Robust Offset-Free Lane-Keeping Control Framework for Vision-Only Automated Vehicles

Der-Hau Lee

cs.ROOct 23, 2026

Robust Offset-Free Lane-Keeping Control Framework for Vision-Only Automated Vehicles

Authors: Der-Hau Lee

Organizations: Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan

Abstract

Achieving accurate, real-time lane-keeping control during high-speed cornering on large-curvature roads while ensuring robust vehicle stability is a critical challenge in autonomous driving. To address this challenge, this study developed a robust offset-free model predictive control (OF-MPC) framework for vision-based autonomous vehicle lane-keeping. The regulation problem in this framework is solved using several algorithms. Numerical simulation results indicated that the interpolation-tube-based constrained iterative linear quadratic regulator (itube-CILQR) algorithm outperformed solvers based on the standard Interior Point Optimizer (IPOPT) and Operator Splitting Quadratic Program (OSQP), achieving a mean computation time of less than 5 ms. The itube-CILQR algorithm was then used for vehicle control in vision-based lane-keeping experiments in a simulation environment to quantify the perceptual uncertainty of a visual perception model (multitask UNet). This quantification was performed using the OF-MPC framework for traffic scenes that were not encountered during model training. Overall, the developed OF-MPC framework and the proposed method for characterizing the perceptual uncertainty of a visual perception system in unseen environments can contribute to the future development of advanced autonomous driving systems.

Figures & tables

Symbol	Values	Symbol	Values
$dt$	0.01 s	${C_{\alpha f}}$	80000 N/rad
$v_{x}$	{20.0, 21.1} m/s	${C_{\alpha r}}$	80000 N/rad
$I_{z}$	2000 kgm 2	$l_{f}$	1.27 m
$m$	1150 kg	$l_{r}$	1.37 m

TABLE I: Model and Vehicle Parameters Used in This Study

Symbol	Values	Symbol	Values
$N$	30	${\bf Q}$	diag([20, 1, 20, 1])
$\Delta$	[-2.0, 2.0] m	${\bf R}$	60 $\bf I$
$\dot{\Delta}$	[13.0, 13.0] m/s	${\bf Q}^{\prime}$	diag([1, 1])
$\theta$	[- $\pi/2$ , $\pi/2$ ] rad	${\bf R}^{\prime}$	60 $\bf I$
$\dot{\theta}$	[-10.0, 10.0] rad/s	${\bf S}$	50 $\bf I$
$\delta$	[- $\pi/6$ , $\pi/6$ ] rad	$q_{s}$	100

TABLE II: Ranges of the Control Parameters Considered in This Study

Fig. 1: Architecture of the proposed OF-MPC framework for closed-loop testing of the controlled system.

Fig. 2: Outer boundaries of sets

\mathbb{X}^{\prime}

\mathbb{\bar{X}}^{\prime}

\mathbb{S}^{e}

, and

\mathbb{S}^{x}

when

v_{x}

= 21.1 or 20.0 m/s and

\kappa

\pm

0.1 or

\pm

0.05 1/m. Here,

x_{1}\equiv\dot{\Delta}

and

x_{3}\equiv\dot{\theta}

Fig. 3: Outer boundaries of sets

\mathbb{\bar{T}}_{02}

and

\mathbb{\bar{T}}_{13}

when

v_{x}

= 20.0 or 21.1 m/s and

c_{i}

10^{-16}

or 20.0. Here,

x_{0}\equiv\Delta

x_{1}\equiv\dot{\Delta}

x_{2}\equiv\theta

, and

x_{3}\equiv\dot{\theta}

Fig. 4: Numerical simulation results obtained with different IPOPT- and OSQP-based solvers under tightened constraints when

v_{x}

= 20.0 m/s,

\left|{x_{1}}\right|\leq

13.0 m/s, and

\left|{x_{3}}\right|\leq

10.0 rad/s: (a) trajectory of the actual system state

x_{0}

(

\Delta

); (b) trajectory of the system control input

u

\delta

; and (c) trajectories of the estimated road curvatures obtained with the tube-OSQP-X algorithm, which were obtained by dividing the estimated disturbance vectors

{\hat{d}}_{0}

and

{\hat{d}}_{1}

\gamma_{0}

and

\gamma_{1}

, respectively.

Fig. 5: Numerical simulation results obtained with different itube-CILQR-based solvers when

v_{x}

= 20.0 m/s,

\left|{x_{1}}\right|\leq

13.0 m/s, and

\left|{x_{3}}\right|\leq

10.0 rad/s: (a) trajectory of the actual system state

x_{0}

(

\Delta

); (b) trajectory of the system control input

u

\delta

; and (c) trajectories of the estimated road curvatures obtained with the itube-CILQR-T-0 algorithm, which were obtained by dividing the estimated disturbance vectors

{\hat{d}}_{0}

and

{\hat{d}}_{1}

\gamma_{0}

and

\gamma_{1}

, respectively.

