Neural L1 Adaptive Control of Vehicle Lateral Dynamics

TL;DR

This work targets stable, robust lane keeping for front-steered vehicles under unknown disturbances. It extends $\mathcal{L}_1$ Adaptive Control by integrating a neural residual learner (Neural-L1) via a dual-time-scale DNN, preserving stability guarantees while enhancing tracking accuracy. The authors provide theoretical stability extensions, implement Neural-L1 for lane keeping on a front-steered Ackermann vehicle, and validate performance through PyBullet simulations and real F1TENTH experiments with intentional disturbances and obstacles, showing superiority over LF, L1adap, and Deep-MRAC. The results suggest Neural-L1 offers a practical, robust approach for autonomous vehicle control in uncertain environments.

Abstract

We address the problem of stable and robust control of vehicles with lateral error dynamics for the application of lane keeping. Lane departure is the primary reason for half of the fatalities in road accidents, making the development of stable, adaptive and robust controllers a necessity. Traditional linear feedback controllers achieve satisfactory tracking performance, however, they exhibit unstable behavior when uncertainties are induced into the system. Any disturbance or uncertainty introduced to the steering-angle input can be catastrophic for the vehicle. Therefore, controllers must be developed to actively handle such uncertainties. In this work, we introduce a Neural L1 Adaptive controller (Neural-L1) which learns the uncertainties in the lateral error dynamics of a front-steered Ackermann vehicle and guarantees stability and robustness. Our contributions are threefold: i) We extend the theoretical results for guaranteed stability and robustness of conventional L1 Adaptive controllers to Neural-L1; ii) We implement a Neural-L1 for the lane keeping application which learns uncertainties in the dynamics accurately; iii)We evaluate the performance of Neural-L1 on a physics-based simulator, PyBullet, and conduct extensive real-world experiments with the F1TENTH platform to demonstrate superior reference trajectory tracking performance of Neural-L1 compared to other state-of-the-art controllers, in the presence of uncertainties. Our project page, including supplementary material and videos, can be found at https://mukhe027.github.io/Neural-Adaptive-Control/

Figures (9)

• Figure 1: A lateral lane keeping system (LKS) for a front-steered Ackermann vehicle, depicting the effect of uncertainties such as signal disturbance in the form $\Delta(x)+\Bar{\Delta}(x)$, potholes and ramp, on the lane keeping performance. The image depicts a simplified linear two-degrees of freedom (2-DOF) bicycle model of the vehicle lateral dynamics derived in rajamani2011vehicle.
• Figure 2: Overview of our approach depicts the L1adaphovakimyan20111 (the red box), the neural network-based adaptive law (the green box) and the neural network training mechanism (the blue box), adopted from joshi2019deep. Unlike joshi2019deep, in our architecture, we append the neural network learned adaptive law $\Delta^{'}(x)$ to the L1adap derived adaptive law $\hat{\Bar{\Delta}}(x)$, to obtain $\Delta^{'}(x_1)+\hat{\Bar{\Delta}}(x_1)$ (indicted with yellow arrow). Here neural network learned adaptive law $\Delta^{'}(x)$ is considered to be the residual uncertainty that is being learned.
• Figure 3: PyBullet simulation of lane-keeping dynamics comparing trajectory tracking performance on arbitrary trajectories for our proposed controller Neural-L1(pink) against existing controllers: LF(red), L1adap(blue) and Deep-MRAC(green).
• Figure 4: Profiles of the states of the system $[e_1, \dot{e}_1, e_2, \dot{e}_2]$ in PyBullet simulation.
• Figure 5: Comparison of uncertainty learned by adaptive controllers for F1TENTH in PyBullet simulation.

Theorems & Definitions (8)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Theorem 1
• proof