Landmarks, Critical Paths and Abstractions: What\u27s the Difference Anyway?

Current heuristic estimators for classical domain-independent planning are usually based on one of four ideas: delete relaxation, abstraction, critical paths, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. In my talk, I will show that these heuristics are in fact very closely related. Moreover, I will introduce a new admissible heuristic called the landmark cut heuristic which exploits this relationship. In our experiments, the landmark cut heuristic provides better estimates than other current admissible planning heuristics, especially on large problem instances

Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.Comment: 8 pages, 11 figures. Videos available at https://www.youtube.com/watch?v=d7dX5MvDYTc and https://www.youtube.com/watch?v=nsl-5MZfwu

Error Analysis and Correction for Weighted A*'s Suboptimality (Extended Version)

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the correction frequently eliminates much of the error.Comment: Published as a short paper in the 12th Annual Symposium on Combinatorial Search, SoCS 201

Planning as Tabled Logic Programming

This paper describes Picat's planner, its implementation, and planning models for several domains used in International Planning Competition (IPC) 2014. Picat's planner is implemented by use of tabling. During search, every state encountered is tabled, and tabled states are used to effectively perform resource-bounded search. In Picat, structured data can be used to avoid enumerating all possible permutations of objects, and term sharing is used to avoid duplication of common state data. This paper presents several modeling techniques through the example models, ranging from designing state representations to facilitate data sharing and symmetry breaking, encoding actions with operations for efficient precondition checking and state updating, to incorporating domain knowledge and heuristics. Broadly, this paper demonstrates the effectiveness of tabled logic programming for planning, and argues the importance of modeling despite recent significant progress in domain-independent PDDL planners.Comment: 27 pages in TPLP 201

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization