Whenever people move through their environments they do not move randomly. Instead, they usually follow specific trajectories or motion patterns corresponding to their intentions. Knowledge about such patterns may enable a mobile robot to robustly keep track of persons in its environment or to improve its obstacle avoidance behavior. This paper proposes a technique for learning collections of trajectories that characterize typical motion patterns of persons. Data recorded with laser-range finders is clustered using the expectation maximization algorithm. Based on the result of the clustering process we derive a Hidden Markov Model (HMM). This HMM is able to estimate the current and future positions of multiple persons given knowledge about their intentions. Experimental results obtained with a mobile robot using laser and vision data collected in a typical office building with several persons illustrate the reliability and robustness of the approach. We also demonstrate that our model...