  This paper investigates the cooperative planning and control problem for
multiple connected autonomous vehicles (CAVs) in different scenarios. In the
existing literature, most of the methods suffer from significant problems in
computational efficiency. Besides, as the optimization problem is nonlinear and
nonconvex, it typically poses great difficultly in determining the optimal
solution. To address this issue, this work proposes a novel and completely
parallel computation framework by leveraging the alternating direction method
of multipliers (ADMM). The nonlinear and nonconvex optimization problem in the
autonomous driving problem can be divided into two manageable subproblems; and
the resulting subproblems can be solved by using effective optimization methods
in a parallel framework. Here, the differential dynamic programming (DDP)
algorithm is capable of addressing the nonlinearity of the system dynamics
rather effectively; and the nonconvex coupling constraints with small
dimensions can be approximated by invoking the notion of semi-definite
relaxation (SDR), which can also be solved in a very short time. Due to the
parallel computation and efficient relaxation of nonconvex constraints, our
proposed approach effectively realizes real-time implementation and thus also
extra assurance of driving safety is provided. In addition, two transportation
scenarios for multiple CAVs are used to illustrate the effectiveness and
efficiency of the proposed method.
