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For many tasks in populated environments, robots need to keep track of current and future motion states of people. Most approaches to people tracking make weak assumptions on human motion such as constant velocity or acceleration. But even over a short period, human behavior is more complex and influenced by factors such as the intended goal, other people, objects in the environment, and social rules. This motivates the use of more sophisticated motion models for people tracking especially since humans frequently undergo lengthy occlusion events. In this paper, we consider computational models developed in the cognitive and social science communities that describe individual and collective pedestrian dynamics for tasks such as crowd behavior analysis. In particular, we integrate a model based on a social force concept into a multi-hypothesis target tracker. We show how the refined motion predictions translate into more informed probability distributions over hypotheses and finally into a more robust tracking behavior and better occlusion handling. In experiments in indoor and outdoor environments with data from a laser range finder, the social force model leads to more accurate tracking with up to two times fewer data association errors.