Temporal Behavior Trees: Robustness and Segmentation

This paper presents temporal behavior trees (TBT), a specification formalism inspired by behavior trees that are commonly used to program robotic applications. We then introduce the concept of trace segmentation, wherein given a TBT specification and a trace, we split the trace optimally into sub-traces that are associated with various portions of the TBT specification. Segmentation of a trace then serves to explain precisely how a trace satisfies or violates a specification, and which portions of a specification are actually violated. We introduce the syntax and semantics of TBT and compare their expressiveness in relation to temporal logic. Next, we define robustness semantics for TBT specification with respect to a trace. Rather than a Boolean interpretation, the robustness provides a real-valued numerical outcome that quantifies how close or far away a trace is from satisfying or violating a TBT specification. We show that computing the robustness of a trace also segments it into subtraces.Finally, we provide efficient approximations for computing robustness and segmentation for long traces with guarantees on the result.We demonstrate how segmentations are useful through applications such as understanding how novice users pilot an aerial vehicle through a sequence of waypoints in desktop experiments and the offline monitoring of automated lander for a drone on a ship. Our case studies demonstrate how TBT specification and segmentation can be used to understand and interpret complex behaviors of humans and automation in cyber-physical systems.