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. The advantages of itube-CILQR over the standard tube-approach include reduced system conservatism and increased computational speed. Numerical and vision-based experiments were conducted to examine the feasibility of the proposed algorithm. The proposed itube-CILQR algorithm is better suited to vehicle lane-keeping than variational CILQR-based methods and model predictive control (MPC) approaches using a classical interior-point solver. Specifically, in evaluation experiments, itube-CILQR achieved an average runtime of 3.16 ms to generate a control signal to guide a self-driving vehicle; itube-MPC typically required a 4.67-times longer computation time to complete the same task. Moreover, the influence of conservatism on system behavior was investigated by exploring the interpolation variable trajectories derived from the proposed itube-CILQR algorithm during lane-keeping maneuvers.