Nondeterministic Domains Research Articles

Temporally extended goal recognition in fully observable non-deterministic domain models

Goal Recognition is the task of discerning the intended goal that an agent aims to achieve, given a set of goal hypotheses, a domain model, and a sequence of observations (i.e., a sample of the plan executed in the environment). Existing approaches assume that goal hypotheses comprise a single conjunctive formula over a single final state and that the environment dynamics are deterministic, preventing the recognition of temporally extended goals in more complex settings. In this paper, we expand goal recognition to temporally extended goals in Fully Observable Non-Deterministic (fond) planning domain models, focusing on goals on finite traces expressed in Linear Temporal Logic (ltlf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_f$$\\end{document}) and Pure-Past Linear Temporal Logic (ppltl). We develop the first approach capable of recognizing goals in such settings and evaluate it using different ltlf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_f$$\\end{document} and ppltl goals over six fond planning domain models. Empirical results show that our approach is accurate in recognizing temporally extended goals in different recognition settings.

Fully Observable Nondeterministic HTN Planning -- Formalisation and Complexity Results

Much progress has been made in advancing the state of the art of HTN planning theory in recent years. However, scarce studies have been made with regards to the theory and complexity of HTN problems on nondeterministic domains. In this paper we provide a novel formalisation for fully observable nondeterministic HTN planning. We propose and study different solution criteria which differ in when nondeterministic action outcomes are considered: at plan generation or at plan execution. We integrate our solution criteria with notions of weak and strong plans canonical in nondeterministic planning and identify similarities and differences with plans in other fields of AI planning. We also provide completeness results for a majority of HTN problem subclasses and show the significant result that problems are not made any harder under nondeterminism for certain solution criteria by using compilation techniques to deterministic HTN planning. This supports and justifies the practicality and scalability of extending HTN problems over nondeterministic domains to deal with real world scenarios.

Computing Contingent Plan Graphs using Online Planning

In contingent planning under partial observability with sensing actions, agents actively use sensing to discover meaningful facts about the world. Recent successful approaches translate the partially observable contingent problem into a non-deterministic fully observable problem, and then use a planner for non-deterministic planning. However, the translation may become very large, encumbering the task of the non-deterministic planner. We suggest a different approach—using an online contingent solver repeatedly to construct a plan tree. We execute the plan returned by the online solver until the next observation action, and then branch on the possible observed values, and replan for every branch independently. In many cases a plan tree can have an exponential width in the number of state variables, but the tree may have a structure that allows us to compactly represent it using a directed graph. We suggest a mechanism for tailoring such a graph that reduces both the computational effort and the storage space. Our method also handles non-deterministic domains, by identifying cycles in the plans. We present a set of experiments, showing our approach to scale better than state-of-the-art offline planners.

Stochastic Fairness and Language-Theoretic Fairness in Planning in Nondeterministic Domains

We address two central notions of fairness in the literature of nondeterministic fully observable domains. The first, which we call stochastic fairness, is classical, and assumes an environment which operates probabilistically using possibly unknown probabilities. The second, which is language-theoretic, assumes that if an action is taken from a given state infinitely often then all its possible outcomes should appear infinitely often; we call this state-action fairness. While the two notions coincide for standard reachability goals, they differ for temporally extended goals. This important difference has been overlooked in the planning literature and has led to the use of a product-based reduction in a number of published algorithms which were stated for state-action fairness, for which they are incorrect, while being correct for stochastic fairness. We remedy this and provide a correct optimal algorithm for solving state-action fair planning for ltl/ltlf goals, as well as a correct proof of the lower bound of the goal-complexity. Our proof is general enough that it also provides, for the no-fairness and stochastic-fairness cases, multiple missing lower bounds and new proofs of known lower bounds. Overall, we show that stochastic fairness is better behaved than state-action fairness.

