Abstractions for Planning with State-Dependent Action Costs

Extending the classical planning formalism with state-dependent action costs (SDAC) allows an up to exponentially more compact task encoding. Recent work proposed to use edge-valued multi-valued decision diagrams (EVMDDs) to represent cost functions, which allows to automatically detect and exhibit structure in cost functions and to make heuristic estimators accurately reflect SDAC. However, so far only the inadmissible additive heuristic has been considered in this context. In this paper, we define informative admissible abstraction heuristics which enable optimal planning with SDAC. We discuss how abstract cost values can be extracted from EVMDDs that represent concrete cost functions without adjusting them to the selected abstraction. Our theoretical analysis shows that this is efficiently possible for abstractions that are Cartesian or coarser. We adapt the counterexample-guided abstraction refinement approach to derive such abstractions. An empirical evaluation of the resulting heuristic shows that highly accurate values can be computed quickly

State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning

Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by distributing action costs among the heuristics. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of our idea with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it has the potential to improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning. Our empirical results give evidence that ignoring the context of actions in the computation of a cost partitioning leads to a significant loss of information

Model checking embedded system designs

We survey the basic principles behind the application of model checking to controller verification and synthesis. A promising development is the area of guided model checking, in which the state space search strategy of the model checking algorithm can be influenced to visit more interesting sets of states first. In particular, we discuss how model checking can be combined with heuristic cost functions to guide search strategies. Finally, we list a number of current research developments, especially in the area of reachability analysis for optimal control and related issues

Increasing the Numeric Expressiveness of the Planning Domain Definition Language

The technology of artificial intelligence (AI) planning is being adopted across many different disciplines. This has resulted in the wider use of the Planning Domain Definition Language (PDDL), where it is being used to model planning problems of different natures. One such area where AI planning is particularly attractive is engineering, where the optimisation problems are mathematically rich. The example used throughout this paper is the optimisation (minimisation) of machine tool measurement uncertainty. This planning problem highlights the limits of PDDL's numerical expressiveness in the absence of the square root function. A workaround method using the Babylonian algorithm is then evaluated before the extension of PDDL to include more mathematics functions is discussed