Strong Cyclic Planning Research Articles

Analyzing generalized planning under nondeterminism

In automated planning, there has been a recent interest in solving a class of problems, where a single solution applies for multiple, possibly infinitely many, instances. This necessitates a generalized notion of plans, such as plans with loops. However, the correctness of such plans is non-trivial to define, making it difficult to provide a clear specification of what we should be looking for. In an influential paper, Levesque proposed a formal specification for analyzing the correctness of such plans. He motivated a logical characterization within the situation calculus that included binary sensing actions. This characterization argued that from each state considered possible initially, the plan should terminate while satisfying the goal. Increasingly, classical plan structures are being applied to stochastic environments such as robotics applications. This raises the question as to what the specification for correctness should look like, since Levesque's account makes the assumption that actions are deterministic.In this work, we aim to generalize Levesque's account to handle actions with nondeterministic outcomes, which may also be accorded probabilities. By appealing to an extension of the situation calculus to handle probabilistic nondeterminism, we will show that Levesque's definition, as well as a notion of goal achievability proposed by Lin and Levesque, have limited appeal under stochastic nondeterminism. In essence, they correspond to one correct execution, which is unlikely to be adequate. Rather, we propose to delineate between goal satisfaction and termination leading to a range of correctness criteria. To better study these criteria, and to position the results in a broader context while still allowing for the generality of the situation calculus, we consider an abstract framework to study the correctness of plans with loops, in domains that are possibly unbounded, and/or stochastic, and/or continuous. Within that framework, we then prove numerous relationships between the criteria, including some impossibility results for categorically satisfying goals. Finally, we show that these notions provide a more granular view than those discussed in the literature, such as strong planning and strong cyclic planning.

Fully Observable Non-deterministic Planning as Assumption-Based Reactive Synthesis

We contribute to recent efforts in relating two approaches to automatic synthesis, namely, automated planning and discrete reactive synthesis. First, we develop a declarative characterization of the standard "fairness" assumption on environments in non-deterministic planning, and show that strong-cyclic plans are correct solution concepts for fair environments. This complements, and arguably completes, the existing foundational work on non-deterministic planning, which focuses on characterizing (and computing) plans enjoying special "structural" properties, namely loopy but closed policy structures. Second, we provide an encoding suitable for reactive synthesis that avoids the naive exponential state space blowup. To do so, special care has to be taken to specify the fairness assumption on the environment in a succinct manner.

Fast strong planning for fully observable nondeterministic planning problems

The ability to find strong solutions to fully observable nondeterministic (FOND) planning problems, if they exist, is desirable because unlike weak and strong-cyclic solutions, strong solutions are guaranteed to achieve the goal. However, only limited work has been done on FOND planning with strong solutions. In this paper, we present a sound and complete strong planning algorithm and incorporate it into our planner, FIP, which has achieved outstanding performance on strong cyclic planning problems. This new strong planning approach enables FIP to first search for strong solutions, and then search for strong-cyclic solutions only if strong solutions do not exist. We conduct extensive experiments to evaluate the new strong planning approach to (1) find a strong solution if one exists and (2) determine the non-existence of a strong solution. Experimental results demonstrate the superior performance of our planner to Gamer and MBP, the two best-known planners capable of solving strong FOND planning problems, on a variety of benchmark problems. Not only is our planner on average three orders of magnitude faster than Gamer and MBP, but it also scales up to larger problems.

Plan aggregation for strong cyclic planning in nondeterministic domains

We describe a planning algorithm, NDP2, that finds strong-cyclic solutions to nondeterministic planning problems by using a classical planner to solve a sequence of classical planning problems. NDP2 is provably correct, and fixes several problems with prior work.We also describe two preprocessing algorithms that can provide a restricted version of the symbolic abstraction capabilities of the well-known MBP planner. The preprocessing algorithms accomplish this by rewriting the planning problems, hence do not require any modifications to NDP2 or its classical planner.In our experimental comparisons of NDP2 (using FF as the classical planner) to MBP in six different planning domains, each planner outperformed the other in some domains but not others. Which planner did better depended on three things: the amount of nondeterminism in the planning domain, domain characteristics that affected how well the abstraction techniques worked, and whether the domain contained unsolvable states.

Pattern Database Heuristics for Fully Observable Nondeterministic Planning

When planning in an uncertain environment, one is often interested in finding a contingent plan that prescribes appropriate actions for all possible states that may be encountered during the execution of the plan. We consider the problem of finding strong cyclic plans for fully observable nondeterministic (FOND) planning problems. The algorithm we choose is LAO*, an informed explicit state search algorithm. We investigate the use of pattern database (PDB) heuristics to guide LAO* towards goal states. To obtain a fully domain-independent planning system, we use an automatic pattern selection procedure that performs local search in the space of pattern collections. The evaluation of our system on the FOND benchmarks of the Uncertainty Part of the International Planning Competition 2008 shows that our approach is competitive with symbolic regression search in terms of problem coverage, speed, and plan quality.

Creating automated plans for Semantic Web applications through planning as model checking

The uncertainties of planning engendered by nondeterminism and partial observability have led to a melding of model checking and artificial intelligence. The result is planning as model checking. Because planning as model checking tests sets of states and sets of transitions at once, rather than single states, the method remains robust and viable in domains of large state spaces and varying levels of uncertainty. We develop a test bench for Semantic Web agents and use model-based planning to derive strong plans, strong cyclic plans, and weak plans. Our results suggest potential robustness and efficacy in devising plans for agent actions in the Semantic Web environment.

Weak, strong, and strong cyclic planning via symbolic model checking

Planning in nondeterministic domains yields both conceptual and practical difficulties. From the conceptual point of view, different notions of planning problems can be devised: for instance, a plan might either guarantee goal achievement, or just have some chances of success. From the practical point of view, the problem is to devise algorithms that can effectively deal with large state spaces. In this paper, we tackle planning in nondeterministic domains by addressing conceptual and practical problems. We formally characterize different planning problems, where solutions have a chance of success (“weak planning”), are guaranteed to achieve the goal (“strong planning”), or achieve the goal with iterative trial-and-error strategies (“strong cyclic planning”). In strong cyclic planning, all the executions associated with the solution plan always have a possibility of terminating and, when they do, they are guaranteed to achieve the goal. We present planning algorithms for these problem classes, and prove that they are correct and complete. We implement the algorithms in the mbp planner by using symbolic model checking techniques. We show that our approach is practical with an extensive experimental evaluation: mbp compares positively with state-of-the-art planners, both in terms of expressiveness and in terms of performance.

OBDD-based Universal Planning for Synchronized Agents in Non-Deterministic Domains

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.