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Intelligent fractional-order sliding mode control based maneuvering of an autonomous vehicle

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Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

This article proposes a new intelligent trajectory tracking control law for the precise maneuvering of an autonomous vehicle in the presence of parametric uncertainties and external disturbances. The controller design includes a fuzzy sliding mode algorithm for smooth motion control subjected to steering saturation and curvature constraints. Along with the Salp Swarm Optimization technique, explored for optimal selection of surface coefficient in fractional order Proportional-Derivative type \(P{D}^{\alpha }\) sliding manifold. The sliding variable on the surface approaches zero in a finite time. Further, the trajectory tracking control rule offers the stability of closed-loop tracking on the predetermined path and ensures finite time convergence to the sliding surface. In addition, to estimate the hitting gain in online mode, a supervisory fuzzy logic controller system is used. Therefore, it is not necessary to determine upper bounds on uncertainty in the dynamic parameters of autonomous vehicles. Lyapunov theory verifies the global asymptotic stability of the entire closed-loop control strategy. The major control issue is the input constraints arising primarily due to the capability of the steering actuating module, which causes significant deviation or vehicle instability. Consequently, it is desirable to design a robust adaptive stable controller, such as Adaptive Backstepping Control (ABC), even though it requires vehicle model information. Therefore, the proposed model-free intelligent sliding mode technique offers better tracking performance and vehicle stability in adverse conditions. Finally, the efficacy of the proposed control technique was confirmed through a comparative analysis based on numerical simulation using MATLAB/SIMULINK and experimental validation using Quanser’s self-driving car module. A quantitative study was conducted to elucidate the superior tracking performance of intelligent control over the traditional SMC and adaptive backstepping control methods.

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The authors declare no additional data and materials are submitted.

Abbreviations

Γ:

Gamma function

S:

Sliding manifold

V:

Lyapunov function

u:

Command control torque (in Newton meters)

x :

State vector

\(\Delta {{f}}\left({{x}},{{t}}\right)\) :

Unmodeled dynamics

\({{d}}\left({{t}}\right)\) :

Disturbance

\({{{e}}}_{{{k}}}\) :

Tracking error function

\({{\Phi }}_{{{k}}}\) :

Boundary layer width

m:

Vehicle mass (in kilograms)

Iz :

Moment of inertia (in kilogram per meter square)

Lf :

Front axle to center of the mass distance (in meters)

Lr :

Rear axle to center of the mass distance (in meters)

Cf :

Front tire cornering stiffness (in kilonewton per radians)

Cr :

Rear tire cornering stiffness (in kilonewton per radians)

Vx :

Velocity along X axis (in meters per second)

Vy :

Velocity along Y axis (in meters per second)

ψ:

Yaw angle (in deg)

β:

Slip angle at center (in deg)

θ:

Heading angle (in degree)

δ:

Front wheel steering angle (in degree)

αf :

Slip angle of front tyre (in degree)

αr :

Slip angle of the rear tyre (in degree)

R:

Tire radius (in meters)

Tw :

Braking wheel torque (in Newton meters)

Tb :

Brake torque (in Newton meters)

Fyf :

Front tire lateral force (in newtons)

Fyr :

Rear tire lateral force (in newtons)

Af :

Longitudinal drag area (in meter square)

Cd :

Longitudinal drag coefficient

Cl :

Longitudinal lift coefficient

Cpm :

Longitudinal drag pitch moment

Tm :

Traction

Tbf :

Braking torque front tire

Tbr :

Braking torque rear tire

μ:

Nominal friction scaling factor

Pabs :

Absolute pressure (in Pascal)

g:

Gravitational acceleration (in meter per square)

ITAE:

Integral of time-weighted absolute error

IAE:

Integral absolute error

ISE:

Integral square error

References

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Acknowledgements

The work is supported by the Center of Intelligent Mobility (CIM), KLE Technological University, Hubli, Karnataka and collaborated with Department of Instrumentation and Control, COEP Technological University, Pune, Maharashtra. The authors would like to express their sincere gratitude to the Editor-in-Chief and anonymous reviewers whose constructive comments have helped us to significantly improve both the technical quality and presentation of this manuscript. Authors are deeply grateful to Head, Department of Instrumentation and Control engineering, COEP Technological University, Pune, M.S., for utilization of laboratory to carrying out research work.

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No financial funding received for the work.

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Authors and Affiliations

  1. School of Electronics and Communication, KLE Technological University, Hubli, Karnataka, India

    Raghavendra M. Shet & Nalini C. Iyer

  2. Department of Instrumentation and Control, COEP Technological University, Pune, Maharashtra, India

    Girish V. Lakhekar

Authors
  1. Raghavendra M. Shet
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  2. Girish V. Lakhekar
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  3. Nalini C. Iyer
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Contributions

Conceptualization, RMS, GVL; Methodology, RMS, GVL; Software, RMS, GVL; Validation, RMS, GVL; Formal analysis, GVL, NCI; Investigation, RMS and GVL.; Resources, NCI.; Data curation, RMS and GVL; Writing—original draft preparation, RMS and GVL; Writing—review and editing, RMS, GVL and NCI.; Visualization, RMS and GVL.; Supervision, NCI; Project administration, NCI; Funding acquisition, NCI. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Raghavendra M. Shet.

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Shet, R.M., Lakhekar, G.V. & Iyer, N.C. Intelligent fractional-order sliding mode control based maneuvering of an autonomous vehicle. J Ambient Intell Human Comput (2024). https://doi.org/10.1007/s12652-024-04770-6

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  • DOI: https://doi.org/10.1007/s12652-024-04770-6

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