  Cooperatively avoiding collision is a critical functionality for robots
navigating in dense human crowds, failure of which could lead to either
overaggressive or overcautious behavior. A necessary condition for cooperative
collision avoidance is to couple the prediction of the agents' trajectories
with the planning of the robot's trajectory. However, it is unclear that
trajectory based cooperative collision avoidance captures the correct agent
attributes. In this work we migrate from trajectory based coupling to a
formalism that couples agent preference distributions. In particular, we show
that preference distributions (probability density functions representing
agents' intentions) can capture higher order statistics of agent behaviors,
such as willingness to cooperate. Thus, coupling in distribution space exploits
more information about inter-agent cooperation than coupling in trajectory
space. We thus introduce a general objective for coupled prediction and
planning in distribution space, and propose an iterative best response
optimization method based on variational analysis with guaranteed sufficient
decrease. Based on this analysis, we develop a sampling-based motion planning
framework called DistNav that runs in real time on a laptop CPU. We evaluate
our approach on challenging scenarios from both real world datasets and
simulation environments, and benchmark against a wide variety of model based
and machine learning based approaches. The safety and efficiency statistics of
our approach outperform all other models. Finally, we find that DistNav is
competitive with human safety and efficiency performance.
