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This paper considers the problem of controlling an autonomous vehicle to arrive at a specific position on a road at a given time and velocity. This ability is particularly useful for a recently introduced autonomous intersection management protocol, called AIM, which has been shown to lead to lower delays than traffic signals and stop signs. Specifically, we introduce a setpoint scheduling algorithm for generating setpoints for the PID controllers for the brake and throttle actuators of an autonomous vehicle. The algorithm constructs a feasible setpoint schedule such that the vehicle arrives at the position at the correct time and velocity. Our experimental results show that the algorithm outperforms a heuristic-based setpoint scheduler that does not provide any guarantee about the arrival time and velocity.

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