Fast Motion Planning in Dynamic Environments With Extended Predicate-Based Temporal Logic

Formal languages effectively outline robots’ task specifications, yet current temporal logic struggles to balance semantic expression with solution speed. To address this challenge, we propose extended predicate-based temporal logic (E-pTL), augmenting conventional linear temporal logic with more expressive atomic predicates to reflect the time, space, and order attributes of task and represent complex tasks with dynamic propositions, time windows, and even relative time window. This approach, blending automata-based task abstraction and extended predicates, offers enhanced expressiveness and conciseness for intricate specifications. To cope with E-pTL, we introduce a novel planning framework, the Planning Decision Tree (PDT). PDT incrementally builds a tree through automata and system state searches, recording potential task plans. The proposed pruning method can reduce the exploration space. This method swiftly handles complex temporal tasks defined by E-pTL. Rigorous analysis confirms PDT-based planning’s feasibility (ensuring satisfactory planning aligned with task specifications) and completeness (guaranteeing a feasible solution if available). Moreover, PDT-based planning proves efficient, with solution times approximately linearly proportional to automaton states squared. Extensive simulations and experiments validate its effectiveness and efficiency.
Note to Practitioners
—Temporal logic, as a formal language, has been widely applied to describe the task of robotic systems. However, linear temporal logic (LTL) struggles with the explicit time constraints, while other temporal logics, e.g., signal temporal logic (STL), cannot compactly represent task progress via an automaton. Consequently, current solutions for complex task with temporal logic specification heavily lean on optimization-based approaches, which are time-consuming and impractical for real-time systems. This work presents a novel approach for fast motion planning in dynamic environments with extended predicate-based temporal logic (E-pTL). The proposed E-pTL not only enhances semantic expression but also can be checked by an automaton, simplifying progress checks. However, existing automata-based methods encounter limitations in dynamic tasks. Graph search methods require replanning at each time step and lack completeness guarantees, while sampling methods can’t efficiently handle the feasibility of each atomic proposition. In contrast, the developed planning decision tree (PDT)-based framework incrementally searches for automata and validates propositions without a transition system, significantly reducing the search space. The suggested pruning method further trims the search space without compromising feasibility. Overall, PDT enables rapid, reliable planning, outperforming optimization-based methods like ILP/MILP and proving well-suited for real-time applications.