Coordination of autonomous non-point agents in four-way crossings is studied in this work. A control scheme based on artificial potential functions is proposed in order to coordinate holonomic agents whose aim is to pass through an intersection while avoiding collisions. To do so, the agents are provided with a decentralized navigation function in which the goal and collision functions are decoupled. The local function defined on each agent requires no global knowledge on the desired destination of other agents. Furthermore, a reachability analysis via Lyapunov functions is proposed in order to guarantee marginal stability in our case study. In addition, conflict-free navigation and convergence properties are verified in simulation.