Planning under LTL Environment Specifications

Planning domains represent what an agent assumes or believes about the environment it acts in. In the presence of nondeterminism, additional temporal assumptions, such as fairness, are often expressed as extra conditions on the domain. Here we consider environment specifications expressed in arbitrary LTL, which generalize many forms of environment specifications, including classical specifications of nondeterministic domains, fairness, and other forms of linear-time constraints on the domain itself. Existing literature typically implicitly or explicitly considers environment specifications as constraints on possible traces. In contrast, in spite of the fact that we use a linear-time formalism, we propose to consider environment specifications as specifications of environment strategies. Planning in this framework is the problem of computing an agent strategy that achieves its goal against all environment strategies satisfying the specification. We study the mathematical and computational properties of planning in this general setting. We observe that not all LTL formulas correspond to legitimate environment specifications, and formally characterize the ones that do. Moreover, we show that our notion of planning generalizes the classical notion of Church’s synthesis, and that in spite this one can still solve it optimally using classical Church’s synthesis.

Synthesis of Cost-Optimal Strong Plans in Non-Deterministic Domains

Automatic planning tools can be a valuable aid to build control systems for a wide range of everyday appliances. Many systems which interact with the real world present a non-deterministic behaviour, often made more complex by nonlinear continuous dynamics. In this context, strong planning, which requires finding a plan that is guaranteed to achieve the goal regardless of non-determinism, plays an important role. With the increasing need for optimising the use of resources, finding strong solutions while minimising a cost function appears a significant research challenge, which has not previously been addressed.In this paper we provide a formal description of the cost-optimal strong planning problem and present an algorithm to solve it with good complexity bounds. The algorithm correctness and completeness are formally proved, and its implementation in the disk-based SUPMurphi tool is described. Finally, two meaningful case studies are presented to show the effectiveness of the proposed approach compared with a state-of-the-art strong planning tool.

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.

Directed Fixed-Point Regression-Based Planning for Non-Deterministic Domains

We present a novel approach to fully-observable nondeterministic planning (FOND) that attempts to bridge the gap between symbolic fix-point computation and recent approaches based on forward heuristic search. Concretely, we formalize the relationship between symbolic and dynamic programming nondeterministic planners, and then exploit such connection to propose a novel familyof planning algorithms that reasons over symbolic policies in a directed manner. By doing so, our proposal reasons over sets of states and executions in a succinct way (as done by symbolic planners) while biasing the reasoning with respect to the initial and goal states of the specific planning problem at hand (as done by heuristic planners). We show empirical results that prove this approach promising in settings where there is an intrinsic tension between plan efficiency and plan "robustness," a feature to be expected in nondeterministic domains.

Automatic Composition of Heterogeneous Models Based on Semantic Web Services

As an important function of a distributed decision support system, model composition aims to aggregate model functions to solve complex decision problems. Most existing methods on model composition only apply to the models which have the same type of input and output data so that they can be linked together directly. Those methods are inadequate for the heterogeneous models, since a heterogeneous model may have different types of input and output data that are represented in either qualitative or quantitative manner. This paper aims to address the problem of heterogeneous model composition by employing the techniques based on semantic web services and artificial intelligence planning. In this paper, the heterogeneous model composition problem is converted to the problem of planning in nondeterministic domains under partial observability. An automatic composition method is presented to generate the composite model based on the planning as model checking technique. The experiment results are also presented in this paper to show the feasibility and capability of our approach in dealing with the complex problems involving heterogeneous models.

Multi-Strategy Learning of Robotic Behaviours via Qualitative Reasoning

When given a task, an autonomous agent must plan a series of actions to perform in order to complete the goal. In robotics, planners face additional challenges as the domain is typically large (even infinite) continuous, noisy, and non- deterministic. Typically stochastic planning has been used to solve robotic control tasks. Such planners have been very successful in their various domains. The downside to such approaches is that the models and planners are highly specialised to a single control task. To change the control task, requires developing an entirely new planner. The research in my thesis focuses on the problem of specialisation in continuous, noisy and non-deterministic robotic domains by developing a more generic planner. It builds on previous research in the area, specifically using the technique of Multi-Strategy Learning. Qualitative Modelling and Qualitative Reasoning is used to provide the generality, from which specific, Quantitative controllers can be quickly learnt. The resulting system is applied to a real world robotic platform for rough terrain navigation.

