Centralized non-convex model predictive control for cooperative collision avoidance of networked vehicles

This paper presents a novel design of a collision avoidance controller of networked vehicles using a centralized Model Predictive Control (MPC) concept. The primary objective is to avoid collisions. The secondary objective is dealing with the quality of the collision-free trajectory, which is defined in comparison to the predefined reference trajectory. The resulted optimization problem is non-convex due to collision avoidance constraints. Two different methods to solve this non-convex program are presented, Mixed Integer Linear Programming (MILP) and convex relaxation. In MILP, using binary variables and the big-M method, the avoidance constraints can be formulated naturally. The other method is Semi-Definite Programming (SDP) relaxation. First, the optimization problem is formulated in the form of a quadratically constrained quadratic program, then it is solved using the SDP relaxation.