Research towards a complete autonomous car has been pushed through by industries as it offers numerous advantages such as the improvement to traffic flow, vehicle and pedestrian safety, and car efficiency. One of the main challenges faced in this area is how to deal with different uncertainties perceived by the sensors on the current state of the car and the environment. An autonomous car needs to employ efficient planning algorithm that generates the vehicle trajectory based on the environmental sensing implemented in real-time. An complete motion planning algorithm is an algorithm that returns a valid solution if one exist in finite time and returns no path exist when none exist. The algorithm is optimal when it returns an optimal path based on some criteria. In this thesis we work on a special case of motion planning problem: to find an optimal trajectory for a robotic car in order to win a car race. We propose an efficient realtime vision based technique for localization and path reconstruction. For our purpose of winning a car race we identify a characterization of the alphabet of optimal maneuvers for the car, an optimal local planning strategy and an optimal graph-based global planning strategy with obstacle avoidance. We have also implemented the hardware and software of this approach on as a testbed of the planning strategy
