We introduce the notion of expansiveness to characterize a family of robot configuration spaces whose connectivity can be effectively captured by a roadmap of randomly-sampled milestones. The analysis of expansive configuration spaces has inspired us to develop a new randomized planning algorithm. This algorithm tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space. Thus, it is well-suited for problems where a single query is submitted for a given environment. The algorithm has been implemented and successfully applied to complex assembly maintainability problems from the automotive industry.

... This paper provides foundations for understanding the effect of passages on the connectedness of probabilistic roadmaps. It also proposes a new random sampling scheme for finding such passages. An initial roadmap is built in a "dilated" free space allowing some penetration distance of the robot into the obstacles. This roadmap is then modified by resampling around the links that do not lie in the true free space. Experiments show that this strategy allows relatively small roadmaps to reliably capture the free space connectivity

Probabilistic roadmap planning methods have been shown to perform well in a number of practical situations, but their performance degrades when paths are required to pass through narrow passages in the free space. We propose a new method of sampling the configuration space in which randomly generated configurations, free or not, are retracted onto the medial axis of the free space. We give algorithms that perform this retraction while avoiding explicit computation of the medial axis, and we show that sampling and retracting in this manner increases the number of nodes found in small volume corridors in a way that is independent of the volume of the corridor and depends only on the characteristics of the obstacles bounding it. Theoretical and experimental results are given to show that this improves performance on problems requiring traversal of narrow passages. 1

We provide an analysis of a recent path planning method which uses probabilistic roadmaps. This method has proven very successful in practice, but the theoretical un- derstanding of its performance is still limited. Assuming that a path 7 exists between two configurations a and b of the robot, we study the dependence of the failure probability to connect a and b on (i) the length of 7, (ii) the distance function of 7 from the obstacles, and (iii) the number of nodes N of the probabilistic roadmap constructed. Importantly, our results do not depend strongly on local irregularities of the configuration space, as was the case with previous analysis. These results are illustrated with a simple but illuminat- ing example. In this example, we provide estimates for N, the principal parameter of the method, in order to achieve failure probability within prescribed bounds. We also compare, through this example, the different approaches to the analysis of the planning method.

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.

This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) single-query instead of pre-computing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hi-directional it explores the robotis free space by concur- rently building a roadmap made of tvo trees rooted at the query configurations; (3) adaptive it makes longer steps in opened areas of the free space and shorter steps in cluttered areas; and (4) lazy in checking collision it delays collision tests along the edges of the roadmap until they are absolutely needed. Experimental results shov that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multi-robot problems in geometrically complex environments.

We present a randomized approach to path planning for articulated robots that have closed kinematic chains. The approach extends the probabilistic roadmap technique which has previously been applied to rigid and elastic objects, and articulated robots without closed chains. Our work provides a framework for path planning problems that must satisfy closure constraints in addition to standard collision constraints. This expands the power of the probabilistic roadmap technique to include a variety of problems such as manipulation planning using two open-chain manipulators that cooperatively grasp an object, forming a system with a closed chain, and planning for reconfigurable robots where the robot links may be rearranged in a loop to ease manipulation or locomotion. We generate the vertices in our probabilistic roadmap by sampling random con gurations that ignore kinematic closure, and by performing randomized gradient descent to force satisfaction of the closure constraints. We generate...

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

Most computational models of protein-ligand interactions consider only the energetics of the final bound state of the complex and do not examine the dynamics of the ligand as it enters the binding site. We have developed a novel approach to study the dynamics of protein-ligand interactions based on motion planning algorithms from the field of robotics. Our algorithm uses electrostatic and van der Waals potentials to compute the most energetically favorable path between any given initial and goal ligand configurations. We use probabilistic motion planning to sample the distribution of possible paths to a given goal configuration and compute an energy-based "difficulty weight" for each path. By statistically averaging this weight over several randomly generated starting configurations, we compute the relative difficulty of entering and leaving a given binding configuration. This approach yields details of the energy contours around the binding site and can be used to cha...

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.