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Typical numerical solutions to planning problems under time-dependent constraints (like traffic signals) involve searching in time plus state space. We consider a sampled discrete spatial formulation of the vehicle dynamics. This allows us to propose an optimal planning algorithm with much reduced search-space and time complexity, for vehicles moving across signalized intersections with full knowledge of the traffic Signal, Phasing and Timing (SPaT) information. Then we extend these results to partial knowledge by casting the problem as a Markov Decision Process (MDP). The proposed algorithms are demonstrated through numerical simulations that show a five-fold improvement in runtime compared with a standard time-state formulation, while providing comparable improvements in fuel economy with no vehicle dynamic constraints or traffic rules violated.
Li et al. (2021) studied this question.