Fig. 6: Numerical simulation results obtained with the itube-CILQR solver when

v_{x}

= 20.0 m/s,

\left|{x_{1}}\right|\leq

13.0 m/s, and

\left|{x_{3}}\right|\leq

10.0 rad/s: trajectories of the actual system states (a)

x_{1}

, (b)

x_{2}

, and (c)

x_{3}

Method	tube-IPOPT-X b	tube-OSQP-X b	itube-CILQR-X	itube-CILQR-T-20	itube-CILQR-T-0
Max. $\Delta$ (m)	0.024333	0.024268	0.023162	0.022097	0.021675
Latency (ms)	6.45	0.84	1.10	4.21	7.35
a All algorithms were implemented in C++.
b The tube-IPOPT-T-0/20 and tube-OSQP-T-0/20 algorithms could not achieve convergence for the considered optimization problem.

TABLE III: Maximum Lateral Offsets and Average Computation Times Achieved by the tube-IPOPT-X, tube-OSQP-X, itube-CILQR-X, itube-CILQR-T-20, and itube-CILQR-T-0 Algorithms a

Fig. 7: Example traffic scene and maps of track A (left) and track B (right) in TORCS. The input of the adopted deep neural network model was an RGB image with a resolution of 228 $\times$ 228 pixels.

Fig. 8: Curvature profiles of tracks A and B.

Fig. 9: Dynamic performance of the itube-CILQR-T-20 algorithm in lane-keeping maneuvers within the central lanes of tracks A and B at a vehicle speed of 72 km/h when the noise level (

\sigma

) was set to 0 and the friction coefficient (

fr

) was set to 1.0.

Fig. 10: Dynamic performance of the itube-CILQR-T-20 algorithm in lane-keeping maneuvers within the central lanes of tracks A and B at a vehicle speed of 72 km/h when

\sigma

= 1.8

\%

and 2.0

\%

and

fr

= 1.0.

$\sigma$	track-A					track-B
	$fr$			Avg	SD	$fr$			Avg	SD
	1.0	0.9	0.8	Avg	SD	1.0	0.9	0.8	Avg	SD
0.5 $\%$	0.9941	0.9159	0.9324	0.9474	0.0412	0.8604	0.8616	0.8720	0.8646	0.0063
0.8 $\%$	1.4989	1.4021	1.4266	1.4425	0.0503	1.3625	1.3294	1.2987	1.3302	0.0319
1.0 $\%$	1.7393	1.6674	1.6334	1.6800	0.0540	1.5741	1.6156	1.4961	1.5619	0.0606
1.3 $\%$	1.9226	1.9093	1.9523	1.9280	0.0220	1.8943	1.8633	1.6802	1.8126	0.1157

TABLE IV: Average and Standard Deviation Values of the

\kappa

-Score During Lane-Keeping Maneuvers Conducted Using the itube-CILQR-T-20 Solver at Different

\sigma

and

fr

Values

Autonomous Driving

Autonomous driving develops vehicles that perceive road scenes, predict interactions, and plan and control safe movement with limited or no human input.

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Tube-Based Robust Control Strategy for Vision-Guided Autonomous Vehicles

Der-Hau Lee

Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan

Autonomous Driving Robust Control Linear Quadratic Regulator

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A robust control strategy for autonomous vehicles can improve system stability, enhance riding comfort, and prevent driving accidents. This paper presents a novel interpolation-tubebased constrained iterative linear quadratic regulator (itubeCILQR) algorithm for autonomous computer-vision-based vehicle lane-keeping. The goal of the algorithm is to enhance robustness during high-speed cornering on tight turns. Compared with standard tube-based approaches, the proposed itube-CILQR algorithm reduces system conservatism and exhibits higher computational speed. Numerical simulations and vision-based experiments were conducted to examine the feasibility of using the proposed algorithm for controlling autonomous vehicles. The results indicated that the proposed algorithm achieved superior vehicle lane-keeping performance to variational CILQRbased methods and model predictive control (MPC) approaches involving the use of a classical interior-point optimizer. Specifically, itube-CILQR required an average runtime of 3.45 ms to generate a control signal for guiding a self-driving vehicle. By comparison, itube-MPC typically required a 4.32 times longer computation time to complete the same task. Moreover, the influence of conservatism on system behavior was investigated by exploring the variations in the interpolation variables derived using the proposed itube-CILQR algorithm during lane-keeping maneuvers.

Abstract

Autonomous Driving

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