Lane-Keeping Control of Autonomous Vehicles Through a Soft-Constrained Iterative LQR

TL;DR

This work addresses the instability caused by jitter in steering inputs for autonomous lane-keeping by introducing soft-CILQR, a real-time capable controller that couples constrained ILQR with soft-constrained MPC through slack variables in barrier functions. The method formulates a finite-horizon, dual-mode MPC with augmented slack dynamics, solves via ILQR with Newton-based Slack updates, and uses an offline MPI-based horizon bound to guarantee constraint satisfaction. Empirical results in numerical simulations and TORCS-based vision experiments show that soft-CILQR achieves smoother steering trajectories under disturbances while maintaining asymptotic convergence, and it outperforms soft-MPC in speed by orders of magnitude. This approach offers a robust, computationally efficient solution for real-time autonomous lane-keeping under adverse conditions, with demonstrated potential for deployment in vision-based driving systems.

Abstract

The accurate prediction of smooth steering inputs is crucial for automotive applications because control actions with jitter might cause the vehicle system to become unstable. To address this problem in automobile lane-keeping control without the use of additional smoothing algorithms, we developed a novel soft-constrained iterative linear quadratic regulator (soft-CILQR) algorithm by integrating CILQR algorithm and a model predictive control (MPC) constraint relaxation method. We incorporated slack variables into the state and control barrier functions of the soft-CILQR solver to soften the constraints in the optimization process such that control input stabilization can be achieved in a computationally simple manner. Two types of automotive lane-keeping experiments (numerical simulations and experiments involving challenging vision-based maneuvers) were conducted with a linear system dynamics model to test the performance of the proposed soft-CILQR algorithm, and its performance was compared with that of the CILQR algorithm. In the numerical simulations, the soft-CILQR and CILQR solvers managed to drive the system toward the reference state asymptotically; however, the soft-CILQR solver obtained smooth steering input trajectories more easily than did the CILQR solver under conditions involving additive disturbances. The results of the vision-based experiments in which an ego vehicle drove in perturbed TORCS environments with various road friction settings were consistent with those of the numerical tests. The proposed soft-CILQR algorithm achieved an average runtime of 2.55 ms and is thus applicable for real-time autonomous driving scenarios.

Figures (17)

• Figure 1: Relationship between $\varepsilon _{\max}$ and the computed $N_\nu$ value when $v_x$ = 20.0 m/s.
• Figure 2: Visualization of $\chi _{MPI}$ for subsystems ($x_0$, $x_1$) = (${\Delta }$, ${\dot \Delta }$) and ($x_2$, $x_3$) = ($\theta$, ${\dot \theta }$) under $\varepsilon _{\max}$ values of 19, 29, and 49.
• Figure 3: Numerical simulation results for the CILQR and soft-CILQR solvers obtained when $v_x$ = 20.0 m/s, $S$ = 0.01, $N$ = 40, $\varepsilon _{\max}$ = 49, and $\sigma$ = 0.0. (a) Trajectories of $\Delta$ and $\theta$. Trajectories of the first component of the optimal (b) steering angle and (c) slack sequences. Dashed lines represent reference data points (zeros).
• Figure 4: Numerical simulations results of the CILQR and soft-CILQR solvers obtained when $v_x$ = 20.0 m/s, $S$ = 0.01, $N$ = 40, $\varepsilon _{\max}$ = 49, and $\sigma$ = 1.0. (a) Trajectories of $\Delta$ and $\theta$. Trajectories of the first component of the optimal (b) steering angle and (c) slack sequences.
• Figure 5: Numerical simulations results obtained for the CILQR and soft-CILQR solvers when $v_x$ = 20.0 m/s, $S$ = 0.01, $N$ = 40, $\varepsilon _{\max}$ = 49, and $\sigma$ = 2.0. (a) Trajectories of $\Delta$ and $\theta$. Trajectories of the first component of the optimal (b) steering angle and (c) slack sequences.