  This paper devotes to the development of an optimal acceleration/speed
profile for autonomous vehicles approaching a traffic light. The design
objective is to achieve both short travel time and low energy consumption as
well as avoid idling at a red light. This is achieved by taking full advantage
of the traffic light information based on vehicle-to-infrastructure
communication. The problem is modeled as a mixed integer programming, which is
equivalently transformed into optimal control problems by relaxing the integer
constraint. Then the direct adjoining approach is used to solve both free and
fixed terminal time optimal control problems subject to state constraints. By
an elaborate analysis, we are able to produce a real-time online analytical
solution, distinguishing our method from most existing approaches based on
numerical calculations. Extensive simulations are executed to compare the
performance of autonomous vehicles under the proposed speed profile and human
driving vehicles. The results show quantitatively the advantages of the
proposed algorithm in terms of energy consumption and travel time.
