Explaining unsolvability of planning problems is of significant research interest in Explainable AI Planning. A number of research efforts on generating explanations of solutions to planning problems have been reported in AI planning literature. 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 article, 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.

In artificial intelligence planning, having an explanation of a plan given by a planner is often desirable. The ability to explain various aspects of a synthesized plan to an end user not only brings in trust on the planner but also reveals insights of the planning domain and the planning process. Contrastive questions such as “Why action A instead of action B?” can be answered with a contrastive explanation that compares properties of the original plan containing A against the contrastive plan containing B. In this article, we explore a set of contrastive questions that a user of a planning tool may raise and propose a re-model and re-plan framework to provide explanations to such questions. Earlier work has reported this framework on planning instances for discrete problem domains described in the Planning Domain Definition Language (PDDL) and its variants. In this article, we propose an extension for planning instances described by PDDL+ for hybrid systems that portray a mix of discrete-continuous dynamics. Specifically, given a mixed discrete-continuous system model in PDDL+ and a plan describing the set of desirable actions on the same to achieve a destined goal, we present a framework that can integrate contrastive questions in PDDL+ and synthesize alternate plans. We present a detailed case study on our approach and propose a comparison metric to compare the original plan with the alternate ones.

In artificial intelligence planning, having an explanation of a plan given by a planner is often desirable. The ability to explain various aspects of a synthesized plan to an end-user not only brings in trust on the planner but also reveals insights of the planning domain and the planning process. Contrastive questions such as "Why action A instead of action B?" can be answered with a contrastive explanation that compares properties of the original plan containing A against the contrastive plan containing B. In this paper, we explore a set of contrastive questions that a user of a planning tool may raise and we propose a re-model and re-plan framework to provide explanations to such questions. Earlier work has reported this framework on planning instances for discrete problem domains described in the Planning Domain Definition Language (PDDL) and its variants. In this paper, we propose an extension for planning instances described by PDDL+ for hybrid systems which portray a mix of discrete-continuous dynamics. Specifically, given a mixed discrete continuous system model in PDDL+ and a plan describing the set of desirable actions on the same to achieve a destined goal, we present a framework that can integrate contrastive questions in PDDL+ and synthesize alternate plans. We present a detailed case study on our approach and propose a comparison metric to compare the original plan with the alternate ones.