Computing Hierarchical Finite State Controllers With Classical Planning

Abstract


 
 
 Finite State Controllers (FSCs) are an effective way to compactly represent sequential plans. By imposing appropriate conditions on transitions, FSCs can also represent generalized plans (plans that solve a range of planning problems from a given domain). In this paper we introduce the concept of hierarchical FSCs for planning by allowing controllers to call other controllers. This call mechanism allows hierarchical FSCs to represent generalized plans more compactly than individual FSCs, to compute controllers in a modular fashion or even more, to compute recursive controllers. The paper introduces a classical planning compilation for computing hierarchical FSCs that solve challenging generalized planning tasks. The compilation takes as input a finite set of classical planning problems from a given domain. The output of the compilation is a single classical planning problem whose solution induces: (1) a hierarchical FSC and (2), the corresponding validation of that controller on the input classical planning problems.
 
 

A review of generalized planning

“…Although one can explicitly encode a call stack using only basic control-flow and variables, more compact solutions are often derived with a call stack (e.g. tasks with recursive solutions [84]). Figure 17 shows a generalized plan for visiting all the nodes of a binary tree implementing a recursive Depth First Search (DFS) with one procedural parameter.…”

“…If the execution of the generalized plan can be compiled into a classical planning task [7,83,84] then an off-the-shelf classical planner can be used to effectively check the previous validation conditions. When actions have nondeterministic effects plan validation becomes more complex since it requires proving that all the possible plan executions reach the goals [14].…”

“…Furthermore, the benefits of using a call stack in generalized planning come from the reuse of existing generalized plans and the incremental building of hierarchical generalized plans (Segovia-Aguas et al ., 2016b). Figure 19 illustrates these benefits showing a two-module generalized plan for sorting lists of numbers that implements the selection sort algorithm and reuses Π 1 , a previously generated generalized plan for finding the minimum number in a list.…”

“…Executing generalized plans that explicitly represent loops, like programs (or FSCs), requires to keep track of the current program line (or controller state). The execution of FSCs and programs can be compiled into classical planning by encoding the corresponding automata (its states and possible transitions) as extra state variables (Baier et al ., 2007; Segovia-Aguas et al ., 2016a; 2016b). Variables .…”

“…Each form with its own expressiveness capacity and own computation and validation complexity. Generalized plans range from programs (Winner and Veloso, 2003; Segovia-Aguas et al ., 2016a) and generalized polices (Martn and Geffner, 2004) to Finite State Controllers (FSCs) (Bonet et al ., 2010; Segovia-Aguas et al ., 2016b), AND/OR graphs, formal grammars (Ramirez and Geffner, 2016) or hierarchical task networks (HTNs) (Nau et al ., 2003). We can classify generalized plans according to their specification of the action to apply next : Fully specified solutions, that unambiguously specify the action to apply next , for solving every instance in a given generalized planning task.…”