Model checking for universal planning in deterministic and non-deterministic domains

This thesis is concerned with solving planning problems in deterministic and non-deterministic domains through explicit model checking techniques. The contribution is twofold: on one side we developed the V-UPMurphi tool, which applies a disk-based planning approach for efficient storage during the plan synthesis. On the other side we developed and formally analysed an algorithm to solve cost-optimal strong planning problems in non-deterministic contexts. Finally, we applied the developed algorithms and tools to several application domains, many of which are inspired by real world scenarios.

Heuristic Planning in Adversarial Dynamic Domains

Agents in highly dynamic adversarial domains, such as RTS games, must continually make time-critical decisions to adapt their behaviour to the changing environment. In such a context, the planning agent must consider his opponent's actions as uncontrollable, or at best influenceable. In general nondeterministic domains where there is no clear turn-taking protocol, most heuristic search methods to date do not explicitly reason about the opponent's actions when guiding the state space exploration towards goal or high-reward states. In contrast, we are investigating a domain-independent heuristic planning approach which reasons about the dynamics and uncontrollability of the opponent's behaviours in order to provide better guidance to the search process of the planner. Our planner takes as input the opponent's behaviours recognized by a plan recognition module and uses them to identify opponent's actions that lead to low-utility projected states. We believe such explicit heuristic reasoning about the potential behaviours of the opponent is crucial when planning in adversarial domains, yet is missing in today's planning approaches.

Formula omitted] and the role of elaboration tolerance in solving the qualification problem

We describe M odular- E ( ME ), a specialized, model-theoretic logic for reasoning about actions. ME is able to represent non-deterministic domains involving concurrency, static laws (constraints), indirect effects (ramifications), and narrative information in the form of action occurrences and observations along a time line. We give formal results which characterize ME 's high degree of modularity and elaboration tolerance, and show how these properties help to separate out, and provide principled solutions to, different aspects of the qualification problem. In particular, we identify the endogenous qualification problem as the problem of properly accounting for highly distributed, and potentially conflicting, causal knowledge when reasoning about the effects of actions. We show how a comprehensive solution to the endogenous qualification problem helps simplify the exogenous qualification problem — the problem of reconciling conflicts between predictions about what should be true at particular times and actual observations. More precisely, we describe how ME is able to use straightforward default reasoning techniques to solve the exogenous qualification problem largely because its robust treatments of the frame, ramification and endogenous qualification problems combine into a particular characteristic of elaboration tolerance that we formally encapsulate as a notion of “free will”.

Task decomposition on abstract states, for planning under nondeterminism

Although several approaches have been developed for planning in nondeterministic domains, solving large planning problems is still quite difficult. In this work, we present a new planning algorithm, called Yoyo, for solving planning problems in fully observable nondeterministic domains. Yoyo combines an HTN-based mechanism for constraining its search and a Binary Decision Diagram (BDD) representation for reasoning about sets of states and state transitions. We provide correctness theorems for Yoyo, and an experimental comparison of it with MBP and ND-SHOP2, the two previously-best algorithms for planning in nondeterministic domains. In our experiments, Yoyo could easily deal with problem sizes that neither MBP nor ND-SHOP2 could scale up to, and could solve problems about 100 to 1000 times faster than MBP and ND-SHOP2.

Measures of Uncertainty in Rule-Based Systems: One is Not Enough

The solution of most commercial rule-based expert systems consists of two components — the conclusion reached and its calculated measure of belief, expressed as a single number. In non-deterministic domains, this number is often the most critical factor in analyzing the solution. However, as this paper reviews, a robust calculus for this number has yet to be documented. Thus reliance on it alone poses a risk to users of commercial systems. This paper demonstrates how supplemental statistics can be calculated and used to decrease this risk. We hope these ideas will lead to better commercial expert systems and better user decision making.

The Planning Spectrum - One, Two, Three, Infinity

Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula f, which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretation A.f, which requires that the formula be satisfied for all execution paths, and the existential interpretation E.f, which requires that the formula be satisfied for some execution path. When LTL is applied to the definition of goals in planning problems on nondeterministic domains, these two extreme cases are too restrictive. It is often impossible to develop plans that achieve the goal in all the nondeterministic evolutions of a system, and it is too weak to require that the goal is satisfied by some execution. In this paper we explore alternative interpretations of an LTL formula that are between these extreme cases. We define a new language that permits an arbitrary combination of the A and E quantifiers, thus allowing, for instance, to require that each finite execution can be extended to an execution satisfying an LTL formula (AE.f), or that there is some finite execution whose extensions all satisfy an LTL formula (EA.f). We show that only eight of these combinations of path quantifiers are relevant, corresponding to an alternation of the quantifiers of length one (A and E), two (AE and EA), three (AEA and EAE), and infinity ((AE)* and (EA)*). We also present a planning algorithm for the new language that is based on an automata-theoretic approach, and study its complexity.

