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.