The Grid-Based Path Planning Competition has just completed its third iteration. The entriesused in the competition have improved significantly during this time, changing the view ofthe state of the art of grid-based pathfinding. Furthermore, the entries from the competition have beenmade publicly available, improving the ability of researchers to compare their work. Thispaper summarizes the entries to the 2014 competition, presents the 2014 competition results,and talks about what has been learned and where there is room for improvement.

Paths found on grid graphs are often unrealistic looking in the continuous environment that the grid graph represents and often need to be smoothed after a search. The well-known algorithm for path smoothing is greedy in nature and does not necessarily eliminate all heading changes in freespace. We present a new path-smoothing algorithm based on “string pulling” and show experimentally that it consistently finds shorter paths than the greedy algorithm and produces paths with no heading changes in freespace.

We report on an experiment that we performed when we taught the undergraduate artificial intelligence class at the University of Southern California. We taught it – under very similar conditions – once with and once without an attendance requirement. The attendance requirement substantially increased the attendance of the students. It did not substantially affect their performance but decreased their course ratings across all categories in the official course evaluation, whose results happened to be biased toward the opinions of the students attending the lectures. For example, the overall rating of the instructor was 0.89 lower (on a 1-5 scale) with the attendance requirement and the overall rating of the class was 0.85 lower. Thus, the attendance requirement, combined with the policy for administering the course evaluation, had a large impact on the course ratings, which is a problem if the course ratings influence decisions on promotions, tenure, and salary increments for the instructors but also demonstrates the potential for the manipulation of course ratings.

In this paper, we define Jump Point Graphs (JP), a preprocessing-based path-planning technique similar to Subgoal Graphs (SG). JP allows for the first time the combination of Jump Point Search style pruning in the context of abstraction-based speedup techniques, such as Contraction Hierarchies. We compare JP with SG and its variants and report new state-of-the-art results for grid-based pathfinding.

In this paper, we define Jump Point Graphs (JP), a preprocessing-based path-planning technique similar to Subgoal Graphs (SG). JP allows for the first time the combination of Jump Point Search style pruning in the context of abstraction-based speedup techniques, such as Contraction Hierarchies. We compare JP with SG and its variants and report new state-of-the-art results for grid-based pathfinding.

Multi-Agent Motion Planning (MAMP) is the task of finding conflict-free kinodynamically feasible plans for agents from start to goal states. While MAMP is of significant practical importance, existing solvers are either incomplete, inefficient or rely on simplifying assumptions. For example, Multi-Agent Path Finding (MAPF) solvers conventionally assume discrete timesteps and rectilinear movement of agents between neighboring vertices of a graph. In this paper, we develop MAMP solvers that obviate these simplifying assumptions and yet generalize the core ideas of state-of-the-art MAPF solvers. Specifically, since different motions may take arbitrarily different durations, MAMP solvers need to efficiently reason with continuous time and arbitrary wait durations. To do so, we adapt (Enhanced) Conflict-Based Search to continuous time and develop a novel bounded-suboptimal extension of Safe Interval Path Planning, called Soft Conflict Interval Path Planning. On the theoretical side, we justify the completeness, optimality and bounded-suboptimality of our MAMP solvers. On the experimental side, we show that our MAMP solvers scale well with increasing suboptimality bounds.

Subgoal graphs can be constructed on top of graphs during a preprocessing phase to speed-up shortest path queries. They have an undominated query-time/memory trade-off in the Grid-Based Path Planning Competitions. While grids are useful for path planning, other kinds of graphs, such as state lattices, have to be used for motion planning. While state lattices are regular graphs like grids, subgoal graphs improve query times by a much smaller factor on state lattices than on grids. In this paper, we present a new version of subgoal graphs that forfeits its optimality guarantee for smaller query times. It guarantees completeness, and our experimental results on state lattices suggest that it can find paths that are close to optimal.

Contraction hierarchies and (N-level) subgoal graphs are two preprocessing-based path-planning algorithms that have so far only been compared experimentally through the grid-based path-planning competitions, where both algorithms had undominated runtime/memory trade-offs. Subgoal graphs can be considered as a framework that can be customized to different domains through the choice of a reachability relation R that identifies pairs of nodes on a graph between which it is easy to find shortest paths. Subgoal graphs can exploit R in various ways to speed-up query times and reduce memory requirements. In this paper, we break down the differences between N-level subgoal graphs and contraction hierarchies, and augment contraction hierarchies with ideas from subgoal graphs to exploit R. We propose three different modifications, analyze their runtime/memory trade-offs, and provide experimental results on grids using canonical-freespace-reachability as R, which show that both N-level subgoal graphs and contraction hierarchies are dominated in terms of the runtime/memory trade-off by some of our new variants.

