LTL-D*: Incrementally Optimal Replanning for Feasible and Infeasible Tasks in Linear Temporal Logic Specifications

TL;DR

This work addresses the challenge of replanning for long-horizon tasks specified in Linear Temporal Logic (LTL) under dynamically changing environments, where some task realizations may be infeasible and require relaxation. It introduces LTL-D*, an incremental replanning approach that combines $D^*$ Lite with a distance-based violation metric on the product automaton to obtain optimal or near-optimal plans while reusing prior computations. The method handles both feasible and infeasible cases by modifying edge costs with a violation penalty and, for infeasible cases, introducing auxiliary estimates to drive minimal task violation. Empirical results across benchmark grid maps and a realistic drone simulation demonstrate two orders of magnitude speedups over baselines, sustained optimality, and scalability to large problem sizes.

Abstract

This paper presents an incremental replanning algorithm, dubbed LTL-D*, for temporal-logic-based task planning in a dynamically changing environment. Unexpected changes in the environment may lead to failures in satisfying a task specification in the form of a Linear Temporal Logic (LTL). In this study, the considered failures are categorized into two classes: (i) the desired LTL specification can be satisfied via replanning, and (ii) the desired LTL specification is infeasible to meet strictly and can only be satisfied in a "relaxed" fashion. To address these failures, the proposed algorithm finds an optimal replanning solution that minimally violates desired task specifications. In particular, our approach leverages the D* Lite algorithm and employs a distance metric within the synthesized automaton to quantify the degree of the task violation and then replan incrementally. This ensures plan optimality and reduces planning time, especially when frequent replanning is required. Our approach is implemented in a robot navigation simulation to demonstrate a significant improvement in the computational efficiency for replanning by two orders of magnitude.

Figures (9)

• Figure 1: Top: The trajectory of a drone starting from A and executing the mission of carrying goods from each room F, B, C, and D to the central dropoff location E sequentially. The color of the trajectory representing time transitions from dark blue to orange as time progresses. Multiple replanning events take place along the way where task specifications remain feasible to meet. Loading goods at D becomes infeasible because the access to the room is closed. Therefore, the drone hovers around at its current location because all other tasks have been finished. Bottom: We show our revision strategies based on the current phase of the run that the robot is executing.
• Figure 2: An illustration of the framework for synthesizing product automaton given the Weighted Transition System (WTS) and non-deterministic Büchi automaton (NBA).
• Figure 3: A conceptual illustration of feasible and infeasible tasks in our study. Assume the robot's mission is to eventually always reach the flag. In the beginning, the robot is not aware of the existence of any obstacles represented by red blocks, so it plans a direct path to the flag in (a). At runtime, it notices the obstacle in the front, so it rewires its path to the flag by a U-turn as shown in (b). This case is considered a feasible task where the task can still be fulfilled with a modified action. (c) represents a replanning in an infeasible scenario where the task is impossible to meet. When the robot reaches the bottom-right cell, it detects another obstacle, obstructing its next move. Now the robot's new plan would be to stay in the closest cell to the flag cell and maintain a minimal task violation, as it has the minimum cost in terms of traversal distance.
• Figure 4: States in D* Lite are expanded in a reversed order from $s_{\rm goal}$ to $s_{\rm start}$ where $k_m$ is considered as the heuristic from the initial state $s_{\rm init}$ to the current robot state $s_{\rm start}$, and rhs-value of a state $s$ is updated through summation of g-value of its successor $s'$ and the edge weight of $\langle s, s' \rangle$.
• Figure 5: An illustration for replanning strategies when modification is performed in the prefix or suffix phase of a run. This adaptation is caused by the modification within WTS, and corresponding edge changes in PA impact the optimality of the original run. Note that, $f$ and $f'$ denote the index of the accepting states, and $n$, $n'$ and $n"$ denote the index of the last element of the suffixes.