Extended model predictive control scheme for smooth path following of autonomous vehicles

doi:10.1007/s11465-021-0660-4

Front. Mech. Eng.

2022, Vol. 17

Issue (1) : 4 https://doi.org/10.1007/s11465-021-0660-4

RESEARCH ARTICLE

Extended model predictive control scheme for smooth path following of autonomous vehicles

Qianjie LIU¹, Shuang SONG¹, Huosheng HU², Tengchao HUANG¹, Chenyang LI¹, Qingyuan ZHU¹(

)

¹. Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361102, China
². School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK

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Abstract

This paper presents an extended model predictive control (MPC) scheme for implementing optimal path following of autonomous vehicles, which has multiple constraints and an integrated model of vehicle and road dynamics. Road curvature and inclination factors are used in the construction of the vehicle dynamic model to describe its lateral and roll dynamics accurately. Sideslip, rollover, and vehicle envelopes are used as multiple constraints in the MPC controller formulation. Then, an extended MPC method solved by differential evolution optimization algorithm is proposed to realize optimal smooth path following based on driving path features. Finally, simulation and real experiments are carried out to evaluate the feasibility and the effectiveness of the extended MPC scheme. Results indicate that the proposed method can obtain the smooth transition to follow the optimal drivable path and satisfy the lateral dynamic stability and environmental constraints, which can improve the path following quality for better ride comfort and road availability of autonomous vehicles.

Keywords autonomous vehicles vehicle dynamic modeling model predictive control path following optimization algorithm

Corresponding Author(s): Qingyuan ZHU

Just Accepted Date: 23 December 2021 Issue Date: 28 January 2022

Cite this article:

Qianjie LIU,Shuang SONG,Huosheng HU, et al. Extended model predictive control scheme for smooth path following of autonomous vehicles[J]. Front. Mech. Eng., 2022, 17(1): 4.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0660-4
https://academic.hep.com.cn/fme/EN/Y2022/V17/I1/4

Fig.1 Vehicle dynamic modeling with road bank: (a) lateral dynamics, (b) roll dynamics.

Fig.2 Phase plane trajectories of nonlinear vehicle dynamics: (a) lateral dynamic, (b) tire slip angle.

Fig.3 Extended MPC-based control scheme.

Fig.4 Optimization procedure of DE algorithm in path following.

Fig.5 Nominal path and road bank: (a) nominal path, (b) road bank.

Fig.6 Comparison of LTR, LTR_d, and LTR_d without considering φ_r.

Fig.7 Simulation results of path following for considering multiple constraints and road bank: (a) lateral error, (b) yaw error, (c) lateral velocity versus yaw rate, and (d) steer angle.

Tab.1 RMS and Max values of path following for conventional MPC controller

Fig.8 Simulation results of path following for conventional and extended MPC controllers at 20 m/s: (a) path following, (b) steer angle, (c) path curvature, (d) yaw rate, and (e) rollover threshold.

Fig.9 Simulation results of path following for conventional and extended MPC controllers at 30 m/s: (a) path following, (b) steer angle, (c) path curvature, (d) yaw rate, and (e) rollover threshold.

Tab.2 RMS and Max values of path following for conventional and extended MPC controllers

Fig.10 HIL test system based on Simulink and dSPACE system.

Fig.11 Experiment comparison results performed in HIL system: (a) path following, (b) steer angle, (c) path curvature, and (d) lateral velocity versus yaw rate.

y_R	Lateral position of rear axle
?y	Distance between two adjacent points in y direction
α_hj	Saturation slip angle
α_j	Tire slip angle
α_f	Front tire slip angle
α_r	Rear tire slip angle
α_t	Limit tire slip angle
β	Vehicle sideslip angle
δ_f	Front steer angle
δ_fmax	Maximum value of δ_f
δ_fmin	Minimum value of δ_f
ε	Slack variable
φ	Roll angle of vehicle
φ_r	Road bank angle
η_r	Robust mutation factor
$κ$	Reference road curvature
λ	Slack weight
σ	Penalty factor
ρ	Driving path curvature
ψ	Yaw angle
ψ_ref	Reference heading angle
?δ_fmax	Maximum of steer angle increment
?δ_fmin	Minimum of steer angle increment
Δδ_fij	Initial individual
$Г κ$	Weight factor of ρ
Г_s	Weight factor of S
Г_u	Weight factor of ?u
Г_ψ	Weight factor of e_ψ
A	Augmented state matrix
A_c	State matrix
A_d	Discrete state matrix
A_m	System state matrix
$A ~$	Predicted state matrix for output system
$A ~ h$ , $B ~ uh$ , $B ~ vh$	Coefficient matrices for hard constraints
$A ~ s$ , $B ~ us$ , $B ~ vs$	Coefficient matrices for soft constraints
$A ~ x$	Predicted state matrix
B_u	Augmented input matrix
B_uc	Input matrix
B_ud	Discrete input matrix
B_um	System input matrix
B_v	Augmented disturbance matrix
B_vc	Disturbance matrix
B_vd	Discrete disturbance matrix
B_vm	System disturbance matrix
$B ~ u$	Predicted input matrix for output system
$B ~ u x$	Predicted input matrix
$B ~ v$	Predicted disturbance matrix for output system
$B ~ v x$	Predicted disturbance matrix

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