The autonomous vehicle is one of the greatest challenges in modern vehicle design. This paper proposes a new technique to define the optimal trajectory in a feedback form for an autonomous car, moving on a track. The algorithm defines the trajectory taking into the account the vehicle dynamic instead of kinematic constraints, leading to a more robust path. The technique is also used to control the vehicle in feedback, providing the optimal maneuvers to track the defined path. The method is based on the control law named FLOP, Feedback Local Optimality Principle, recently developed by the authors. The technique, starting from the Pontryagin's theory, introduces a new optimality principle that minimizes a sequence of individual functionals with the chance of a direct feedback control. The control acts on the steering and torques of a two-wheeled vehicle.
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