We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation of the search space based on Binary Decision Diagrams (BDDs), which is the basis for search techniques derived from symbolic model checking. The symbolic representation makes it possible to analyze potentially large sets of states and transitions in a single computation step, thus providing for an efficient implementation. Third, we present CMBP (Conformant Model Based Planner), an efficient implementation of the data structures and algorithm described above, directly based on BDD manipulations, which allows for a compact representation of the search layers and an efficient implementation of the search steps. Finally, we present an experimental comparison of our approach with the state-of-the-art conformant planners CGP, QBFPLAN and GPT. Our analysis includes all the planning problems from the distribution packages of these systems, plus other problems defined to stress a number of specific factors. Our approach appears to be the most effective: CMBP is strictly more expressive than QBFPLAN and CGP and, in all the problems where a comparison is possible, CMBP outperforms its competitors, sometimes by orders of magnitude.

Recently model checking representation and search techniques were shown to be efficiently applicable to planning, in particular to non-deterministic planning. Such planning approaches use Ordered Binary Decision Diagrams (OBDDs) to encode a planning domain as a non-deterministic finite automaton and then apply fast algorithms from model checking to search for a solution. OBDDs can effectively scale and can provide universal plans for complex planning domains. We are particularly interested in addressing the complexities arising in non-deterministic, multi-agent domains. In this article, we present UMOP, a new universal OBDD-based planning framework for non-deterministic, multi-agent domains. We introduce a new planning domain description language, NADL, to specify non-deterministic, multi-agent domains. The language contributes the explicit definition of controllable agents and uncontrollable environment agents. We describe the syntax and semantics of NADL and show how to build an efficient OBDD-based representation of an NADL description. The UMOP planning system uses NADL and different OBDD-based universal planning algorithms. It includes the previously developed strong and strong cyclic planning algorithms. In addition, we introduce our new optimistic planning algorithm that relaxes optimality guarantees and generates plausible universal plans in some domains where no strong nor strong cyclic solution exists. We present empirical results applying UMOP to domains ranging from deterministic and single-agent with no environment actions to non-deterministic and multi-agent with complex environment actions. UMOP is shown to be a rich and efficient planning system.

This paper presents GRT, a domain-independent heuristic planning system for STRIPS worlds. GRT solves problems in two phases. In the pre-processing phase, it estimates the distance between each fact and the goals of the problem, in a backward direction. Then, in the search phase, these estimates are used in order to further estimate the distance between each intermediate state and the goals, guiding so the search process in a forward direction and on a best-first basis. The paper presents the benefits from the adoption of opposite directions between the preprocessing and the search phases, discusses some difficulties that arise in the pre-processing phase and introduces techniques to cope with them. Moreover, it presents several methods of improving the efficiency of the heuristic, by enriching the representation and by reducing the size of the problem. Finally, a method of overcoming local optimal states, based on domain axioms, is proposed. According to it, difficult problems are decomposed into easier sub-problems that have to be solved sequentially. The performance results from various domains, including those of the recent planning competitions, show that GRT is among the fastest planners.

We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defines labeled disjunctive metric point-based constraints, where each disjunct in each input disjunctive constraint is univocally associated to a label. Reasoning algorithms manage labeled constraints, associated label lists, and sets of mutually inconsistent disjuncts. These algorithms guarantee consistency and obtain a minimal network. Additionally, constraints can be organized in a hierarchy of alternative temporal contexts. Therefore, we can reason on context-dependent disjunctive metric constraints on intervals and points. Moreover, the model is able to represent non-binary constraints, such that logical dependencies on disjuncts in constraints can be handled. The computational cost of reasoning algorithms is exponential in accordance with the underlying problem complexity, although some improvements are proposed.

Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite dierent from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantied Boolean formulae. We discuss three formalizations of conditional planning as quantied Boolean formulae, and present experimental results obtained with a theorem-prover. Plans consist of operators that make a set of facts true whenever their preconditions are fullled. The most basic { and the most common in earlier research { form of plans is sequence of operators that are executed unconditionally in the specied order. Plans of this form are sucient only if the world where a plan is carried out is completely predictable and known, and the execution of the plan always starts in the same state. When not all changes in the world can be predicted or not all facts aecting plan execution are known in advance, the structure of plans has to be more general. If the task is to move object A, that is in room 1 or in room 2, to a trash can, the operations that achieve the goal depend on the initial location of A. There is no single sequence of operations that achieves the goal in both cases.

This article studies the problem of modifying the action ordering of a plan in order to optimise the plan according to various criteria. One of these criteria is to make a plan less constrained and the other is to minimize its parallel execution time. Three candidate definitions are proposed for the first of these criteria, constituting a sequence of increasing optimality guarantees. Two of these are based on deordering plans, which means that ordering relations may only be removed, not added, while the third one uses reordering, where arbitrary modifications to the ordering are allowed. It is shown that only the weakest one of the three criteria is tractable to achieve, the other two being NP-hard and even difficult to approximate. Similarly, optimising the parallel execution time of a plan is studied both for deordering and reordering of plans. In the general case, both of these computations are NP-hard. However, it is shown that optimal deorderings can be computed in polynomial time for a class of planning languages based on the notions of producers, consumers and threats, which includes most of the commonly used planning languages. Computing optimal reorderings can potentially lead to even faster parallel executions, but this problem remains NP-hard and difficult to approximate even under quite severe restrictions.

The implementation is based on two insights: that many of the graph construction operations can be implemented as bit-level logical operations on bit vectors, and that the graph should not be explicitly constructed beyond the x point. A more detailed discussion of the competition, from the competitors' point of view, is in preparation. First, we observe that action pre-and post-conditions can be represented using bit vectors. Checking for mutual exclusion between pairs of actions which directly interact can be implemented using logical operations on these bit vectors. Mutual exclusion (mutex relations) between facts can be implemented in a similar way. Second, we observe that there is no advantage in explicit construction of the graph beyond the stage at which the x point is reached. Since no new facts, actions or mutex relations are added beyond the x point these goal sets can be considered without explicit copying of the fact and action layers. For example, using a heuristic discussed in Section 5.1, Sta In this paper we describe the spike and wave front mechanisms and provide experimental results indicating the performance advantages obtained. The layers correspond to snapshots of possible states at instants on a time line from the initial to the goal state.

We present a new approach to path planning, called the "Ariadne's clew algorithm". It is designed to find paths in high-dimensional continuous spaces and applies to robots with many degrees of freedom in static, as well as dynamic environments - ones where obstacles may move. The Ariadne's clew algorithm comprises two sub-algorithms, called Search and Explore, applied in an interleaved manner. Explore builds a representation of the accessible space while Search looks for the target. Both are posed as optimization problems. We describe a real implementation of the algorithm to plan paths for a six degrees of freedom arm in a dynamic environment where another six degrees of freedom arm is used as a moving obstacle. Experimental results show that a path is found in about one second without any pre-processing.

A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered first: it is the composition of a temporal logic TL -- able to express interval temporal networks -- together with the non-temporal logic F -- a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF. The former adds disjunction both at the temporal and non-temporal sides of the language, the latter extends the non-temporal side with set-valued features (i.e., roles) and a propositionally complete language.

As planning is applied to larger and richer domains the effort involved in constructing domain descriptions increases and becomes a significant burden on the human application designer. If general planners are to be applied successfully to large and complex domains it is necessary to provide the domain designer with some assistance in building correctly encoded domains. One way of doing this is to provide domain-independent techniques for extracting, from a domain description, knowledge that is implicit in that description and that can assist domain designers in debugging domain descriptions. This knowledge can also be exploited to improve the performance of planners: several researchers have explored the potential of state invariants in speeding up the performance of domain-independent planners. In this paper we describe a process by which state invariants can be extracted from the automatically inferred type structure of a domain. These techniques are being developed for exploitation by STAN, a Graphplan based planner that employs state analysis techniques to enhance its performance.