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.
翻译:行为树是将若干低层次控制政策合并为高层次任务转换政策的一种等级和模块化方式。 混合动态系统也可以从不同政策的任务转换的角度来看待,因此,对行为树和混合动态系统进行了若干比较,但只是非正式的,而且只在离散的时间里进行。 缺乏一种正式的连续时间行为树结构。 此外,对行为树设计的具体类别进行了趋同分析,但对于一般设计却不是如此。 在本信中,我们提供了行为树的第一次连续时间配制,表明它们可以被视为不连续的动态系统(混合动态系统的一个子类),从而能够将存在和独特性结果应用于行为树,最后,提供了充分的条件,使这种系统能够与一般设计所需的状态空间的区域相融合。有了这些结果,在设计行为树控制器时可以使用大量连续时间动态系统的结果。