  For autonomous service robots to successfully perform long horizon tasks in
the real world, they must act intelligently in partially observable
environments. Most Task and Motion Planning approaches assume full
observability of their state space, making them ineffective in stochastic and
partially observable domains that reflect the uncertainties in the real world.
We propose an online planning and execution approach for performing long
horizon tasks in partially observable domains. Given the robot's belief and a
plan skeleton composed of symbolic actions, our approach grounds each symbolic
action by inferring continuous action parameters needed to execute the plan
successfully. To achieve this, we formulate the problem of joint inference of
action parameters as a Hybrid Constraint Satisfaction Problem (H-CSP) and solve
the H-CSP using Belief Propagation. The robot executes the resulting
parameterized actions, updates its belief of the world and replans when
necessary. Our approach is able to efficiently solve partially observable tasks
in a realistic kitchen simulation environment. Our approach outperformed an
adaptation of the state-of-the-art method across our experiments.
