Among the considerable technical problems that self-driving vehicles have to face, there is the path planning, that is a function for autonomous vehicles. Path planning is defined as the problem of finding a continuous collision free path from an initial configuration to a predetermined goal. In this context, the present thesis work focuses on the design and implementation of a real-time local trajectory planning method using Rapidly-Exploring Random Tree Algorithm based on Dubins curves for an AWD electric racing vehicle in different scenarios, straight, left and right bends. The key contribution of this work is to present a framework able to generate a feasible free collision path considering differential constraints for non-holonomic car-like robot and its real-time computation ability in solving the dynamic motion planning problem.