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Improved sliding mode control for mobile manipulators based on an adaptive neural network

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Abstract

In this study, a wheeled mobile manipulator was modeled while considering the case of wheel-ground slippage. Considering the whole system, the number of states in the dynamic system equation was reduced by the kinematic solution, which facilitates the control of the system. For the system state equation, the improved sliding mode control method was applied, a flush continuous control term and a super-twisting algorithm were used to achieve the improved sliding mode control, and the gain of the super-twisting algorithm was adaptively controlled. The modeling error in the subsystem and the uncertain slippage were approximated by a neural network. The middle layer weights of the neural network were updated by the adaptive control law, and the stability of the system was demonstrated by a quadratic Lyapunov function. The simulation results show the superiority of the control method proposed in this paper by comparing them with results for the traditional sliding-mode control method and the improved sliding-mode control method.

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Abbreviations

q :

Mobile manipulator orientation matrix

θ :

Rotation angles of the mobile platform

θ 1 :

Rotation angle at manipulator joint 1

θ 2 :

Rotation angle at manipulator joint 2

θ R :

Rotational velocity of the right wheel of the mobile platform

θ l :

Rotational velocity of the left wheel of the mobile platform

v r :

Linear velocity of the right wheel of the mobile platform

v L :

Linear velocity of the left wheel of the mobile platform

T :

System kinetic energy

P :

System potential energy

2b :

Wheelbase of the rear wheels

d :

Distance between the rear wheel axis and the center of mass of the mobile platform

l :

Wheelbase of the front and rear wheels

2r :

Diameter of each wheel

I w :

Rotational inertia of each linkage

l m :

Length of each linkage in the mechanical arm

I :

Rotational inertia of the platform

I m :

Rotational inertia of each linkage

I p :

Rotational inertia of the robot with respect to the pitch axis

I q :

Rotational inertia of the robot with respect to the rotation axis

k :

Stiffness coefficient of each suspension

M(q):

Mass matrix

M ij :

Element in the mass matrix

M :

Mass of the mobile platform

M i :

Mass of manipulator joint i

\(V(q,\dot q)\) :

Coriolis force and centrifugal force matrix

V ij :

Coriolis and centrifugal force matrix elements

G(q):

Gravity matrix

B(q):

Input transformation matrix

τ :

Control input matrix

τ 1 :

Right driving torque of the platform wheels

τ 2 :

Left driving torque of the platform wheels

τ 3 :

Driving torque of two-link arm lever 1

τ 4 :

Driving torque of two-link arm lever 2

u :

Lateral sliding disturbance of the mobile platform

ζ L :

Angular velocity disturbance when the left wheel slips

ζ R :

Angular velocity disturbance when the right wheel slips

A(q):

Null subspace set of bases

Λ:

Perturbation matrix that exists when the mobile platform slips

s :

Sliding-mode surface function

u nom :

Homogeneous continuous control term

u ast :

Super-twisting function

α :

Super-twisting l function control gain

β :

Super-twisting function control gain

h j :

Output of the gaussian function

W :

Weights of the intermediate layer

V i (ξ):

Lyapunov stability function

PD :

PD controller

SMC :

Traditional sliding-mode controller

ISMC :

Improved sliding-mode controller

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Acknowledgments

The authors would like to thank the National Key R&D Program of China for Robot Projects (grant number 2018YFB 1308700), the Shanxi Provincial Key Core Technologies and Common Technology Special Projects (grant number 2020 XXX009), the Shanxi Provincial Special Project of Scientific and Technological Cooperation and Exchange (grant number 202104041101031), the Science and Technology Project of Shanxi Provincial Department of Transportation (grant number 2019-01-09).

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Authors and Affiliations

  1. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Zhengnan Li, Lidong Ma, Zhijuan Meng, Jin Zhang & Yufeng Yin

  2. College of Intelligent Manufacturing, Shanxi Vocational University of Engineering Science and Technology, Jinzhong, 030031, China

    Jin Zhang

Authors
  1. Zhengnan Li
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  2. Lidong Ma
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  3. Zhijuan Meng
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  4. Jin Zhang
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  5. Yufeng Yin
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Corresponding author

Correspondence to Lidong Ma.

Additional information

Lidong Ma is a Professor and Ph.D. He received his Ph.D. degree from Yanshan University in 2010. Then, he studied at Auburn University, USA, as a visiting scholar from December 2016 to January 2018. His research areas include intelligent robotic systems and advanced detection technologies. Now, his major researches include the National Key Research and Development Program, R&D Tackling Projects of Core Technology, and Generic Technology in Shanxi Province.

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Li, Z., Ma, L., Meng, Z. et al. Improved sliding mode control for mobile manipulators based on an adaptive neural network. J Mech Sci Technol 37, 2569–2580 (2023). https://doi.org/10.1007/s12206-023-0432-7

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  • DOI: https://doi.org/10.1007/s12206-023-0432-7

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