We study driver's optimal trajectory planning under uncertainty in the duration of a traffic light's green phase.
We interpret this as an optimal control problem with an objective of minimizing the expected cost based on the fuel use, discomfort from rapid velocity changes, and time to destination.
Treating this in the framework of dynamic programming, we show that the probability distribution on green phase durations gives rise to a sequence of Hamilton-Jacobi-Bellman PDEs,
which are then solved numerically to obtain optimal acceleration/braking policy in feedback form.
Our numerical examples illustrate the approach and highlight the role of conflicting goals and uncertainty in shaping drivers' behavior.
The authors are grateful to April Nellis, Jacob van Hook, and Nhu Do for their preliminary work on the Phase R problem during the summer 2018 REU Program at Cornell University.
The authors also thank Elliot Cartee for providing the website template.
The 1st author's work is supported by a National Defense Science and Engineering Graduate (NDSEG) Fellowship.
The 2nd author's work is supported by the NSF DMS (awards 1645643, 1738010, 2111522).