  Behavior trees (BTs) are an optimally modular framework to assemble
hierarchical hybrid control policies from a set of low-level control policies
using a tree structure. Many robotic tasks are naturally decomposed into a
hierarchy of control tasks, and modularity is a well-known tool for handling
complexity, therefor behavior trees have garnered widespread usage in the
robotics community. In this paper, we study the convergence of BTs, in the
sense of reaching a desired part of the state space. Earlier results on BT
convergence were often tailored to specific families of BTs, created using
different design principles. The results of this paper generalize the earlier
results and also include new cases of cyclic switching not covered in the
literature.
