— We propose to classify the behaviors of a mobile robot thanks to topological methods as an alternative to metric ones. To do so, we adapt an analysis scheme from Physics of nonlinear systems in chaotic regime, assuming a dissipative dynamics that relaxes on a low-dimensional manifold. Sensor data recorded from a mobile robot during a wall-following experiment allows to compute topological invariants that give a standardized representation of the structure of the set of trajectories, and enable us to discriminate among similar behaviors in a systematic and quantitative way. I. DESCRIBING THE BEHAVIOR OF A MOBILE ROBOT In this article we address the problem of classifying the behavior of a mobile robot, where by behavior, we mean how the robot interacts with its environment, not only where the robot is located. Whether they favor a deterministic or random treatment, most works addressing this topic in the literature adopt a metric stand, we shall see in what sense. On one hand, when ...