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Improved grey wolf optimizer based on opposition and quasi learning approaches for optimization: case study autonomous vehicle including vision system

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Abstract

The adapting of lateral deviation during the change of road curvature with less error, system settling time, and overshoot is the main challenge against the steering angle control of autonomous vehicles (AVs). In this regard, this paper introduces new learning techniques defined opposition-based learning (OBL) and quasi OBL (QOBL) to improve the exploration as well as exploitation manner of the grey wolf optimizer (GWO). The involved approach can enhance the searching behavior of the original GWO against the trapping in local optima. The proposed modified GWO (MGWO) is applied to detect the optimal factors of the adaptive model predictive control (AMPC) for AVs. The suggested MGWO-based AMPC is evaluated with the classical MPC and the adaptive fuzzy logic controller. Furthermore, the inspired MGWO is compared with the original GWO, neural network algorithm (NNA), heap-based optimizer, and equilibrium optimizer in literature. The performance of the introduced technique is tested to follow different road curvatures. Moreover, the presented method is approved against the time delay of the vision system and the produced uncertainty of system variables from the change of vehicle speed and look–ahead distance. Furthermore, the introduced MGWO-based AMPC can tackle the system settling time and overshoot to be less than 1 s and 1.696% respectively for the response of lateral deviation compared to other techniques. The attained results emphasize that the proposed MGWO-based AMPC controller has high damped and effective performance evaluated with other controllers.

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Abbreviations

AI:

Artificial intelligence

AMPC:

Adaptive model predictive control

AV:

Autonomous vehicle

EO:

Equilibrium optimizer

FL:

Fuzzy logic

FOD:

Figure of demerit

GWO:

Grey wolf optimizer

HBO:

Heap-based optimizer

KF:

Kalman filter

LTI:

Linear time invariant

MGWO:

Modified grey wolf optimizer

MPC:

Model predictive control

NL:

Negative large

NM:

Negative medium

NNA:

Neural network algorithm

OBL:

Opposition-based learning

PI:

Proportional–integral

PID:

Proportional–integral–derivative

PL:

Positive large

PM:

Positive medium

QOBL:

Quasi opposition-based learning

ZE:

Zero

v :

The velocity coordination (vx, vy)

v x :

Longitudinal x-axis velocity

v y :

Lateral y-axis velocity

δ f :

Front wheel steering angle

l f :

Front axle space

l r :

Rear axle space

\(\dot{\phi }\) :

The vehicle yaw rate

c f , c r :

The front and rear tires stiffness

m :

The weight of the vehicle mass

I ψ :

The vehicle inertia across CoG

y L :

Vehicle lateral deviation

R L :

The road radius from the target position

K L :

The disturbance in road curvature

\(\varepsilon_{L}\) :

The angle within the orientation of vehicle and the tangent of road

L :

Look-ahead distance

Δu j :

The control moves and equal uj – uj–1

Q, R :

Weighting factors

r k + i :

The reference value

k :

The sample index of time

x :

System state variables

u :

Control signal

v :

The system measured outside effects

d :

The system unmeasured outside effects

y :

Predicted response

\(\overline{x}\) :

The system normal state variables

\(\Delta \overline{x}\) :

The change in states

\(\overline{u}_{t}\) :

The normal control input

\(\overline{y}\) :

Normal output

T s :

Sample time

P :

Prediction zone

M :

Control zone

K P :

Proportional gain

K I :

Integral gain

K si :

Scaling factor, i = 1,..,4

\(X^{p} (t)\) :

Prey position

\(X(t)\) :

Wolf position

t :

Iteration number

a :

Linear function decreased from 2 to 0

r 1 , r 2 :

Random numbers in [0, 1]

M P :

The response maximum overshoot

E SS :

The response steady-state error

t s :

The response settling time

β :

Weighting factor

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Acknowledgements

This work was supported by the Ministry of Science and Technology (MOST) of Taiwan (Grant No.: MOST 110-2222-E-011-013-) and the Center for Cyber-physical System Innovation from the Featured Areas Research Center Program in the Agenda of the Ministry of Education (MOE), Taiwan.

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  1. Industry 4.0 Implementation Center, Center for Cyber-Physical System Innovation, National Taiwan University of Science and Technology, Taipei, 10607, Taiwan

    M. Elsisi

  2. Department of Electrical Engineering, Faculty of Engineering (Shoubra), Benha University, 108 Shoubra St., B. O. Box 11241, Cairo, Egypt

    M. Elsisi

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Elsisi, M. Improved grey wolf optimizer based on opposition and quasi learning approaches for optimization: case study autonomous vehicle including vision system. Artif Intell Rev 55, 5597–5620 (2022). https://doi.org/10.1007/s10462-022-10137-0

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