Partially observable planning is one of the most general and useful models for dealing with complex problems. In recent years there have been significant progress on the development of planners for deterministic models that offer strong theoretical guarantees over certain subclasses of tasks. These guarantees however are difficult to establish as they often involve reasoning about features that are specific to the planner and subclass of tasks. In this paper we develop a formal framework for reasoning about online planning over deterministic tasks, identify a set of general conditions that are sufficient to guarantee completeness, and obtain novel and simple planners that are complete over non-trivial and interesting classes of tasks. Building on top state-of-the-art online planners, we implement some of our ideas and make a comparison with a state-of-the-art online planner.

Most applications of planning to real problems involve complex and often non-linear equations, including matrix operations. PDDL is ill-suited to express such calculations since it only allows basic operations between numeric fluents. To remedy this restriction, a generic PDDL planner can be connected to a specialised advisor, which equips the planner with the ability to carry out sophisticated mathematical operations. Unlike related techniques based on semantic attachment, our planner is able to exploit an approximation of the numeric information calculated by the advisor to compute informative heuristic estimators. Guided by both causal and numeric information, our planning framework outperforms traditional approaches, especially against problems with numeric goals. We provide evidence of the power of our solution by successfully solving four completely different problems.

Plan-Verification is the task of determining whether a plan is a solution to a given planning problem. Any plan verifier has, apart from showing that verifying plans is possible in practice, a wide range of possible applications. These include mixed-initiative planning, where a user is integrated into the planning process, and local search, e.g., for post-optimising plans or for plan repair. In addition to its practical interest, plan verification is also a problem worth investigating for theoretical reasons. Recent work showed plan verification for hierarchical planning problems to be NP-complete, as opposed to classical planning where it is in P. As such, plan verification for hierarchical planning problem was — until now — not possible. We describe the first plan verifier for hierarchical planning. It uses a translation of the problem into a SAT formula. Further we conduct an empirical evaluation, showing that the correct output is produced within acceptable time.

We investigate compositional bounding of transition system diameters, with application in bounding the lengths of plans. We establish usefully-tight bounds by exploiting acyclicity in state-spaces. We provide mechanised proofs in HOL4 of the validity of our approach. Evaluating our bounds in a range of benchmarks, we demonstrate exponentially tighter upper bounds compared to existing methods. Treating both solvable and unsolvable benchmark problems, we also demonstrate the utility of our bounds in boosting planner performance. We enhance an existing planning procedure to use our bounds, and demonstrate significant coverage improvements, both compared to the base planner, and also in comparisons with state-of-the-art systems.

Cost partitioning is a general method for adding multiple heuristic values admissibly. In the setting of optimal classical planning, saturated cost partitioning has recently been shown to be the cost partitioning algorithm of choice for pattern database heuristics found by hill climbing, systematic pattern database heuristics and Cartesian abstraction heuristics. To evaluate the synergy of the three heuristic types, we compute the saturated cost partitioning over the combined sets of heuristics and observe that the resulting heuristic is outperformed by the heuristic that simply maximizes over the three saturated cost partitioning heuristics computed separately for each heuristic type. Our new algorithm for choosing the orders in which saturated cost partitioning considers the heuristics allows us to compute heuristics outperforming not only the maximizing heuristic but even state-of-the-art planners.

The separation of planner logic from domain knowledge supports the use of reformulation and configuration techniques, such as macro-actions and entanglements, which transform the model representation in order to improve a planner's performance. One drawback of such an approach is that it may require a potentially expensive training phase. In this paper, we introduce heuristic approaches for the online configuration of planning domain models. The proposed heuristics consider different aspects of PDDL-encoded operators for reordering such operators in the domain model, relying on the assumption that the way in which operators are encoded carries useful information about their expected use.

In this paper we solve fundamental graph optimization problems like Maximum Clique and Minimum Coloring with recent advances of Monte-Carlo Search. The optimization problems are implemented as single-agent games in a generic state-space search framework, roughly comparable to what is encoded in PDDL for an action planner.

We propose an approach to solving Markov Decision Processes with non-Markovian rewards specified in Linear Temporal Logic interpreted over finite traces (LTL-f). Our approach integrates automata representations of LTL-f formulae into compiled MDPs that can be solved by off-the-shelf MDP planners, exploiting reward shaping to help guide search. Experiments with state-of-the-art UCT-based MDP planner PROST show automata-based reward shaping to be an effective method to guide search, producing solutions of superior quality, while maintaining policy optimality guarantees.

We adapt the relaxation heuristics h max , h add and h FF to interval based numeric relaxation frameworks, combining them with two different relaxation techniques and with two different search techniques. In contrast to previous approaches, the heuristics presented here are not limited to a subset of numeric planning and support action costs.

Any-angle path finding on grids is an important problem with applications in autonomous robot navigation. In this paper, we show that a well-known pre-processing technique, namely subgoal graphs, originally proposed for (non any-angle) 8-connected grids, can be straightforwardly adapted to the 2 k neighborhoods, a family of neighborhoods that allow an increasing number of movements (and angles) as k is increased. This observation yields a pathfinder that computes 2 k -optimal paths very quickly. Compared to ANYA, an optimal true any-angle planner, over a variety of benchmarks, our planner is one order of magnitude faster while being less than 0.0005% suboptimal. Important to our planner's performance was the development of an iterative 2 k heuristic, linear in k, which is also a contribution of this paper.