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with an A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data-mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic.

Multi-agent path finding (MAPF) is well-studied in artificial intelligence, robotics, theoretical computer science and operations research. We discuss issues that arise when generalizing MAPF methods to real-world scenarios and four research directions that address them. We emphasize the importance of addressing these issues as opposed to developing faster methods for the standard formulation of the MAPF problem.

Search using subgoal graphs is a recent preprocessing-based path-planning algorithm that can find shortest paths on 8-neighbor grids several orders of magnitude faster than A*, while requiring little preprocessing time and memory overhead. In this paper, we first generalize the ideas behind subgoal graphs to a framework that can be specialized to different types of environments (represented as weighted directed graphs) through the choice of a reachability relation. Intuitively, a reachability relation identifies pairs of vertices for which a shortest path can be found quickly. A subgoal graph can then be constructed as an overlay graph that is guaranteed to have edges only between vertices that satisfy the reachability relation, which allows one to find shortest paths on the original graph quickly. In the context of this general framework, subgoal graphs on grids use freespace-reachability (originally called h-reachability) as the reachability relation, which holds for pairs of vertices if and only if their distance on the grid with blocked cells is equal to their distance on the grid without blocked cells (freespace assumption). We apply this framework to state lattices by using variants of freespace-reachability as the reachability relation. We provide preliminary results on (x,y,theta)-state lattices, which shows that subgoal graphs can be used to speed up path planning on state lattices as well, although the speed-up is not as significant as it is on grids.

The authors present an overview of a hierarchical framework for coordinating task- and motion-level operations in multirobot systems. Their framework is based on the idea of using simple temporal networks to simultaneously reason about precedence/causal constraints required for task-level coordination and simple temporal constraints required to take some kinematic constraints of robots into account. In the plan-generation phase, the framework provides a computationally scalable method for generating plans that achieve high-level tasks for groups of robots and take some of their kinematic constraints into account. In the plan-execution phase, the framework provides a method for absorbing an imperfect plan execution to avoid time-consuming re-planning in many cases. The authors use the multirobot path-planning problem as a case study to present the key ideas behind their framework for the long-term autonomy of multirobot systems.

Multi-Agent Path Finding (MAPF) with the objective to minimize the sum of the travel times of the agents along their paths is a hard combinatorial problem. Recent work has shown that bounded-suboptimal MAPF solvers, such as Enhanced Conflict-Based Search or ECBS(w1) for short, run often faster than optimal MAPF solvers at the cost of incurring a suboptimality factor w1, that is due to using focal search. Other recent work has used experience graphs to guide the search of ECBS(w1) and speed it up, at the cost of incurring a separate suboptimality factor w2, that is due to inflating the heuristic values. Thus, the combination has suboptimality factor w1w2. In this first feasibility study, we develop a bounded-suboptimal MAPF solver, Improved-ECBS or iECBS(w1) for short, that has suboptimality factor w1 rather than w1w2 (because it uses experience graphs to guide its search without inflating the heuristic values) and can run faster than ECBS(w1). We also develop two first approaches for automatically generating experience graphs for a given MAPF instance. Finally, we observe heavy-tailed behavior in the runtimes of these MAPF solvers and develop a simple rapid randomized restart strategy that can increase the success rate of iECBS(w1) within a given runtime limit.

Situated agents frequently need to solve search problems in partially known terrains in which the costs of the arcs of the search graphs can increase (but not decrease) when the agents observe new information. An example of such search problems is goal-directed navigation with the freespace assumption in partially known terrains, where agents repeatedly follow cost-minimal paths from their current locations to given goal locations. Incremental heuristic search is an approach for solving the resulting sequences of similar search problems potentially faster than with classical heuristic search, by reusing information from previous searches to speed up its current search. There are two classes of incremental heuristic search algorithms, namely those that make the \(h\)-values of the current search more informed (such as Adaptive A*) and those that reuse parts of the A* search trees of previous searches during the current search (such as D* Lite). In this article, we introduce Path-Adaptive A* and its generalization Tree-Adaptive A*. Both incremental heuristic search algorithms terminate their searches before they expand the goal state, namely when they expand a state that is on a provably cost-minimal path to the goal. Path-Adaptive A* stores a single cost-minimal path to the goal state (the reusable path), while Tree-Adaptive A* stores a set of cost-minimal paths to the goal state (the reusable tree), and is thus potentially more efficient than Path-Adaptive A* since it uses information from all previous searches and not just the last one. Tree-Adaptive A* is the first incremental heuristic search algorithm that combines the principles of both classes of incremental heuristic search algorithms. We demonstrate experimentally that both Path-Adaptive A* and Tree-Adaptive A* can be faster than Adaptive A* and D* Lite, two state-of-the-art incremental heuristic search algorithms for goal-directed navigation with the freespace assumption.

