This paper presents a robust control framework for lane-keeping and obstacle avoidance of semiautonomous ground vehicles. It presents a systematic way of enforcing robustness during the MPC design stage. A robust nonlinear Model Predictive Controller (RNMPC) is used to help the driver avoid obstacles and track the road center line. A force-input nonlinear bicycle vehicle model is developed for the RNMPC control design. A robust invariant set is used in the RNMPC design to ensure robust satisfaction of state and input constraints in the presence of disturbances and model errors. Simulations and experiments on testing vehicles show the effectiveness of the proposed framework.