In this paper we consider the motion planning problem for arbitrary articulated structures with one or more closed kinematic chains in a workspace with obstacles. This is an important class of problems and there are applications in many areas such as robotics, closed molecular chains, graphical animation, reconfigurable robots. We use the kinematics-based probabilistic roadmap (kbprm) strategy proposed in [7] that conceptually partitions the linkage into a set of open chains and applies random generation methods to some of the chains and traditional inverse kinematics methods to the others. The efficiency of the method depends critically on how the linkage is partitioned into open chains, and the original method assumed the partition was provided as input to the problem. In this paper, we propose a fully automated method for partitioning an arbitrary linkage into open chains and for determining which should be positioned using the inverse kinematic solver. Even so, the size (number of links) of the closed loops that can be handled by this method is limited because the inverse solver can only be applied to small chains. To handle high dof closed loops, we show how we can use the Iterative Relaxation of Constraints (IRC) strategy [3] to efficiently handle large loops while still only using inverse kinematics for small chains. Our results in 3-dimensional workspace both for planar and spatial linkages show that our framework performs well for general linkage. We also use our planner to simulate an adjustable lamp called Luxo. Using IRC, our planner can handle a single loop of up to 44 links.

Probabilistic roadmap planners have been very successful in path planning for a wide variety of problems, especially applications involving robots with many degrees of freedom. These planners randomly sample the configuration space, building up a roadmap that connects the samples. A major problem is finding valid configurations in tight areas, and many methods have been proposed to more effectively sample these regions. By constructing a skeleton-like subset of the free regions of the workspace, these heuristics can be strengthened. The skeleton provides a concise description of the workspace topology and an efficient means of finding points with maximal clearance from the obstacles. We examine the medial axis as a skeleton, including a method to compute an approximation to it. The medial axis is a twoequidistant surface in the workspace. We form a heuristic for finding difficult configurations using the medial axis, and demonstrate its effectiveness in a planner for rigid objects in a three dimensional workspace.

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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

Closed kinematic chains in mechanical systems represent a challenge for their motion analysis, and therefore, for path planning. Closed mechanisms appear in dierent areas where path planning algorithms are applied. We propose a method to handle them within Probabilistic RoadMap (PRM) techniques. This method is an extension of the approach proposed in [5]. Our main contribution concerns the generation of random con gurations. The structure of the mechanism is analyzed in a preprocessing step. Then, in the roadmap construction phase, an algorithm called Random Loop Generator uses data from this analysis. This algorithm increases the probability of randomly generating valid con gurations of the closed mechanism. Experimental results demonstrate the eciency of the approach.

Probabilistic roadmap planners have been used with success to plan paths for flexible objects such as metallic plates or plastic flexible pipes. This paper improves the performance of these planners by using the medial axis of the workspace to guide the random sampling. At a preprocessing stage, the medial axis of the workspace is computed using a recent efficient algorithm. Then the flexible object is fitted at random points along the medial axis. The energy of all generated configurations is minimized and the planner proceeds to connect them with low-energy quasi-static paths in a roadmap that captures the connectivity of the free space. Given an initial and a final configuration, the planner connects these to the roadmap and searches the roadmap for a path. Our experimental results show that the new sampling scheme is successful in identifying critical deformations of the object along solution paths which results in a significant reduction of the computation time. Our work on planning for flexible objects has applications in industrial settings, virtual reality environments, and medicine.

We present a novel approach for studying the kinetics of protein folding. The framework has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMS) that have been applied in many diverse fields with great success. In our previous work, we used a PRMbased technique to study protein folding pathways of several small proteins and obtained encouraging results. In this paper, we describe how our motion planning framework can be used to study protein folding kinetics. In particular, we present a refined version of our PRM-based framework and describe how it can be used to produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap which is computed in a few hours on a desktop PC. Results are presented for 14 proteins. Our ability to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics, such as proteins that exhibit both two-state and three-state kinetics, that are not captured by other theoretical techniques. 1.

We present an algorithm for computing stable collision-free motions for humanoid robots given fullbody posture goals. The motion planner is part of a simulation environment under development for providing high-level software control for humanoid robots. Given a robot's internal model of the environment and a statically-stable desired posture, we use a randomized path planner to search the configuration space of the robot for a collision-free path. Balance constraints are imposed on incremental search motions in order to maintain the overall dynamic stability of the computed trajectories. The algorithm is presented along with preliminary results using an experimental implementation on a dynamic model of the H5 humanoid robot.

We present an approach to path planning for humanoid robots that computes dynamically-stable, collision-free trajectories from full-body posture goals. Given a geometric model of the environment and a statically-stable desired posture, we search the configuration space of the robot for a collision-free path that simultaneously satisfies dynamic balance constraints. We adapt existing randomized path planning techniques by imposing balance constraints on incremental search motions in order to maintain the overall dynamic stability of the final path. A dynamics filtering function that constrains the ZMP (zero moment point) trajectory is used as a post-processing step to transform statically-stable, collision-free paths into dynamically-stable, collision-free trajectories for the entire body. Although we have focused our experiments on biped robots with a humanoid shape, the method generally applies to any robot subject to balance constraints (legged or not). The algorithm is presented along with computed examples using the humanoid robot "H6".

In this paper, we propose a new approach for building and querying probabilistic roadmaps. In the roadmap construction stage, we build coarse roadmaps by performing only an approximate validation of the roadmap nodes and/or edges. In the query stage, the roadmap is validated and refined only in the area of interest for the query, and moreover, is customized in accordance with any specified query preferences. This approach, which postpones some of the validation checks (e.g., collision checks) to the query phase, yields more ecient solutions to many problems. An important benefit of our approach is that it gives one the ability to customize the same roadmap in accordance with multiple, variable, query preferences. For example, our approach enables one to find a path which maintains a particular clearance, or makes at most some specified number of sharp turns. Our preliminary results on problems drawn from diverse application domains show that this new approach dramatically improves performan...