A lithography system and method for calculating an optimal discrete time trajectory for a movable device is described. A trajectory planner of the lithography system calculates an optimal discrete time trajectory subject to maximum velocity and maximum acceleration constraints. The trajectory planner begins by calculating a continuous time, three-segment trajectory for a reticle stage, a wafer stage or a framing blade, including a first phase for acceleration at the maximum acceleration to the maximum velocity, a second phase for travel at the maximum velocity and a third phase for deceleration at the negative maximum acceleration to a final velocity. Next, the trajectory planner converts said continuous time, three-segment trajectory to a discrete time trajectory. The time of execution of the resulting trajectory is at most three quanta greater than the time of execution of the continuous time trajectory. One advantage of the system is the reduction of scanning times of a lithography system. This advantage increases throughput and reduces manufacturing costs for a lithography system.