Convex modeling of conflict resolution at traffic intersections

We stud the problem of optimally controlling autonomous vehicles to safely cross an intersection. The problem is approached by solving an optimal control subproblem for all permutations of crossing sequences. For a chosen crossing sequence, we show that the subproblem of optimal longitudinal vehicle control, subject to collision avoidance constraints, can be formulated as a convex program. The proposed method transforms the problem from the original time domain to a space domain, and introduces a change of optimization variables by replacing vehicles' speed with its inverse. A case study is provided showing the effectiveness of the proposed method.