Modelling Mixed Discrete-Continuous Domains for Planning

In this paper we present pddl+, a planning domain description language for modelling mixed discrete-continuous planning domains. We describe the syntax and modelling style of pddl+, showing that the language makes convenient the modelling of complex time-dependent effects. We provide a formal semantics for pddl+ by mapping planning instances into constructs of hybrid automata. Using the syntax of HAs as our semantic model we construct a semantic mapping to labelled transition systems to complete the formal interpretation of pddl+ planning instances. An advantage of building a mapping from pddl+ to HA theory is that it forms a bridge between the Planning and Real Time Systems research communities. One consequence is that we can expect to make use of some of the theoretical properties of HAs. For example, for a restricted class of HAs the Reachability problem (which is equivalent to Plan Existence) is decidable. pddl+ provides an alternative to the continuous durative action model of pddl2.1, adding a more flexible and robust model of time-dependent behaviour

OCL Plus:Processes and Events in Object-Centred Planning

An important area in AI Planning is the expressiveness of planning domain specification languages such as PDDL, and their aptitude for modelling real applications. This paper presents OCLplus, an extension of a hierarchical object centred planning domain definition language, intended to support the representation of domains with continuous change. The main extension in OCLplus provides the capability of interconnection between the planners and the changes that are caused by other objects of the world. To this extent, the concept of event and process are introduced in the Hierarchical Task Network (HTN), object centred planning framework in which a process is responsible for either continuous or discrete changes, and an event is triggered if its precondition is met. We evaluate the use of OCLplus and compare it with a similar language, PDDL+

Validating plans with exogenous events

We are concerned with the problem of deciding the validity of a complex plan involving interacting continuous activity. In these situations there is a need to model and reason about the continuous processes and events that arise as a consequence of the behaviour of the physical world in which the plan is expected to execute. In this paper we describe how events, which occur as the outcome of uncontrolled physical processes, can be taken into account in determining whether a plan is valid with respect to the domain model. We do not consider plan generation issues in this paper but focus instead on issues in domain modelling and plan validation

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

VAL : automatic plan validation, continuous effects and mixed initiative planning using PDDL

This paper describes aspects of our plan validation tool, VAL. The tool was initially developed to support the 3rd International Planning Competition, but has subsequently been extended in order to exploit its capabilities in plan validation and development. In particular, the tool has been extended to include advanced features of PDDL2.1 which have proved important in mixed-initiative planning in a space operations project. Amongst these features, treatment of continuous effects is the most significant, with important effects on the semantic interpretation of plans. The tool has also been extended to keep abreast of developments in PDDL, providing critical support to participants and organisers of the 4th IPC

PDDL2.1: An extension of PDDL for expressing temporal planning domains

In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover ex ploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power --- exceeding the capabilities of current planning technology --- and presents a number of important challenges to the research community

CASP Solutions for Planning in Hybrid Domains

CASP is an extension of ASP that allows for numerical constraints to be added in the rules. PDDL+ is an extension of the PDDL standard language of automated planning for modeling mixed discrete-continuous dynamics. In this paper, we present CASP solutions for dealing with PDDL+ problems, i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP CASP solver in order to solve CASP programs arising from PDDL+ domains. An experimental analysis, performed on well-known linear and non-linear variants of PDDL+ domains, involving various configurations of the EZCSP solver, other CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

A Synthesis of Automated Planning and Model Predictive Control Techniques and its Use in Solving Urban Traffic Control Problem

Most desired applications for planning and scheduling typically have the characteristics of a continuous changing world. Unfortunately, traditional classical planning does not possess this characteristic. This drawback is because most real-world situations involve quantities and numeric values, which cannot be adequately represented in classical planning. Continuous planning in domains that are represented with rich notations is still a great challenge for AI. For instance, changes occurring due to fuel consumption, continuous movement, or environmental conditions may not be adequately modelled through instantaneous or even durative actions; rather these require modelling as continuously changing processes. The development of planning tools that can reason with domains involving continuous and complex numeric fluents would facilitate the integration of automated planning in the design and development of complex application models to solve real world problems. Traditional urban traffic control (UTC) approaches are still not very efficient during unforeseen situations such as road incidents when changes in traffic are requested in a short time interval. For such anomalies, we need systems that can plan and act effectively in order to restore an unexpected road traffic situation into a normal order. In the quest to improve reasoning with continuous process within the UTC domain, we investigate the role of Model Predictive Control (MPC) approach to planning in the presence of mixed discrete and continuous state variables within a UTC problem. We explore this control approach and show how it can be embedded into existing, modern AI Planning technology. This approach preserves the many advantages of the AI Planning approach, to do with domain independence through declarative modelling, and explicit reasoning while leveraging the capability of MPC to deal with continuous processes. We evaluate the possibility of reasoning with the knowledge of UTC structures to optimise traffic flow in situations where a given road within a network of roads becomes unavailable due to unexpected situations such as road accidents. We specify how to augment the standard AI planning engine with the incorporation of MPC techniques into the central reasoning process of a continuous domain. This approach effectively utilises the strengths of search-based and model-simulation-based methods. We create a representation that can be used to capture declaratively, the definitions of processes, actions, events, resources resumption and the structure of the environment in a UTC scenario. This representation is founded on world states modelled by mixed discrete and continuous state variables. We create a planner with a hybrid algorithm, called UTCPLAN that combines both AI planning and MPC approach to reason with traffic network and control traffic signal at junctions within the network. The experimental objective of minimising the number of vehicles in a queue is implemented to validate the applicability and effectiveness of the algorithm. We present an experimental evaluation showing that our approach can provide UTC plans in a reasonable time. The result also shows that the UTCPLAN approach can perform well in dealing with heavy traffic congestion problems, which might result from heavy traffic flow during rush hours