This work is dedicated to the study of how uncertainty estimation of the human motion prediction can be embedded into constrained optimization techniques, such as Model Predictive Control (MPC) for the social robot navigation. We propose several cost objectives and constraint functions obtained from the uncertainty of predicting pedestrian positions and related to the probability of the collision that can be applied to the MPC, and all the different variants are compared in challenging scenes with multiple agents. The main question this paper tries to answer is: what are the most important uncertainty-based criteria for social MPC? For that, we evaluate the proposed approaches with several social navigation metrics in an extensive set of scenarios of different complexity in reproducible synthetic environments. The main outcome of our study is a foundation for a practical guide on when and how to use uncertainty-aware approaches for social robot navigation in practice and what are the most effective criteria.

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