  Robots that can effectively understand human intentions from actions are
crucial for successful human-robot collaboration. In this work, we address the
challenge of a robot navigating towards an unknown goal while also accounting
for a human's preference for a particular path in the presence of obstacles.
This problem is particularly challenging when both the goal and path preference
are unknown a priori. To overcome this challenge, we propose a method for
encoding and inferring path preference online using a partitioning of the space
into polytopes. Our approach enables joint inference over the goal and path
preference using a stochastic observation model for the human. We evaluate our
method on an unknown-goal navigation problem with sparse human interventions,
and find that it outperforms baseline approaches as the human's inputs become
increasingly sparse. We find that the time required to update the robot's
belief does not increase with the complexity of the environment, which makes
our method suitable for online applications.
