Preprint: Exploring Inevitable Waypoints for Unsolvability Explanation in Hybrid Planning Problems

TL;DR

This work targets explainable AI planning for hybrid systems by proposing inevitable waypoints—sub-problems that any valid plan must satisfy. It combines a graph- and string-based abstraction (via the longest common subsequence of all path strings up to a depth) with bounded reachability checks on a hybrid automaton to identify the earliest unreachable waypoint, which explains unsolvability. The approach yields an explanation artifact by constructing a chain of sub-problems and validating each with symbolic reachability; the first infeasible sub-problem in the chain localizes the root cause. Empirical evaluation on diverse hybrid-domain benchmarks demonstrates the method’s ability to reveal interpretable causal explanations and to guide system designers toward remedies (e.g., adjusting depth, resources, or domain constraints). This framework thus bridges discrete abstractions and continuous dynamics to produce actionable insights into planning failures in hybrid domains.

Abstract

Explaining unsolvability of planning problems is of significant research interest in Explainable AI Planning. AI planning literature has reported several research efforts on generating explanations of solutions to planning problems. However, explaining the unsolvability of planning problems remains a largely open and understudied problem. A widely practiced approach to plan generation and automated problem solving, in general, is to decompose tasks into sub-problems that help progressively converge towards the goal. In this paper, we propose to adopt the same philosophy of sub-problem identification as a mechanism for analyzing and explaining unsolvability of planning problems in hybrid systems. In particular, for a given unsolvable planning problem, we propose to identify common waypoints, which are universal obstacles to plan existence; in other words, they appear on every plan from the source to the planning goal. This work envisions such waypoints as sub-problems of the planning problem and the unreachability of any of these waypoints as an explanation for the unsolvability of the original planning problem. We propose a novel method of waypoint identification by casting the problem as an instance of the longest common subsequence problem, a widely popular problem in computer science, typically considered as an illustrative example for the dynamic programming paradigm. Once the waypoints are identified, we perform symbolic reachability analysis on them to identify the earliest unreachable waypoint and report it as the explanation of unsolvability. We present experimental results on unsolvable planning problems in hybrid domains.

Figures (8)

• Figure 1: Rover-domain is depicted. Initially, the rover is at cell 11. Mountains and craters are impassable regions of the terrain such as cells 7, 12, etc. The rover needs to collect soil samples from cell 1 and rock samples from cell 14. The base station is at cell 25. The up-slope areas in the terrain are shown in Orange. The inevitable waypoints in the domain are cells $w1$ to $w7$ marked in Blue.
• Figure 2: A hybrid automaton model of the planetary rover domain (partially shown).
• Figure 3: Proposed Explanation Framework.
• Figure 4: All runs of valid plans from initial to the goal must pass through the blue doorway. We envision the blue region as an inevitable way-point to the planning problem.
• Figure 5: A depiction of a graph of a HA. Let S and D be the source and the goal locations in a planning problem $\Pi$. Every path from S to D visits locations A and B in sequence. Thus, S-A-B-D is the LCS of paths in PS($\Pi$). Clearly, if a valid run of a plan exists in the HA, the run must visit the invariants of S, A, B, and D sequentially.

Theorems & Definitions (20)

• definition 1
• definition 2
• definition 3
• definition 4
• definition 5
• definition 6
• Example 1
• definition 7
• proposition 1
• proof