Plan Generation via Behavior Trees Obtained from Goal-Oriented LTLf Formulas

Temporal logic can be used to formally specify autonomous agent goals, but synthesizing planners that guarantee goal satisfaction can be computationally prohibitive. This paper shows how to turn goals specified using a subset of finite trace Linear Temporal Logic ( \(LTL_{f}\) ) into a behavior tree (BT) that guarantees that successful traces satisfy the \(LTL_{f}\) goal. Useful \(LTL_{f}\) formulas for achievement goals can be derived using achievement-oriented task mission grammars, leading to missions made up of tasks combined using LTL operators. Constructing BTs from \(LTL_{f}\) formulas leads to a relaxed behavior synthesis problem in which a wide range of planners can implement the action nodes in the BT. Importantly, any successful trace induced by the planners satisfies the corresponding \(LTL_{f}\) formula. The usefulness of the approach is demonstrated in two ways: a) exploring the alignment between two planners and \(LTL_{f}\) goals, and b) solving a sequential key-door problem for a Fetch robot.