Semi-Definite Relaxation Based ADMM for Cooperative Planning and Control of Connected Autonomous Vehicles

TL;DR

This paper introduces a parallel ADMM-based framework utilizing semi-definite relaxation to efficiently solve nonlinear, nonconvex cooperative planning problems for connected autonomous vehicles, enabling real-time control and safety assurance.

Contribution

It proposes a novel parallel computation framework combining ADMM, DDP, and SDR to address computational challenges in multi-vehicle autonomous driving optimization.

Findings

Achieves real-time implementation for cooperative vehicle control

Demonstrates improved computational efficiency over existing methods

Ensures enhanced driving safety through effective optimization

Abstract

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.