Abstract: Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method – smallstep retraction – that helps PRM planners find paths through such passages. This method consists of slightly “fattening ” robot’s free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual free space. Fattened free space is not explicitly computed. Instead, the geometric models of workspace objects (robot links and/or obstacles) are “thinned ” around their medial axis. A robot configuration lies in fattened free space if the thinned objects do not collide at this configuration. Two repair strategies are proposed. The “optimist ” strategy waits until a complete path has been found in fattened free space before repairing it. Instead, the “pessimist ” strategy repairs the roadmap as it is being built. The former is usually very fast, but may fail in some pathological cases. The latter is more reliable, but not as fast. A simple combination of the two strategies yields an integrated planner that is both fast and reliable. This planner was implemented as an extension of a pre-existing single-query PRM planner. Comparative tests show that it is significantly faster (sometimes by several orders of magnitude) than the pre-existing planner. 1.

Many motion planning techniques, like the probabilistic roadmap method (PRM), generate low quality paths. In this paper, we will study a number of di#erent quality criteria on paths in particular length and clearance. We will describe a number of techniques to improve the quality of paths. These are based on a new approach to increase the path clearance. Experiments showed that the heuristics were able to generate paths of a much higher quality than previous approaches.

In this paper, we discuss the field of sampling-based motion planning. In contrast to methods that construct boundary representations of configuration space obstacles, sampling-based methods use only information from a collision detector as they search the configuration space. The simplicity of this approach, along with increases in computation power and the development of efficient collision detection algorithms, has resulted in the introduction of a number of powerful motion planning algorithms, capable of solving challenging problems with many degrees of freedom. First, we trace how samplingbased motion planning has developed. We then discuss a variety of important issues for sampling-based motion planning, including uniform and regular sampling, topological issues, and search philosophies. Finally, we address important issues regarding the role of randomization in sampling-based motion planning.

Abstract — This paper shows how to effectively combine a sampling-based method primarily designed for multiple query motion planning (Probabilistic Roadmap Method- PRM) with sampling-based tree methods primarily designed for single query motion planning (Expansive Space Trees, Rapidly-Exploring Random Trees, and others) in a novel planning framework that can be efficiently parallelized. Our planner not only achieves a smooth spectrum between multiple query and single query planning but it combines advantages of both. We present experiments which show that our planner is capable of solving problems that cannot be addressed efficiently withPRM or single-query planners. A key advantage of our planner is that it is significantly more decoupled thanPRM and sampling-based tree planners. Exploiting this property, we designed and implemented a parallel version of our planner. Our experiments show that our planner distributes well and can easily solve high-dimensional problems that exhaust resources available to single machines and cannot be addressed with existing planners. Index Terms — Motion planning, sampling-based planning, parallel algorithms, roadmap, tree, PRM, EST, RRT, SRT.

Path planning plays an important role in many computer games. Currently the motion of entities is often planned using a combination of scripting, grid-search methods, and reactive approaches. In this paper we describe a new approach, based on a technique from robotics, that computes a roadmap of smooth, collision-free, high-quality paths. This roadmap can be used to obtain instantly good paths for entities. We also describe applications of the technique for planning the motion of groups of entities and for creating smooth camera movements through an environment.

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subcontract No. B4U528968 and prime contract No. W911W6-04-C-0058 with the US Army. The views and conclusions contained herein are those of the author, and do not necessarily reflect the position or policy of the sponsoring institutions, and no official endorsement should be inferred. Keywords: Robotics, Robot Navigation, Motion Planning, Path Planning, Multi-Robot

The decades of research in motion planning have resulted in numerous algorithms. Many of the most successful algorithms are randomized and can have widely differing run-times for the same problem instance from run to run. While this property is known to be undesirable from user’s point of view, it has been largely ignored in past research. This paper introduces the large run-cost variance of randomized motion planners as a distinct issue to be addressed in future research. Run-cost variance is an important performance characteristic of an algorithm that should be studied together with the mean run-cost. As a positive example of possibilities for reducing the run-cost variance of a randomized motion planner, simple heuristic techniques are introduced and investigated empirically. 1.

One of the fundamental tasks robots have to perform is planning their motions while avoiding collisions with obstacles in the environment. This is the central topic of the thesis. We restrict ourselves to motion planning for two- and three-dimensional rigid bodies and articulated robots moving in static and known virtual environments. This thesis has been divided into two parts. The first part deals with comparing and analyzing sampling-based motion planning techniques, in particular variants of the Probabilistic Roadmap Method (PRM). The PRM consists of two phases: a construction and a query phase. In the construction phase, a roadmap (graph) is built, approximating the motions that can be made in the environment. First, a free random sample is created. Such a sample describes a particular placement of the moving object (robot) in the workspace. Then, a simple local planner is employed to connect the sample to some neighbors. Samples and connections are added to the graph until the roadmap is dense enough. In the query phase, the start and goal samples are connected to the graph. The path is obtained by a Dijkstra's shortest path algorithm. Many variants of the PRM have been developed over the past decade. Using both time-based as well as reachability-based analysis, we compare some of the most prominent techniques. The results are surprising in the sense that techniques often perform differently than claimed by the designers. In addition, contrary to general belief, the main challenge is not getting the free space covered but getting the nodes connected, especially when the problems get more complicated, e.g. when a narrow passage is present. By using this knowledge, we can tackle the narrow passage problem by incorporating a more powerful local planner, a refined neighbor selection strategy and a hybrid sampling strategy. The analysis also shows why the PRM successfully deals with many motion planning problems. The second part deals with quality aspects of paths and roadmaps. A good path is relatively short, keeps some distance (clearance) from the obstacles, and is smooth. We will provide algorithms that increase path clearance. A big advantage of these algorithms is that high-clearance paths can now be efficiently created without using complex data structures and algorithms. We also elaborate on algorithms that successfully decrease path length. Then, we introduce the Reachability Roadmap Method which creates small roadmaps for two- and three-dimensional problems. Such a small roadmap has many advantages over a roadmap that is created by the PRM. In particular, the method assures low query times, low memory consumption, and the roadmap can be optimized easily. The algorithm also ensures that a path is always found (if one exists) at a given resolution. We unify the techniques to create high-quality roadmaps for interactive virtual environments. That is, we use the Reachability Roadmap Method to create an initial roadmap. We add useful cycles to provide alternative routes and short paths, and we add clearance to the roadmap to obtain high-clearance paths in real-time.

Path planning plays an important role in many virtual worlds, like computer games. Currently the motion of entities is often planned using a combination of scripting, grid-search methods, local reactive methods, flocking and crowd behavior. In this paper we describe a new approach, based on a technique from robotics, that computes a roadmap of smooth, collision-free, high-quality paths. This roadmap can be used to obtain instantly good paths for entities. We also describe applications of the technique for planning the motion of groups of entities and for creating smooth camera movements through an environment. 1