Abstract
Behavior trees represent a hierarchical and modular way of combining several low-level control policies into a high-level task-switching policy. Hybrid dynamical systems can also be seen in terms of task switching between different policies, and therefore several comparisons between behavior trees and hybrid dynamical systems have been made, but only informally, and only in discrete time. A formal continuous-time formulation of behavior trees has been lacking. Additionally, convergence analyses of specific classes of behavior tree designs have been made, but not for general designs. In this letter, we provide the first continuous-time formulation of behavior trees, show that they can be seen as discontinuous dynamical systems (a subclass of hybrid dynamical systems), which enables the application of existence and uniqueness results to behavior trees, and finally, provide sufficient conditions under which such systems will converge to a desired region of the state space for general designs. With these results, a large body of results on continuous-time dynamical systems can be brought to use when designing behavior tree controllers.
Highlights
B EHAVIOR trees (BTs) are a way to combine a set of controllers into higher-level controllers in a hierarchical and modular way
We show that the proposed formulation can be seen as a discontinuous dynamical system (DDS) (Theorem 2), with corresponding results regarding existence and uniqueness (Theorem 3)
We provide sufficient conditions under which a BT execution will converge to a desired region of the state space (Theorem 4)
Summary
B EHAVIOR trees (BTs) are a way to combine a set of controllers (policies) into higher-level controllers in a hierarchical and modular way. Improved modularity is the reason that BTs were conceived in the first place [2] as an expressive [3] alternative to finite-state machines (FSMs) in the design of non-player characters in video games In this virtual setting, the world is predictable by design and many low-level policies can be developed with relative ease. Even though there is an increasing interest in BTs from the robotics and AI communities (see the recent survey in [4] with over 180 papers) there is still no continuoustime formulation available The need for such a formulation is clear from the fact that almost all major branches of control theory, from linear systems to optimal control, have been developed for both continuous-time and discrete-time systems, but BTs have so far only had a discrete-time formulation.
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