  Many methods in learning from demonstration assume that the demonstrator has
knowledge of the full environment. However, in many scenarios, a demonstrator
only sees part of the environment and they continuously replan as they gather
information. To plan new paths or to reconstruct the environment, we must
consider the visibility constraints and replanning process of the demonstrator,
which, to our knowledge, has not been done in previous work. We consider the
problem of inferring obstacle configurations in a 2D environment from
demonstrated paths for a point robot that is capable of seeing in any direction
but not through obstacles. Given a set of \textit{survey points}, which
describe where the demonstrator obtains new information, and a candidate path,
we construct a Constraint Satisfaction Problem (CSP) on a cell decomposition of
the environment. We parameterize a set of obstacles corresponding to an
assignment from the CSP and sample from the set to find valid environments. We
show that there is a probabilistically-complete, yet not entirely tractable,
algorithm that can guarantee novel paths in the space are unsafe or possibly
safe. We also present an incomplete, but empirically-successful,
heuristic-guided algorithm that we apply in our experiments to 1) planning
novel paths and 2) recovering a probabilistic representation of the
environment.
