CAVs coordination at intersections in mixed traffic via feasibility-enforcing ADMM

This paper proposes a feasibility-enforcing Alternating-Direction Methods of Multipliers (ADMM) to solve a Mixed-Integer Quadratic Program (MIQP) problem resulting from a platoon-based coordination problem of connected and automated vehicles (CAVs) in mixed traffic scenarios, with human-driven vehicles (HDVs). In such an optimal coordination (MIQP) problem, solving for the binary variables enabling the optimal crossing order and enforcing the safety constraint activation is notoriously complex. Thus, we propose an ADMM-based approach to derive an approximate solution in a computationally faster way than standard MIQP solvers. The ADMM consists of outer and inner loops, where the first provides randomized initial guesses and the latter updates primal and dual solutions by solving a low-complexity linear system of equations. To enforce feasibility w.r.t. the safety constraint, feasibility checking functions are deployed within the ADMM iterations. Performance comparison with the benchmark MIQP via numerical simulations shows that ADMM can yield feasibly safe trajectories and close-to-optimal solutions multiple times faster than the benchmark.