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.

Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: space-time volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., space-time volume intersection is particularly suited to a CSG representation), others do not. The multiple interference detection approach has been the most widely used under a variety of sampling strategies, reducing the collision detection problem to multiple calls to static interference tests. In most cases, these tests boil down to detecting intersections between simple geometric entities, such as spheres, boxes aligned with the coordinate axes, or polygons and segments. The computational cost of a collision detection algorithm depends not only on the complexity of the basic interference test used, but also on the ...

Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot' s configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilistically complete: if a path exists, they will find one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characterizing the "goodness" of the robot's free space, we show that the running time only grows as the absolute value of the logarithm of the probability of failure that we are willing to tolerate. We also show that it increases at a reasonable rate as the space goodness degrades. In the last section we suggest directions for future research.

solid models

A complete, precise, and systematic analysis on the geometrical nature of contacts between two arbitrary polygons and derivation of the geometric contact constraints between two such polygons are provided. Based on the results, a general algorithm is presented to identify the geometrically valid contact formations (CFs) from a given set S pc of possible principal contacts (PCs) between two polygonal objects with location uncertainties. For any (non-empty) subset of S pc , the algorithm tests if the PCs in the set form a possible CF by verifying the geometrical contact constraints. The obtained set of geometrically valid CFs can serve as input to an additional verifier based on force sensing which can extract the actual CF from the set. The notion of equivalent CFs is introduced to describe those contact situations constraining the relative location between two objects to the same region. This concept proves to be extremely useful to the completeness of the analysis and efficiency of th...

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An implemented algorithm is presented for finding all principal contacts possibly established between two surface features (i.e., faces, edges, or vertices) of two polyhedral objects due to location (i.e., position and orientation) uncertainties. The algorithm FAPRIC (for Finding All PRIncipal Contacts) requires as inputs: the estimated locations of the two objects, the geometric models of the objects, and the bounds on position and orientation uncertainties. The algorithm is based on checking intersections between the grown regions of the objects by location uncertainties [12] with the S-tope model [5]. It is very efficient and apt for real-time processing. The information obtained can serve as a guide for more accurate extraction and further reasoning of the contact data, possibly with additional sensors. As the surface of an arbitrary object can be approximated by planar patches, the algorithm can also be applied to general objects. The work is motivated by the need for automaticall...

This paper investigates the partition of the configuration space induced by basic contacts between polyhedra, using their combinatorial interpretation in terms of oriented matroids. It is shown that solving motion planning problems using this cellular decomposition can be analytically expressed in terms of invariants, without explicit use of artificial coordinate frames. One ofthe main aims of this paper is to draw the attention of the reader to some results from the Theory of Matroids which are directly applicable to path planning, and many other geometric problems arising in Robotics. In particular, the relevance of the concept of mutation in the context of collision-free path planning is highlighted. Moreover, it is proved that the set of mutations contains the walls of a given cell in configuration space, and that this set, as one moves from one cell to a neighbor one, can be updated in linear time with the number of vertices. This provides a simple way to detect a large amount of redundant constraints from purely combinatorial considerations, without relying on the manipulation of algebraic equations.

This paper presents fast algorithms for penetration and contact determination between general polyhedral models in dynamic environments. The main contribution is an extension of an earlier expected constant time algorithm between convex polytopes to detect penetrations and contacts. For each pair of non-convex polyhedral models, the algorithm uses the convex hull of each object to determine which regions of the objects are colliding. After identifying these regions, it uses a new dynamic technique, sweep and prune, to overcome the bottleneck of O(n 2 ) pairwise feature checks of these regions. The resulting algorithm has been implemented and in practice its performance in dynamic environments is O(n +m), where m corresponds to the number of feature pairs close to each other. 1 Introduction The problem of determining whether objects are penetrating or separated is of great importance in many areas. It has been extensively studied in robotics, molecular-based modeling, computational ...

Autonomous path planning addresses the problem of nding collision-free paths for moving objects { robots { among obstacles. In this paper we consider robots operating in workspaces occupied by stationary, completely known obstacles. We describe 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. Our algorithm builds a roadmap in the conguration space, whose nodes are the user-dened initial and goal congurations and a number of randomly generated congurations. Neighboring nodes are connected by edges representing the straight line path 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 th...