In a context of autonomous robots, one of the most important task is to ensure the safety of the robot and its surrounding. Most of the time, the risk of navigation is simply said to be the probability of collision. This notion of risk is not well defined in the literature, especially when dealing with occupancy grids. The Bayesian occupancy grid is the most used method to deal with complex environments. However, this is not fitted to compute the risk along a path by its discrete nature, hence giving poor results. In this article, we present a new way to store the occupancy of the environment that allows the computation of risk for a given path. We then define the risk as the force of collision that would occur for a given obstacle. Using this framework, we are able to generate navigation paths ensuring the safety of the robot.