We compare five any-angle path-planning algorithms, Theta*, Block A*, Field D*, ANYA, and Any-Angle Subgoal Graphs in terms of solution quality and runtime. Any-angle path-planning is a fairly new research area, and no direct comparison exists between these algorithms. We implement each algorithm from scratch and use similar implementations to provide a fair comparison.

Simple Subgoal Graphs are constructed from grids by placing subgoals at the corners of obstacles and connecting them. They are analogous to visibility graphs for continuous terrain but have fewer edges and can be used to quickly find shortest paths on grids. The vertices of a Simple Subgoal Graph can be partitioned into different levels to create N-Level Subgoal Graphs, which can be used to find shortest paths on grids even more quickly by ignoring subgoals that are not relevant for the search, which significantly reduces the size of the graph being searched. Search using Two-Level Subgoal Graphs was a non-dominated entry in the Grid-Based Path Planning Competitions 2012 and 2013. In this paper, we take advantage of the similarities between Subgoal Graphs and visibility graphs to show that Subgoal Graphs can be used, with small modifications, to quickly find “any-angle” paths, thus extending their applicability. Any-angle paths are usually shorter and more realistic looking than grid paths since the movement along any-angle paths is not constrained to grid edges. Our algorithm has the advantage that it is a simple extension of searching Subgoal Graphs and is up to two orders of magnitude faster than Theta* and up to an order of magnitude faster than Block A* (using 5 × 5 blocks), two of the most well-known any-angle pathplanning algorithms, while still finding any-angle paths of comparable lengths.

Video-game designers often tessellate continuous 2-dimensional terrain into a grid of blocked and unblocked square cells. The three main ways to calculate short paths on such a grid are to determine truly shortest paths, shortest vertex paths and shortest grid paths, listed here in decreasing order of computation time and increasing order of resulting path length. We show that, for both vertex and grid paths on both 4-neighbor and 8-neighbor grids, placing vertices at cell corners rather than at cell centers tends to result in shorter paths. We quantify the advantage of cell corners over cell centers theoretically with tight worst-case bounds on the ratios of path lengths, and empirically on a large set of benchmark test cases. We also quantify the advantage of 8-neighbor grids over 4-neighbor grids.

A growing interest in the industrial sector for autonomous ground vehicles has prompted significant investment in fleet management systems. Such systems need to accommodate on-line externally imposed temporal and spatial requirements, and to adhere to them even in the presence of contingencies. Moreover, a fleet management system should ensure correctness, i.e., refuse to commit to requirements that cannot be satisfied. We present an approach to obtain sets of alternative execution patterns (called trajectory envelopes) which provide these guarantees. The approach relies on a constraint-based representation shared among multiple solvers, each of which progressively refines trajectory envelopes following a least commitment principle.

Search with Subgoal Graphs (Uras, Koenig, and Hernandez 2013) was a non-dominated optimal path-planning algorithm in the Grid-Based Path Planning Competitions 2012 and 2013. During a preprocessing phase, it computes a Simple Subgoal Graph from a given grid, which is analogous to a visibility graph for continuous terrain, and then partitions the vertices into global and local subgoals to obtain a Two-Level Subgoal Graph. During the path-planning phase, it performs an A* search that ignores local subgoals that are not relevant to the search, which significantly reduces the size of the graph being searched. In this paper, we generalize this partitioning process to any undirected graph and show that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further. We distinguish between basic partitioning, which only partitions the vertices into different levels, and advanced partitioning, which can also add new edges.We show that the construction of Simple-Subgoal Graphs from grids and the construction of Two-Level Subgoal Graphs from Simple Subgoal Graphs are instances of generalized partitioning. We then report on experiments on Subgoal Graphs that demonstrate the effects of different types and levels of partitioning. We also report on experiments that demonstrate that our new N-Level Subgoal Graphs achieve a speed up of 1.6 compared to Two-Level Subgoal graphs from (Uras, Koenig, and Hern´andez 2013) on maps from the video games StarCraft and Dragon Age: Origins.