This paper presents an autonomous vehicle's path planning and tracking system optimized for collision avoidance on slippery roads. During path planning, a path that can induce the maximum possible lateral acceleration is generated through the fifth-order spline in consideration of the tire-road friction. The generated path is tracked based on the model predictive control (MPC), and the nonlinearity generated by the tire and low friction surface is reflected through the extended bicycle model and the combined brushed tire model. Inside the controller, a new type of yaw rate constraint considering side-slip angles is utilized to prevent the vehicle from becoming unstable on slippery roads and maximize lateral maneuver of the vehicle at the same time. The proposed system is verified by the vehicle dynamics software CarSim, and the simulation results show that it significantly increases the possibility of collision avoidance in slippery road conditions.