Autonomous driving is gaining popularity in research interest and industry investment over the last decade, due to its potential to increase driving safety to avoid driver errors which account for over 90% of all motor vehicle crashes. It could also help to improve public mobility especially for the disabled, and to boost the productivity due to enlarged traffic capacity and accelerated traffic flows. The path planning and following control, as the two essential modules for autonomous driving, still face critical challenges in implementations in a dynamically changing driving environment. For the local path/trajectory planning, multifold requirements need to be satisfied including reactivity to avoid collision with other objects, smooth curvature variation for passenger comfort, feasibility in terms of vehicle control, and the computation efficiency for real-time implementations. The feedback control is required afterward to accurately follow the planned path or trajectory by deciding appropriate actuator inputs, and favors smooth control variations to avoid sudden jerks. The control may also subject to instability or performance deterioration due to continuously changing operating conditions along with the model uncertainties. The dissertation contributes by raising the framework of path planning and control to address these challenges. Local on-road path planning methods from two-dimensional (2D) geometric path to the model-based state trajectory is explored. The latter one is emphasized due to its advantages in considering the vehicle model, state and control constraints to ensure dynamic feasibility. The real-time simulation is made possible with the adoption of control parameterization and lookup tables to reduce computation cost, with scenarios showing its smooth planning and the reactivity in collision avoidance with other traffic agents. The dissertation also explores both robust gain-scheduling law and model predictive control (MPC) for path following. The parameter-space approach is introduced in the former with validated robust performance under the uncertainty of vehicle load, speed and tire saturation parameter through hardware-in-the-loop and vehicle experiments. The focus is also put on improving the safety of the intended functionality (SOTIF) to account for the potential risks caused by lack of situational awareness in the absence of a system failure. Such safety hazards include the functional inability to comprehend the situation and the insufficient robustness to diverse conditions. The dissertation enhanced the SOTIF with parameter estimation through sensor fusion to increase the vehicle situational awareness of its internal and external conditions, such as the road friction coefficient. The estimated road friction coefficient helps in planning a dynamically feasible trajectory under adverse road condition. The integration of vehicle stability control with autonomous driving functions is also explored in the case that the road friction coefficient estimation is not responsive due to insufficiency in time and excitations.