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According to some embodiments, a system calculates a first trajectory based on a map and a route information. The system generates a path profile based on the first trajectory, traffic rules, and an obstacle information describing one or more obstacles perceived by the ADV, where for each of the obstacles, the path profile includes a decision to yield or nudge to left or right of the obstacle. The system generates a speed profile based on the path profile in view of the traffic rules. The system performs a gradient descent optimization based on the path profile and the speed profile to generate a second trajectory representing an optimized first trajectory and controls the ADV according to the second trajectory.