This paper presents a mathematical framework for performance analysis of Behavior Trees (BTs). BTs are a recent alternative to Finite State Machines (FSMs), for doing modular task switching in robot control architectures. By encoding the switching logic in a tree structure, instead of distributing it in the states of a FSM, modularity and reusability are improved. In this paper, we compute performance measures, such as success/failure probabilities and execution times, for plans encoded and executed by BTs. To do this, we first introduce Stochastic Behavior Trees (SBT), where we assume that the probabilistic performance measures of the basic action controllers are given. We then show how Discrete Time Markov Chains (DTMC) can be used to aggregate these measures from one level of the tree to the next. The recursive structure of the tree then enables us to step by step propagate such estimates from the leaves (basic action controllers) to the root (complete task execution). Finally, we verify our analytical results using massive Monte Carlo simulations, and provide an illustrative example of the results for a complex robotic task.

This paper presents a unified framework for Behavior Trees (BTs), a plan representation and execution tool. The available literature lacks the consistency and mathematical rigor required for robotic and control applications. Therefore, we approach this problem in two steps: first, reviewing the most popular BT literature exposing the aforementioned issues; second, describing our unified BT framework along with equivalence notions between BTs and Controlled Hybrid Dynamical Systems (CHDSs). This paper improves on the existing state of the art as it describes BTs in a more accurate and compact way, while providing insight about their actual representation capabilities. Lastly, we demonstrate the applicability of our framework to real systems scheduling open-loop actions in a grasping mission that involves a NAO robot and our BT library.

We focus on autonomous robot action planning problem from Linear Temporal Logic (LTL) specifications, where the action refers to a “simple” motion or manipulation task, such as “go from A to B” or “grasp a ball”. At the high-level planning layer, we propose an algorithm to synthesize a maximally satisfying discrete control strategy while taking into account that the robot's action executions may fail. Furthermore, we interface the high-level plan with the robot's low-level controller through a reactive middle-layer formalism called Behavior Trees (BTs). We demonstrate the proposed framework using a NAO robot capable of walking, ball grasping and ball dropping actions.