We present three new ideas for grid-based path-planning algorithms that improve the search speed and quality of the paths found. First, we introduce a new type of database, the Local Distance Database (LDDB), that contains distances between boundary points of a local neighborhood. Second, an LDDB-based algorithm is introduced, called Block A*, that calculates the optimal path between start and goal locations given the local distances stored in the LDDB. Third, our experimental results for any-angle path planning in a wide varietyof test domains, including real game maps, show that Block A* is faster than both A* and the previously best grid-based any-angle search algorithm, Theta*.

This paper presents an approach to differentially constrained robot motion planning and efficient re-planning. Satisfaction of differential constraints is guaranteed by the search space which consists of motions that satisfy the constraints by construction. Any systematic replanning algorithm, e.g. D*, can be utilized to search the state lattice to find a motion plan that satisfies the differential constraints, and to repair it efficiently in the event of a change in the environment. Further efficiency is obtained by varying the fidelity of representation of the planning problem. High fidelity is utilized where it matters most, while it is lowered in the areas that do not affect the quality of the plan significantly. The paper presents a method of modifying the fidelity between replans, thereby enabling dynamic flexibility of the search space, while maintaining its compatibility with replanning algorithms. The approach is especially suited for mobile robotics applications in unknown challenging environments. We successfully applied the motion planner on a real robot: the planner featured 10Hz average replan rate on minimal computing hardware, while satisfying the car-like differential constraints.

In a number of graph search-based planning problems, the value of the cost function that is being minimized also affects the set of possible actions at some or all the states in the graph. In such planning problems, the cost function typically becomes one of the state variables thereby increasing the dimensionality of the planning problem, and consequently the size of the graph that represents the problem. In this paper, we show how to avoid this increase in the dimensionality for weighted search (with bounded suboptimality) whenever the availability of the actions is monotonically non-increasing with the increase in the cost function.

Multi-robot path planning is abstracted as the problem of computing a set of non-colliding paths on a graph for multiple robots. A naive search of the composite search space, although complete, has exponential complexity and becomes computationally prohibitive for problems with just a few robots. This work proposes an efficient and complete algorithm for solving a general class of multi-robot path planning problems, specifically those where there are at most n-2 robots in a connected graph of n vertices. The algorithm employs two primitives: a "push" operation where a robot moves toward its goal until no further progress can be made, and a "swap" operation that allows two robots to swap positions without altering the configuration of any other robot. Simulated experiments compare the proposed approach with several other centralized and decoupled planners, and show that the proposed technique has highly competitive computation time and easily scales to problems involving 100s of robots, solving them in under 5 seconds.

Path planning quickly becomes computationally hard as the dimensionality of the state-space increases. In this paper, we present a planning algorithm intended to speed up path planning for high-dimensional state-spaces such as robotic arms. The idea behind this work is that while planning in a high-dimensional state-space is often necessary to ensure the feasibilityof the resulting path, large portions of the path have a lower-dimensional structure. Based on this observation, our algorithm iteratively constructs a state-space of an adaptive dimensionality--a state-space that is high-dimensional only where the higher dimensionality is absolutely necessary for finding a feasible path. This often reduces drastically the size of the state-space, and as a result, the planning time and memory requirements. Analytically, we show that our method is complete and is guaranteed to find a solution if one exists, within a specified suboptimality bound. Experimentally, we apply the approach to 3D vehicle navigation (x, y, heading), and to a 7 DOF robotic arm on the Willow Garage’s PR2 robot. The results from our experiments suggest that ourmethod can be substantially faster than some of the state-of-the-art planning algorithms optimized for those tasks.

Complexity analysis of planning is problematic. Even very simple planning languages are PSPACE-complete, yet cannot model many simple problems naturally. Many languages with much more powerful features are also PSPACE-complete. It is thus difficult to separate planning languages in a useful way and to get complexity figures that better reflect reality. This paper introduces new methods for complexity analysis of planning and similar combinatorial search problems, in order to achieve more precision and complexity separations than standard methods allow. Padding instances with the solution size yields a complexity measure that is immune to this factor and reveals other causes of hardness, that are otherwise hidden. Further combining this method with limited non-determinism improves the precision, making even finer separations possible. We demonstrate with examples how these methods can narrow the gap between theory and practice.

Rapidly-exploring random trees (RRTs) are data structures and search algorithms designed to be used in continuous path planning problems. They are one of the most successful state-of-the-art techniques as they offer a great degree of flexibility and reliability. However, their use in other search domains has not been thoroughly analyzed. In this work we propose the use of RRTs as a search algorithm for automated planning. We analyze the advantages that this approach has over previously used search algorithms and the challenges of adapting RRTs for implicit and discrete search spaces.

Many known planning tasks have inherent constraints concerning the best order in which to achieve the goals. A number of research efforts have been made to detect such constraints and to use them for guiding search, in the hope of speeding up the planning process. We go beyond the previous approaches by considering ordering constraints not only over the (top-level) goals, but also over the sub-goals that will necessarily arise during planning. Landmarks are facts that must be true at some point in every valid solution plan. We extend Koehler and Hoffmann's definition of reasonable orders between top level goals to the more general case of landmarks. We show how landmarks can be found, how their reasonable orders can be approximated, and how this information can be used to decompose a given planning task into several smaller sub-tasks. Our methodology is completely domain- and planner-independent. The implementation demonstrates that the approach can yield significant runtime performance improvements when used as a control loop around state-of-the-art sub-optimal planning systems, as exemplified by FF and LPG.

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.

This paper reports the outcome of the third in the series of biennial international planning competitions, held in association with the International Conference on AI Planning and Scheduling (AIPS) in 2002. In addition to describing the domains, the planners and the objectives of the competition, the paper includes analysis of the results. The results are analysed from several perspectives, in order to address the questions of comparative performance between planners, comparative difficulty of domains, the degree of agreement between planners about the relative difficulty of individual problem instances and the question of how well planners scale relative to one another over increasingly difficult problems. The paper addresses these questions through statistical analysis of the raw results of the competition, in order to determine which results can be considered to be adequately supported by the data. The paper concludes with a discussion of some challenges for the future of the competition series.