The probabilistic roadmap approach is one of the leading motion planning techniques. Over the past eight years the technique has been studied by many different researchers. This has led to a large number of variants of the approach, each with its own merits. It is difficult to compare the different techniques because they were tested on different types of scenes, using different underlying libraries, implemented by different people on different machines. In this paper we provide a comparative study of a number of these techniques, all implemented in a single system and run on the same test scenes and on the same computer. In particular we compare collision checking techniques, basic sampling techniques, and node adding techniques. The results should help future users of the probabilistic roadmap planning approach to choose the correct techniques.

The basic motion-planning problem is to plan a collision-free motion for an object moving among obstacles between free initial and goal positions, or to determine that no such motion exists. The basic problem as well as numerous variants of it have been intensively studied over the past two decades yielding a wealth of results and techniques, both theoretical and practical. In this paper, we propose a novel approach to motion planning, hybrid motion planning, in which we integrate complete solutions along with probabilistic roadmap (PRM) methods in order to combine their strengths and oset their weaknesses. We incorporate robust tools, that have not been available before, in order to implement the complete solutions. We exemplify our approach in the case of two discs moving among polygonal obstacles in the plane. The planner we present easily solves problems where a narrow passage in the workspace can be arbitrarily small. Our planner is also capable of providing correct nontrivial \no" answers, namely it can, for some queries, detect the situation where no solution exists. We envision our planner not as a total solution but rather as a new tool that cooperates with existing planners. We demonstrate the advantages and shortcomings of our planner with experimental results.

The probabilistic roadmap approach is a commonly used motion planning technique. A crucial ingredient of the approach is a sampling algorithm that samples the configuration space of the moving object for free configurations. Over the past decade many sampling techniques have been proposed. It is difficult to compare the different techniques because they were tested on different types of scenes, using different underlying libraries, implemented by different people on different machines. We compared 12 of such sampling techniques within a single environment on the same scenes. The results were surprising in the sense that techniques often performed differently than claimed by the designers. The study also showed how difficult it is to evaluate the quality of the techniques. The results should help users in deciding which technique is suitable for their situation.

Abstract. Although there are many motion planning techniques, there is no method that outperforms all others for all problem instances. Rather, each technique has different strengths and weaknesses which makes it best-suited for certain types of problems. Moreover, since an environment can contain vastly different regions, there may not be a single planner that will perform well in all its regions. Ideally, one would use a suite of planners in concert and would solve the problem by applying the best-suited planner in each region. In this paper, we propose an automated framework for feature-sensitive motion planning. We use a machine learning approach to characterize and partition C-space into regions that are well suited to one of the methods in our library of roadmapbased motion planners. After the best-suited method is applied in each region, the resulting region roadmaps are combined to form a roadmap of the entire planning space. Over a range of problems, we demonstrate that our simple prototype system reliably outperforms any of the planners on their own. 1

We propose a novel single-shot motion planning algorithm based on adaptive random walks. The proposed algorithm turns out to be simple to implement and the solution it produces can be easily and efficiently optimized. Furthermore the algorithm can incorporate adaptive components. So the developer is not required to specify all the parameters of the random distributions involved, and the algorithm itself can adapt to the environment it is moving in. Proofs of the theoretical soundness of the algorithm are provided as well as implementation details. Numerical comparisons with well known algorithms illustrate its effectiveness.

The probabilistic roadmap approach is one of the leading motion planning techniques. Over the past decade the technique has been studied by many different researchers. This has led to a large number of variants of the approach, each with its own merits. It is difficult to compare the different techniques because they were tested on different types of scenes, using different underlying libraries, implemented by different people on different machines. In this paper we provide a comparative study of a number of these techniques, all implemented in a single system and run on the same test scenes and on the same computer. In particular we compare collision checking techniques, sampling techniques, and node adding techniques. The results were surprising in the sense that techniques often performed differently than claimed by the designers. The study also showed how difficult it is to evaluate the quality of the techniques. The results should help future users of the probabilistic roadmap planning approach in deciding which technique is suitable for their situation. c ○ 2005 Elsevier B.V. All rights reserved.

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.

This thesis presents a novel approach to address the challenge of planning paths for real-world multi-agent systems operating in complex environments. The technique developed, the Decentralized Multi-Agent Rapidly-exploring Random Tree (DMA-RRT) algorithm, is an extension of the CL-RRT algorithm to the multi-agent case, retaining its ability to plan quickly even with complex constraints. Moreover, a merit-based token passing coordination strategy is also presented as a core component of the DMA-RRT algorithm. This coordination strategy makes use of the tree of feasible trajectories grown in the CL-RRT algorithm to dynamically update the order in which agents plan. This reordering is based on a measure of each agent’s incentive to replan and allows agents with a greater incentive to plan sooner, thus reducing the global cost and improving the team’s overall performance. An extended version of the algorithm, Cooperative DMA-RRT, is also presented to introduce cooperation