J e + Rg2 ( J wr + J wf + mh 2 ))
Rg h
.
Te denotes the engine and brake torque and ∆E(t) represents uncertainties and external disturbances. Equation (4) may be viewed both as a state equation for v and as a means for determining the necessary brake or engine torque required to produce a given acceleration (Gerdes and Hedrick, 1997).
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Assumption 1: The unknown non-linear function ∆E is bounded above by known function ∆E 0) and Tb (t ) > 0 then
u (t ) = Te (t )
if (Te (t ) < 0) and (Tb (t ) < 0) and e > eswitch then
u (t ) = Tb (t )
else u (t ) = 0
With the logic above, it is clear that if Te(t) and Tb(t) are both positive, the throttle control is activated. The brake control is activated, if Te(t) and Tb(t) are both negative, as well as the absolute value of velocity error e greater than threshold value eswitch. The switching strategy designed in this paper avoids frequent changes between the throttle actuator and brake actuator.
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Simulation and experiment
To examine the performance of proposed control algorithms, here, numerical simulation and experimental tests in presence of heavy disturbances were performed. In addition, SMC, which is widely used in the design of longitudinal controller, is also used for comparison. The results, described in the following sections, provide some compelling evidence that the proposed controller, which works through switching throttle actuator and brake actuator, is indeed capable of tracking velocity, even in the presence of parametric uncertainties and external disturbances. The vehicle parameter values can be found in Table 2. The desired velocity trajectory produced from a trapezoidal acceleration profile is shown in Figure 7. The measurement noises and disturbances are given in Figure 8. Table 2
The values of vehicle parameters
Parameters ∆t
Values
Parameters
Values
0.02 s
h
0.30 m
Jwf/Jwr
1.583 kg m2
f
0.05
J
169.5 kg m
kb
1.18
Rg
0.276
λ
1
m
1975 kg
τe
0.45 s
cx
0.533 kg/m
τb
0.25 s
Figure 7
Desired velocity trajectory (see online version for colours)
Figure 8
Disturbances (see online version for colours)
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The results of simulation are shown in Figures 9 – 11, the initial condition error of velocity −0.5 m/s. Figure 9 shows the response of velocity error, the solid lines denote the system controlled by the FLSMC and the dotted lines denote the system controlled by the SMC. It can be seen that the FLSMC has faster tracking with smaller error values than SMC. Figure 9
The simulation results of tracking velocity error (see online version for colours)
The response of control inputs including throttle angle and brake pressure are given in Figures 10 and 11. Figures 10 and 11 indicate that both the FLSMC and the SMC were switched to the braker control at the segment of 37–48 s as the desired velocity decreasing, and the transition between throttle actuator and brake actuator is quite smooth, even in presence of uncertainties and disturbance. Moreover, they clearly point that the proposed FLSMC favourably attenuates the chattering. Figure 10 The simulation results of throttle angle (see online version for colours)
Figure 11 The simulation results of brake pressure (see online version for colours)
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The experimental response of the longitudinal control system with vehicle tracking velocity curve as shown in Figure 7 (starting from 0.5 m/s initial error) is tested, and the response results are given in Figure 11-Figure 13. The closed-loop system response with the FLSMC controller is shown in Figure 12, and the maximum velocity error is seen to be 0.1 m/s. Figures 13 and 14 show the response of throttle and brake pressure, respectively. The experimental results demonstrate that the proposed control algorithm is robust enough to reject disturbances and uncertainties. Figure 12 The experimental results of velocity error (see online version for colours)
Figure 13 The experimental results of throttle angle (see online version for colours)
Figure 14 The experimental results of brake pressure (see online version for colours)
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Conclusion
A robust SMC based on fuzzy logic strategy for longitudinal control of autonomous ground vehicle in presence of uncertainties and external disturbances is presented in this paper. To improve the performance of SMC and eliminate the chattering phenomenon, the gains of SMC are tuned by fuzzy logic. Simulation and experiment have been performed to investigate the performance of the proposed control strategy, and the results of simulation and experiment show the strong robustness and good tracking performance of proposed control strategy.
Acknowledgement This work was funded by the Key Project of the National Natural Science Foundation of China (No. 10932003), ‘973’ National Basic Research Project of China (No. 2010CB832700) and ‘04’ Great Project of Ministry of Industrialization and Information of China (No. 2011ZX04001-21). These supports are gratefully acknowledged. Many thanks are due to the referees for their valuable comments.
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Toulotte, P.F., Delprat, S., Guerra, T.M. and Boonaert, J. (2008) ‘Vehicle spacing control using robust fuzzy control with pole placement in LMI region’, Engineering Application of Artificial Intelligence, Vol. 21, No. 5, pp.756–768. Yagiz, N. and Hacioglu, Y. (2005) ‘Fuzzy sliding modes with moving surface for the robust control of a planar robot’, Journal of Vibration and Control, Vol. 11, No. 7, pp.903–922. Zadeh, L.A. (1965) ‘Fuzzy sets’, Information and Control, Vol. 8, pp.338–353.
