Explaining Unsolvability of Planning Problems in Cyber-Physical Systems
In this work, we propose an algorithm to explain why a planning problem is unsolvable in a domain modeled as linear hybrid automata. The explanation algorithm uses BACH, a bounded reachability checking tool for linear hybrid automata models of hybrid systems. The algorithm computes source-target paths of bounded length from the automaton, extracted from the planning problem, and converts them into a partial automata representation. Reachability queries are then solved progressively toward the target using BACH, identifying the first infeasible transition on the path. By repeating this process across all paths, we identify the most frequent infeasible transition (MFIT) in the planning domain. In the next phase, we begin a constraint relaxation process on the paths iteratively. Starting from the destination location of the MFIT transition, we traverse backward toward the source, relaxing the continuous dynamics at each location. After each relaxation, a reachability query is solved using BACH to check whether the relaxed path becomes feasible. This process continues until either a feasible path is found or all paths remain infeasible, indicating that no explanation can be derived. When a feasible path is identified, we provide an explanation detailing the set of locations whose dynamics were overly restrictive for the planning problem. We believe these explanations can offer valuable insights for design engineers.
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