  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.