Strong planning under uncertainty in domains with numerous but identical elements (a generic approach)

The typical AI problem is that of making a plan of the actions to be performed by a robot so that the robot could get into a set of final situations, if it started with a certain initial situation. The planning problem is known to be generally very complex. Even within the case of ‘well-balanced’ actions, strong planning under uncertainty about the effects of actions, or games such as ‘Robot against Nature’, is EXPTIME-complete. As a result, AI planners are very sensitive to the number of the variables involved in making a plan, the inherent symmetry of the problem, and the nature of the logical formalisms being used. This paper shows that linear logic provides a convenient and adequate tool for representing strong and weak planning problems in non-deterministic domains. A particular focus of this paper is on planning problems with an unbounded number of functionally identical objects. We show that for such problems linear logic is especially effective and leads to a dramatic contraction of the search space from exponential to polynomial in size. We employ the ability of linear logic to reason about multisets, which in this instance are created by identifying several distinct objects as being functionally equivalent for the problem at hand (think of a number of balls, each of which must be moved to some new location — the balls are distinct, but are functionally equivalent for the problem). In linear logic terms, we establish a clear syntactic condition that allows us to show that solving a generic planning problem where there is only one generic object, directly implies a solution to the original real planning problem over several real objects, the isomorphic copies of the generic object. Moreover, this correspondence also guarantees to produce a real solution that works in polynomial time.

Strong planning under partial observability

Rarely planning domains are fully observable. For this reason, the ability to deal with partial observability is one of the most important challenges in planning. In this paper, we tackle the problem of strong planning under partial observability in nondeterministic domains: find a conditional plan that will result in a successful state, regardless of multiple initial states, nondeterministic action effects, and partial observability. We make the following contributions. First, we formally define the problem of strong planning within a general framework for modeling partially observable planning domains. Second, we propose an effective planning algorithm, based on and-or search in the space of beliefs. We prove that our algorithm always terminates, and is correct and complete. In order to achieve additional effectiveness, we leverage on a symbolic, bdd-based representation for the domain, and propose several search strategies. We provide a thorough experimental evaluation of our approach, based on a wide selection of benchmarks. We compare the performance of the proposed search strategies, and identify a uniform winner that combines heuristic distance measures with mechanisms that reduce runtime uncertainty. Then, we compare our planner mbp with other state-of-the art-systems. mbp is able to outperform its competitor systems, often by orders of magnitude.

Performance bounds for planning in unknown terrain

Planning in nondeterministic domains is typically intractable due to the large number of contingencies. Two techniques for speeding up planning in nondeterministic domains are agent-centered search and assumption-based planning. Both techniques interleave planning in deterministic domains with plan execution. They differ in how they make planning deterministic. To determine how suboptimal their plans are, we study two planning methods for robot navigation in initially unknown terrain that have successfully been used on mobile robots but not been analyzed before. The planning methods differ both in the technique they use to speed up planning and in the robot-navigation task they solve. Greedy Mapping uses agent-centered search to map unknown terrain. Dynamic A∗ uses assumption-based planning to navigate to a given goal location in unknown terrain. When we formalize abstractions of these planning methods on undirected graphs G=( V, E), they turn out to be similar enough that we are able to analyze their travel distance in a unified way. We discover that neither method is optimal in a worst-case sense, by a factor of Ω( log|V|/ loglog|V|) . We also derive factor O( |V| ) upper bounds to show that these methods are not very badly sub-optimal in this sense. These results provide a first step towards explaining the good empirical results that have been reported about Greedy Mapping and Dynamic A∗ in the experimental literature. More generally, they show how to use tools from graph theory to analyze the plan quality of practical planning methods for nondeterministic domains.

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.