this paper we consider an obstacle-based prm

This paper describes a new approach to probabilistic roadmap planners (PRMs). The overall theme of the algorithm, called Lazy PRM, is to minimize the number of collision checks performed during planning and hence minimize the running time of the planner. Our algorithm builds a roadmap in the configuration space, whose nodes are the user-defined initial and goal configurations and a number of randomly generated nodes. Neighboring nodes are connected by edges representing paths between the nodes. In contrast with PRMs, our planner initially assumes that all nodes and edges in the roadmap are collision-free, and searches the roadmap at hand for a shortest path between the initial and the goal node. The nodes and edges along the path are then checked for collision. If a collision with the obstacles occurs, the corresponding nodes and edges are removed from the roadmap. Our planner either finds a new shortest path, or first updates the roadmap with new nodes and edges, and then searches for a shortest path. The above process is repeated until a collision-free path is returned.

Figure 1: Symmetry detection on a sculpted model. From left to right: Original model, detected partial and approximate symmetries, color-coded deviations from perfect symmetry as a fraction of the bounding box diagonal. “Symmetry is a complexity-reducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and man-made objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important highlevel information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc.

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query -- instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional -- it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions -- it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results

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.

During the last three decades motion planning has emerged as a crucial and productive research area in robotics. In the mid-80's the most advanced planners were barely able to compute collisionfree paths for objects crawling in planar workspaces. Today, planners e ciently deal with robots with many degrees of freedom in complex environments. Techniques also exist to generate quasioptimal trajectories, coordinate multiple robots, deal with dynamic and kinematic constraints, and handle dynamic environments. This paper describes some of these achievements, presents new problems that have recently emerged, discusses applications likely to motivate future research, and nally gives expectations for the coming years. It stresses the fact that non-robotics applications (e.g., graphic animation, surgical planning, computational biology) are growing in importance and are likely to shape future motion planning research more than robotics itself. 1

Humanoid robotics hardware and control techniques have advanced rapidly during the last five years. Presently, several companies have announced the commercial availability of various humanoid robot prototypes. In order to improve the autonomy and overall functionality of these robots, reliable sensors, safety mechanisms, and general integrated software tools and techniques are needed. We believe that the development of practical motion planning algorithms and obstacle avoidance software for humanoid robots represents an important enabling technology. This paper gives an overview of some of our recent efforts to develop motion planning methods for humanoid robots for application tasks involving navigation, object grasping and manipulation, footstep placement, and dynamically-stable full-body motions. We show experimental results obtained by implementations running within a simulation environment as well as on actual humanoid robot hardware.

We present and implement an efficient algorithm for performing nearest-neighbor queries in topological spaces that usually arise in the context of motion planning. Our approach extends the Kd tree-based ANN algorithm, which was developed by Arya and Mount for Euclidean spaces. We argue the correctness of the algorithm and illustrate its efficiency through computed examples. We have applied the algorithm to both probabilistic roadmaps (PRMs) and Rapidly-exploring Random Trees (RRTs). Substantial performance improvements are shown for motion planning examples.

In this paper, we investigate methods for enabling a human operator and an automatic motion planner to cooperatively solve a motion planning query. Our work is motivated by our experience that automatic motion planners sometimes fail due to the difficulty of discovering `critical' configurations of the robot that are often naturally apparent to a human observer. Our goal is to develop techniques by which the automatic planner can utilize (easily generated) user-input, and determine `natural' ways to inform the user of the progress made by the motion planner. We show that simple randomized techniques inspired by probabilistic roadmap methods are quite useful for transforming approximate, usergenerated paths into collision-free paths, and describe an iterative transformation method which enables one to transform a solution for an easier version of the problem into a solution for the original problem. We also illustrate that simple visualization techniques can provide meaningful represen...

Probabilistic roadmap planners (PRMs) form a relatively new technique for motion planning that has shown great potential. A critical aspect of PRM is the probabilistic strategy used to sample the free configuration space. In this paper we present a new, sample sampling strategy, which we call the Gaussian sampler, that gives a much better coverage of the dificult parts of the free Configuration space. The approach uses only elementary operations which makes it suitable for many different planning problems. Experiments indicate that the technique is very eficient indeed. 1