  Manipulation tasks often require a robot to adjust its sensorimotor skills
based on the state it finds itself in. Taking peg-in-hole as an example: once
the peg is aligned with the hole, the robot should push the peg downwards.
While high level execution frameworks such as state machines and behavior trees
are commonly used to formalize such decision-making problems, these frameworks
require a mechanism to detect the high-level symbolic state. Handcrafting
heuristics to identify symbolic states can be brittle, and using data-driven
methods can produce noisy predictions, particularly when working with limited
datasets, as is common in real-world robotic scenarios. This paper proposes a
Bayesian state estimation method to predict symbolic states with predicate
classifiers. This method requires little training data and allows fusing noisy
observations from multiple sensor modalities. We evaluate our framework on a
set of real-world peg-in-hole and connector-socket insertion tasks,
demonstrating its ability to classify symbolic states and to generalize to
unseen tasks, outperforming baseline methods. We also demonstrate the ability
of our method to improve the robustness of manipulation policies on a real
robot.
