We address the problem of applying reactive navigation methods to non-holonomic robots. Rather than embedding the motion constraints when designing a navigation method, we propose to introduce the robot’s kinematic constraints directly in the spatial representation. In this space - the Ego-Kinematic Space - the robot moves as a “free-flying object”. Hence, standard reactive navigation methods applied to this space will automatically take into account the robot’s kinematic constraints, without additional modifications. This methodology can be used with a large class of constrained mobile platforms (e.g. differential-driven robots, car-like robots, tri-cycle robots). We show experiments involving non-holonomic robots with two reactive navigation methods whose original formulation does not take the robot kinematic constraints into account (the Nearness Diagram Navigation and a Potential Field method).