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

TL;DR

The paper addresses robust vision-guided lane-keeping for autonomous vehicles encountering large road curvatures by developing itube-CILQR, a barrier-based, interpolation-tube MPC variant that integrates CILQR with adaptive tightened constraints. It introduces an online interpolation framework that blends tightened constraint sets using weights and a curvature-aware κ-table, while solving a convex ILQR-based optimization for real-time performance. Key findings show that itube-CILQR achieves superior lateral tracking with significantly lower computation times (~3.45 ms) compared to IPOPT-based MPC, and reduces conservatism relative to standard tube-MPC, as demonstrated in numerical simulations and TORCS-based vision experiments. The method promises real-time robustness for practical autonomous driving and sets the stage for further validation with vehicle-in-the-loop or real-world hardware tests.

Abstract

A robust control strategy for autonomous vehicles can improve system stability, enhance riding comfort, and prevent driving accidents. This paper presents a novel interpolation-tube-based constrained iterative linear quadratic regulator (itube-CILQR) 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 CILQR-based 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.

Figures (16)

• Figure 1: Visualization of sets $\mathbb{X}'$, $\mathbb{\bar{X}}'$, and $\mathbb{S}_{RPI}$ when $v_x$ = 20.0 or 22.2 m/s and $\kappa$ = $\pm$0.05 and $\pm$0.1 1/m. Here, $x_1 \equiv \dot \Delta$ and $x_3 \equiv \dot \theta$.
• Figure 2: Visualization of sets $\mathbb{\bar{T}}'$ and $\mathbb{\bar{T}}'_{lir}$ when $v_x$ = 20.0 or 22.2 m/s and $\kappa$ = $\pm$0.1 1/m. In (a), $\mathbb{\bar{T}}'$ is defined by 14 inequalities, and the corresponding vertex coordinates in the first and third quadrants are identical to those of $\mathbb{\bar{X}}'$ in Fig. 1(a).
• Figure 3: Profile of an example exponential barrier function $B\left( x \right) = \exp \left[ {q\left( {x - 1} \right)} \right] + \exp \left[ {q\left( { - 1 - x} \right)} \right]$, where $x$ can be a state or control variable. As the penalty parameter $q$ increases, $B(x)$ increases rapidly when $x > 1$ and $x < -1$ but approaches 0 when $x =0$.
• Figure 4: Curvature profile for numerical simulations.
• Figure 5: Numerical simulation results obtained with different CILQR algorithms when $v_x$ = 20.0 m/s, $D$ = 0.22, $\left| {x_1 } \right| \le$ 9.0 m/s, and $\left| {x_3 } \right| \le$ 4.0 rad/s. (a) Trajectory of the actual system state $x_0$. (b) Trajectory of the actual system control input. (c) Trajectories of the first components of the optimal interpolation variable sequences for $x_0 \equiv \Delta$ and $u \equiv \delta$. In (a), the $x_0$ values obtained with the tube-CILQR-up and itube-CILQR algorithms at $t$ = 700 are -0.2221 and -0.2201 m, respectively. In (c), $\Delta \lambda$ = 0.0331, 0.1283, and 0.0834 at $t$ = 0, 600, and 1100, respectively. The experimental results obtained at different $D$ values are presented in Table III.

Theorems & Definitions (3)

• Proposition 1
• Proposition 2
• Proposition 3