Generalized Planning via Abstraction: Arbitrary Numbers of Objects

Abstract

We consider a class of generalized planning problems based on the idea of quantifying over sets of similar objects. We show how we can adapt fully observable nondeterministic planning techniques to produce generalized solutions that are easy to instantiate over particular problem instances. We also describe how we can reformulate a classical planning problem into a quantified one. The reformulation allows us to solve the original planning task without grounding every action with respect to all objects in the problem, and a single solution can be applied to a possibly infinite set of related classical planning tasks. We report experimental results that show our approach is a practical and promising technique for solving an interesting class of problems.

A Uniform Abstraction Framework for Generalized Planning

“…Transitive closure is often used to define counting terms. Following transitive closure logic [Immerman and Vardi, 1997], we introduce the notation [T Cx ,ȳ ϕ](ū,v), where ϕ(x,ȳ) is a formula with 2k free variables,ū andv are two k-tuples of terms, which says that the pair (ū,v) is contained in the reflexive transitive closure of the binary relation on k-tuples that is defined by ϕ. It is defined as an abbreviation in the situation calculus using a formula in second-order logic.…”

“…If G bq is a sound abstraction of G c and δ is a strong solution to G bq , then m(δ) is a strong solution to G c . Illanes and McIlraith[2019] considered solving a class of generalized classical planning problems by automatically deriving a sound QNP abstraction from an instance of the problem. The automatic abstraction process is based on introducing a counter for each set of indistinguishable objects using the idea from [Fuentetaja and de la Rosa, 2016].…”

“…Generalized planning, where a single plan works for possibly infinitely many similar planning problems, has received continual attention in the AI community [Srivastava et al, 2008;Hu and De Giacomo, 2011;Srivastava et al, 2011;Segovia-Aguas et al, 2016;Bonet and Geffner, 2018;Illanes and McIlraith, 2019]. For example, the generalized plan "while the block A is not clear, pick the top block above A and place it on the table" meets the goal clear(A) no matter how many blocks the tower has.…”

“…They showed that if such a problem P can be abstracted into a QNP problem P and if the abstraction is sound, then the solution of P is a solution of P . Illanes and McIlraith [2019] considered solving a class of generalized classical planning problems by automatically deriving a sound QNP abstraction from an instance of the problem, by introducing a counter for each set of indistinguishable objects.…”

Abstraction for Non-ground Answer Set Programs

“…Illanes and McIlraith [65] studied abstraction for numeric planning problems by compiling them into classical planning. Recently, they used abstraction for problems with quantifiable objects [66], e.g., a number of packages to deliver to points A and B, to find by abstracting from the quantification generalized plans that work for multiple instances. For this, they built a quantified planning problem by clustering indistinguishable objects using reformulation techniques [105] to reduce symmetry, and then compute a general policy.…”