  We consider the problem of cooperative intersection management. It arises in
automated transportation systems for people or goods but also in multi-robots
environment. Therefore many solutions have been proposed to avoid collisions.
The main problem is to determine collision-free but also deadlock-free and
optimal algorithms. Even with a simple definition of optimality, finding a
global optimum is a problem of high complexity, especially for open systems
involving a large and varying number of vehicles. This paper advocates the use
of a mathematical framework based on a decomposition of the problem into a
continuous optimization part and a scheduling problem. The paper emphasizes
connections between the usual notion of vehicle priority and an abstract
formulation of the scheduling problem in the coordination space. A constructive
locally optimal algorithm is proposed. More generally, this work opens up for
new computationally efficient cooperative motion planning algorithms.
