1,741 research outputs found
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
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
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
Temporal Planning with Intermediate Conditions and Effects
Automated temporal planning is the technology of choice when controlling
systems that can execute more actions in parallel and when temporal
constraints, such as deadlines, are needed in the model. One limitation of
several action-based planning systems is that actions are modeled as intervals
having conditions and effects only at the extremes and as invariants, but no
conditions nor effects can be specified at arbitrary points or sub-intervals.
In this paper, we address this limitation by providing an effective
heuristic-search technique for temporal planning, allowing the definition of
actions with conditions and effects at any arbitrary time within the action
duration. We experimentally demonstrate that our approach is far better than
standard encodings in PDDL 2.1 and is competitive with other approaches that
can (directly or indirectly) represent intermediate action conditions or
effects
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
Combined heuristic task and motion planning for bi-manual robots
Planning efficiently at task and motion levels allows the setting of new challenges for robotic manipulation problems, like for instance constrained table-top problems for bi-manual robots. In this scope, the appropriate combination of task and motion planning levels plays an important role. Accordingly, a heuristic-based task and motion planning approach is proposed, in which the computation of the heuristic addresses a geometrically relaxed problem, i.e., it only reasons upon objects placements, grasp poses, and inverse kinematics solutions. Motion paths are evaluated lazily, i.e., only after an action has been selected by the heuristic. This reduces the number of calls to the motion planner, while backtracking is reduced because the heuristic captures most of the geometric constraints. The approach has been validated in simulation and on a real robot, with different classes of table-top manipulation problems. Empirical comparison with recent approaches solving similar problems is also reported, showing that the proposed approach results in significant improvement both in terms of planing time and success rate.Peer ReviewedPostprint (author's final draft
Partial Weighted MaxSAT for Optimal Planning
Abstract. We consider the problem of computing optimal plans for proposi-tional planning problems with action costs. In the spirit of leveraging advances in general-purpose automated reasoning for that setting, we develop an approach that operates by solving a sequence of partial weighted MaxSAT problems, each of which corresponds to a step-bounded variant of the problem at hand. Our ap-proach is the first SAT-based system in which a proof of cost-optimality is ob-tained using a MaxSAT procedure. It is also the first system of this kind to incor-porate an admissible planning heuristic. We perform a detailed empirical eval-uation of our work using benchmarks from a number of International Planning Competitions.
Optimal Planning with State Constraints
In the classical planning model, state variables are assigned
values in the initial state and remain unchanged unless
explicitly affected by action effects. However, some properties
of states are more naturally modelled not as direct effects of
actions but instead as derived, in each state, from the primary
variables via a set of rules. We refer to those rules as state
constraints. The two types of state constraints that will be
discussed here are numeric state constraints and logical rules
that we will refer to as axioms.
When using state constraints we make a distinction between
primary variables, whose values are directly affected by action
effects, and secondary variables, whose values are determined by
state constraints. While primary variables have finite and
discrete domains, as in classical planning, there is no such
requirement for secondary variables. For example, using numeric
state constraints allows us to have secondary variables whose
values are real numbers. We show that state constraints are a
construct that lets us combine classical planning methods with
specialised solvers developed for other types of problems. For
example, introducing numeric state constraints enables us to
apply planning techniques in domains involving interconnected
physical systems, such as power networks.
To solve these types of problems optimally, we adapt commonly
used methods from optimal classical planning, namely state-space
search guided by admissible heuristics. In heuristics based on
monotonic relaxation, the idea is that in a relaxed state each
variable assumes a set of values instead of just a single value.
With state constraints, the challenge becomes to evaluate the
conditions, such as goals and action preconditions, that involve
secondary variables. We employ consistency checking tools to
evaluate whether these conditions are satisfied in the relaxed
state. In our work with numerical constraints we use linear
programming, while with axioms we use answer set programming and
three value semantics. This allows us to build a relaxed planning
graph and compute constraint-aware version of heuristics based on
monotonic relaxation.
We also adapt pattern database heuristics. We notice that an
abstract state can be thought of as a state in the monotonic
relaxation in which the variables in the pattern hold only one
value, while the variables not in the pattern simultaneously hold
all the values in their domains. This means that we can apply the
same technique for evaluating conditions on secondary variables
as we did for the monotonic relaxation and build pattern
databases similarly as it is done in classical planning.
To make better use of our heuristics, we modify the A* algorithm
by combining two techniques that were previously used
independently – partial expansion and preferred operators. Our
modified algorithm, which we call PrefPEA, is most beneficial in
cases where heuristic is expensive to compute, but accurate, and
states have many successors
Partial Weighted MaxSAT for Optimal Planning
We consider the problem of computing optimal plans for propositional planning problems with action costs. In the spirit of leveraging advances in general-purpose automated reasoning for that setting, we develop an approach that operates by solving a sequence of partial weighted MaxSAT problems, each of which corresponds to a step-bounded variant of the problem at hand. Our approach is the first SAT-based system in which a proof of cost-optimality is obtained using a MaxSAT procedure. It is also the first system of this kind to incorporate an admissible planning heuristic. We perform a detailed empirical evaluation of our work using benchmarks from a number of International Planning Competitions.NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy
and the Australian Research Council through the ICT Centre of Excellence program.
This work was also supported by EC FP7-IST grant 215181-CogX
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