Learning to predict trajectories of cooperatively navigating agents

The problem of modeling the navigation behavior of multiple interacting agents arises in different areas including robotics, computer graphics, and behavioral science. In this paper, we present an approach to learn the composite navigation behavior of interacting agents from demonstrations. The decision process that ultimately leads to the observed continuous trajectories of the agents often also comprises discrete decisions, which partition the space of composite trajectories into homotopy classes. Therefore, our method uses a mixture probability distribution that consists of a discrete distribution over the homotopy classes and continuous distributions over the composite trajectories for each homotopy class. Our approach learns the model parameters of this distribution that match, in expectation, the observed behavior in terms of user-defined features. To compute the feature expectations over the high-dimensional continuous distributions, we use Hamiltonian Markov chain Monte Carlo sampling. We exploit that the distributions are highly structured due to physical constraints and guide the sampling process to regions of high probability. We apply our approach to learning the behavior of pedestrians and demonstrate that it outperforms state-of-the-art methods.