An important challenge for autonomous robots is to navigate efficiently and safely in human populated environments. It requires that the robots perceive human motions and take into account human flows to plan and navigate. In this context we address the problem of modeling human flows from the perception of the robots, by defining a grid of the human motion likelihood over the environment, called flow grid. We define the computation of this grid as a counting based mapping. Then we define a path planning taking into account the risk of encountering humans in opposite direction. We first evaluate the approach in simulation by considering different navigation tasks in a crowded environment. For this purpose, we compare three A*-based path planning models using different levels of information about human presence. Simulations involving 200 moving persons and 4 collaborative robots allow to evaluate simultaneously the flow mapping and the related path planning efficiency. Finally we experiment the model with a real robot that maps human displacements in its environment.