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
Cαf
80000 N/rad
vx
{20.0, 21.1} m/s
Cαr
80000 N/rad
Iz
2000 kgm 2
lf
1.27 m
m
1150 kg
lr
1.37 m
TABLE I: Model and Vehicle Parameters Used in This Study
Symbol
Values
Symbol
Values
N
30
Q
diag([20, 1, 20, 1])
Δ
[-2.0, 2.0] m
R
60 I
Δ˙
[13.0, 13.0] m/s
Q′
diag([1, 1])
θ
[- π/2 , π/2 ] rad
R′
60 I
θ˙
[-10.0, 10.0] rad/s
S
50 I
δ
[- π/6 , π/6 ] rad
qs
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 X′ , Xˉ′ , Se , and Sx when vx = 21.1 or 20.0 m/s and κ = ± 0.1 or ± 0.05 1/m. Here, x1≡Δ˙ and x3≡θ˙ .
Fig. 3: Outer boundaries of sets Tˉ02 and Tˉ13 when vx = 20.0 or 21.1 m/s and ci = 10−16 or 20.0. Here, x0≡Δ , x1≡Δ˙ , x2≡θ , and x3≡θ˙ .
Fig. 4: Numerical simulation results obtained with different IPOPT- and OSQP-based solvers under tightened constraints when vx = 20.0 m/s, ∣x1∣≤ 13.0 m/s, and ∣x3∣≤ 10.0 rad/s: (a) trajectory of the actual system state x0 ( Δ ); (b) trajectory of the system control input u = δ ; and (c) trajectories of the estimated road curvatures obtained with the tube-OSQP-X algorithm, which were obtained by dividing the estimated disturbance vectors d^0 and d^1 by γ0 and γ1 , respectively.
Fig. 5: Numerical simulation results obtained with different itube-CILQR-based solvers when vx = 20.0 m/s, ∣x1∣≤ 13.0 m/s, and ∣x3∣≤ 10.0 rad/s: (a) trajectory of the actual system state x0 ( Δ ); (b) trajectory of the system control input u = δ ; 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 d^0 and d^1 by γ0 and γ1 , respectively.
Fig. 6: Numerical simulation results obtained with the itube-CILQR solver when vx = 20.0 m/s, ∣x1∣≤ 13.0 m/s, and ∣x3∣≤ 10.0 rad/s: trajectories of the actual system states (a) x1 , (b) x2 , and (c) x3 .
Method
tube-IPOPT-X b
tube-OSQP-X b
itube-CILQR-X
itube-CILQR-T-20
itube-CILQR-T-0
Max. Δ (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 × 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 ( σ ) 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 σ = 1.8 % and 2.0 % and fr = 1.0.
σ
track-A
track-B
fr
Avg
SD
fr
Avg
SD
1.0
0.9
0.8
1.0
0.9
0.8
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 κ -Score During Lane-Keeping Maneuvers Conducted Using the itube-CILQR-T-20 Solver at Different σ and fr Values
Autonomous driving develops vehicles that perceive road scenes, predict interactions, and plan and control safe movement with limited or no human input.
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.
Der-Hau Lee
Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
Model Predictive Control (MPC) is widely used for autonomous-vehicle (AV) motion planning, but its real-time applicability is often limited by the need for accurate models and online solution of nonlinear, nonconvex optimization problems in dynamic road environments. Actor-critic reinforcement learning offers a promising alternative for online policy generation, yet its policy-learning process often lacks explicit control-theoretic structure. This article proposes a learning predictive control (LPC) framework with deep Koopman operators for efficient real-time motion planning under nonconvex constraints. To address nonlinear and uncertain vehicle dynamics, a deep-Koopman-based predictor is used to lift the system into an interpretable linear observable space in a data-driven manner. Unlike traditional MPC, which computes open-loop control sequences, the proposed LPC framework yields a closed-loop state-feedback policy within each prediction interval through receding-horizon actor-critic learning. To ensure safety under nonconvex environmental constraints, LPC constructs convex local surrogate representations of obstacles and defines corresponding potential-field functions. These functions and their gradients are directly embedded into the actor-critic structure, enabling efficient, safety-aware policy learning. Extensive simulations and real-world experiments on the HongQi-EHS3 platform demonstrate favorable performance in diverse obstacle-avoidance scenarios in terms of safety, computational efficiency, and driving comfort, compared with benchmark methods such as CBF-MPC and LMPCC.
Controlling an agent in an environment solely perceived through onboard vision is challenging: perception yields noisy, variable-length, and partially occluded context, while onboard compute is shared between perception and control, limiting the planning horizon executable in real time. We propose VIGOR-MPC, a modular student-teacher framework, agnostic to the perception pipeline, which addresses reference tracking across navigation tasks by distilling a privileged, field-of-view-aware long-horizon MPC into a computationally lightweight short-horizon MPC whose cost parameters are determined online from vision. The teacher operates in simulation with full state knowledge and a multi-trajectory formulation that guarantees the agent can stay within its field of view. The student observes only the noisy, occluded context produced by a perception module and learns, via a multi-level recurrent mapping, to infer cost parameters that aim to recover the teacher's behavior despite missing information. We evaluate VIGOR-MPC on vision-based autonomous racing in simulation and on hardware. Using only onboard perception of the track, VIGOR-MPC generalizes to tracks unseen during training and approaches the lap times of the privileged long-horizon teacher while reducing per-step computation by over 90%.
Jelena Trisovic, Rahel Rickenbach, Marek Landert +2
Institute for Dynamic Systems and Control, ETH Zurich, Switzerland · ETH AI Center