Formalizing Stateful Behavior Trees

Behavior Trees (BTs) are high-level controllers that are useful in a variety of planning tasks and are gaining traction in robotic mission planning. As they gain popularity in safety-critical domains, it is important to formalize their syntax and semantics, as well as verify properties for them. In this paper, we formalize a class of BTs we call Stateful Behavior Trees (SBTs) that have auxiliary variables and operate in an environment that can change over time. SBTs have access to persistent shared memory (often known as a blackboard) that keeps track of these auxiliary variables. We demonstrate that SBTs are equivalent in computational power to Turing Machines when the blackboard can store mathematical (i.e., unbounded) integers. We further identify syntactic assumptions where SBTs have computational power equivalent to finite state automata, specifically where the auxiliary variables are of finitary types. We present a domain specific language (DSL) for writing SBTs and adapt the tool BehaVerify for use with this DSL. This new DSL in BehaVerify supports interfacing with popular BT libraries in Python, and also provides generation of Haskell code and nuXmv models, the latter of which is used for model checking temporal logic specifications for the SBTs. We include examples and scalability results where BehaVerify outperforms another verification tool by a factor of 100.

Verification of Behavior Trees with Contingency Monitors

Behavior Trees (BTs) are high level controllers that have found use in a wide range of robotics tasks. As they grow in popularity and usage, it is crucial to ensure that the appropriate tools and methods are available for ensuring they work as intended. To that end, we created a new methodology by which to create Runtime Monitors for BTs. These monitors can be used by the BT to correct when undesirable behavior is detected and are capable of handling LTL specifications. We demonstrate that in terms of runtime, the generated monitors are on par with monitors generated by existing tools and highlight certain features that make our method more desirable in various situations. We note that our method allows for our monitors to be swapped out with alternate monitors with fairly minimal user effort. Finally, our method ties in with our existing tool, BehaVerify, allowing for the verification of BTs with monitors.