OMTBT: Online Monitoring of Temporal Behavior Trees with Applications to Closed-Loop Learning

Behavior Trees (BTs) have emerged as a powerful framework for structuring complex and long-horizon robotic behaviors and tasks. To ensure their correctness and safety, rigorous formal verification techniques are essential. Temporal Behavior Trees (TBTs) offer a promising approach by lever-aging temporal logic to specify and verify desired properties of BT executions. However, traditional TBTs are primarily suited for offline analysis. We propose a framework for online monitoring of TBTs (OMTBT). Our method combines Signal Temporal Logic (STL) and propositional ternary logic to define quantitative semantics for partial BT executions. This enables real-time assessment of a BT’s adherence to temporal specifications, allowing for timely feedback and adaptation. By providing a conservative approximation of the final TBT robustness, our online monitoring technique is well-suited for closed-loop control systems. We demonstrate its effectiveness through simulation on a robotic manipulation task, where it is used to define logic-based reward functions to guide reinforcement learning policy optimization, leading to improved performance and safety.