Numerical Integration and Dynamic Discretization in Heuristic Search Planning over Hybrid Domains

In this paper we look into the problem of planning over hybrid domains, where change can be both discrete and instantaneous, or continuous over time. In addition, it is required that each state on the trajectory induced by the execution of plans complies with a given set of global constraints. We approach the computation of plans for such domains as the problem of searching over a deterministic state model. In this model, some of the successor states are obtained by solving numerically the so-called initial value problem over a set of ordinary differential equations (ODE) given by the current plan prefix. These equations hold over time intervals whose duration is determined dynamically, according to whether zero crossing events take place for a set of invariant conditions. The resulting planner, FS+, incorporates these features together with effective heuristic guidance. FS+ does not impose any of the syntactic restrictions on process effects often found on the existing literature on Hybrid Planning. A key concept of our approach is that a clear separation is struck between planning and simulation time steps. The former is the time allowed to observe the evolution of a given dynamical system before committing to a future course of action, whilst the later is part of the model of the environment. FS+ is shown to be a robust planner over a diverse set of hybrid domains, taken from the existing literature on hybrid planning and systems.Comment: 17 page

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

PDDLStream: Integrating Symbolic Planners and Blackbox Samplers via Optimistic Adaptive Planning

Many planning applications involve complex relationships defined on high-dimensional, continuous variables. For example, robotic manipulation requires planning with kinematic, collision, visibility, and motion constraints involving robot configurations, object poses, and robot trajectories. These constraints typically require specialized procedures to sample satisfying values. We extend PDDL to support a generic, declarative specification for these procedures that treats their implementation as black boxes. We provide domain-independent algorithms that reduce PDDLStream problems to a sequence of finite PDDL problems. We also introduce an algorithm that dynamically balances exploring new candidate plans and exploiting existing ones. This enables the algorithm to greedily search the space of parameter bindings to more quickly solve tightly-constrained problems as well as locally optimize to produce low-cost solutions. We evaluate our algorithms on three simulated robotic planning domains as well as several real-world robotic tasks.Comment: International Conference on Automated Planning and Scheduling (ICAPS) 202

Optimal Planning Modulo Theories

Planning for real-world applications requires algorithms and tools with the ability to handle the complexity such scenarios entail. However, meeting the needs of such applications poses substantial challenges, both representational and algorithmic. On the one hand, expressive languages are needed to build faithful models. On the other hand, efficient solving techniques that can support these languages need to be devised. A response to this challenge is underway, and the past few years witnessed a community effort towards more expressive languages, including decidable fragments of first-order theories. In this work we focus on planning with arithmetic theories and propose Optimal Planning Modulo Theories, a framework that attempts to provide efficient means of dealing with such problems. Leveraging generic Optimization Modulo Theories (OMT) solvers, we first present domain-specific encodings for optimal planning in complex logistic domains. We then present a more general, domain- independent formulation that allows to extend OMT planning to a broader class of well-studied numeric problems in planning. To the best of our knowledge, this is the first time OMT procedures are employed in domain-independent planning

Planutils: Bringing Planning to the Masses

PLANUTILS is a general library for setting up Linux-based environments for developing, running, and evaluating planners. Over the last decades, the planning community has produced countless solvers for various planning formalisms, as well as many other tools to help the planning practitioner. From state-of-the-art planners, over validators, to parsing libraries, the planning ecosystem has grown quite large. In the demo, we highlight an effort that aims to unify this ecosystem and make it seamless for users to get started with what the ICAPS community has to offer

Verification and Validation of Planning Domain Models

The verification and validation of planning domain models is one of the biggest challenges to deploying planning-based automated systems in the real world.The state-of-the-art verification methods of planning domain models are vulnerable to false positives, i.e. counterexamples that are unreachable by sound planners when using the domain under verification during planning tasks. False positives mislead designers into believing correct models are faulty. Consequently, designers needlessly debug correct models to remove these false positives. This process might unnecessarily constrain planning domain models, which can eradicate valid and sometimes required behaviours. Moreover, catching and debugging errors without knowing they are false positives can give verification engineers a false sense of achievement, which might cause them to overlook valid errors.To address this shortfall, the first part of this thesis introduces goal-constrained planning domain model verification, a novel approach that constrains the verification of planning domain models with planning goals to reduce the number of unreachable planning counterexamples. This thesis formally proves the correctness of this method and demonstrates the application of this approach using the model checker Spin and the planner MIPS-XXL. Furthermore, it reports the empirical experiments that validate the feasibility and investigates the performance of the goal-constrained verification approach. The experiments show that not only the goal-constrained verification method is robust against false positive errors, but it also outperforms under-constrained verification tasks in terms of time and memory in some cases.The second part of this thesis investigates the problem of validating the functional equivalence of planning domain models. The need for techniques to validate the functional equivalence of planning domain models has been highlighted in previous research and has applications in model learning, development and extension. Despite the need and importance of proving the functional equivalence of planning domain models, this problem attracted limited research interest.This thesis builds on and extends previous research by proposing a novel approach to validate the functional equivalence of planning domain models. First, this approach employs a planner to remove redundant operators from the given domain models; then, it uses a Satisfiability Modulo Theories (SMT) solver to check if a predicate mapping exists between the two domain models that makes them functionally equivalent. The soundness and completeness of this functional equivalence validation method are formally proven in this thesis.Furthermore, this thesis introduces D-VAL, the first planning domain model automatic validation tool. D-VAL uses the FF planner and the Z3 SMT solver to prove the functional equivalence of planning domain models. Moreover, this thesis demonstrates the feasibility and evaluates the performance of D-VAL against thirteen planning domain models from the International Planning Competition (IPC). Empirical evaluation shows that D-VAL validates the functional equivalence of the most challenging task in less than 43 seconds. These experiments and their results provide a benchmark to evaluate the feasibility and performance of future related work

Generalized Planning as Heuristic Search: A new planning search-space that leverages pointers over objects

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not extend trivially to Generalized Planning (GP). GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in the number of objects, the number of state variables, their domain size, or their initial and goal configuration. The generalization requirements of GP make it impractical to perform the state-space search that is usually implemented by heuristic planners. This paper adapts the planning as heuristic search paradigm to the generalization requirements of GP, and presents the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines a set of evaluation and heuristic functions for guiding a combinatorial search in our new GP solution space. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g.~integers. Lastly, the paper defines an upgraded version of our novel algorithm for GP called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space, and that is guided by our evaluation/heuristic functions for GP.Comment: Under review in the Artificial Intelligence Journal (AIJ