D. HSU, L. E. KAVRAKI, J.-C. LATOMBE, R. MOTWANI, and S. SORKIN: On nding narrow passages with probabilistic roadmap planners. P. Agarwal, editor, Robotics: The Algorithmic Perspective, A.K. Peters, Wellesley, MA, 1998, 141 154.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... which connect to guards and bring together two or more connected components of the roadmap [43] Creating nodes in narrow passages has been the main motivation of the enhancement step in [25] the generation of nodes near the con guration space obstacles in [1] the penetration of obstacles in [21], the Gaussian sampling in [8] the retraction to the con guration space medial axis in [50] and the use of the workspace medial axis in [20] and [39] It is dif cult to compare random sampling to deterministic sampling for each variation of the PRM. We speculate that randomization appearing in ....

....by using low resolution sampling. These bene ts are independent of the issue of randomization versus determinism. We note that other researchers have argued that the PRM sampling method must appropriately adapt to the diculty of the problem, as opposed to attempting a uniform covering (e.g. [21], 43] We are in agreement with this idea, independently of whether samples are random or deterministic. The second reason (defeating an opponent) might be valid in the case of true random numbers; however, any machine implementation generates a deterministic sequence of pseudo random ....

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D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In et al. P. Agarwal, editor, Robotics: The Algorithmic Perspective, pages 141-154. A.K. Peters, Wellesley, MA, 1998.

....please note that some of the prior authors called it instead goodness) 1. 1 Probabilistic Roadmap Planners The visibility assumption, in particular, has been used in the analysis of randomized placements of points in the robot s con guration space for probabilistic roadmap (PRM) planners [1, 2]. A classic PRM planner [3, 4] randomly picks in the free space of the robot s con guration space a set of points, called milestones. With these milestones, it constructs a roadmap by connecting each pair of milestones between which a collision free path can be computed using a simple local ....

Hsu, D., Kavraki, L., Latombe, J.C., Motwari, R., Sorkin, S.: On nding narrow passages with probabilistic roadmap planners. In: Proceedings of the 3rd Workshop on Algorithmic Foundations of Robotics. (1998)

....of dof can be reduced to ve using symmetry arguments. Both foldings require some intelligence: the aps have to be folded in the proper order in order to reach the nal folded state. Thus, these problems are not trivial, and in fact, correspond to what is known as the narrow passage problem [26], which is thought to be the last major challenge for path planning of rigid bodies in static environments. The protein (a peptide chain) is a small amino acid chain that consists of ten Alanine amino acids, corresponding to 20 degrees of freedom. It folds from its extended (straight) ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998. 14

....phase; this graph is exploited as a roadmap to ef ciently answer subsequent path queries [13, 19, 1] Currently, probabilistic roadmap methods are very popular. However, they su er a major di culty in dealing with narrow passages o ering minimal visibility between connected components of Cfree [11]. Furthermore, the expensive preprocessing phase is only amortized if multiple planning queries are made in the same workspace. On the other hand, probabilistic potential eld methods such as RPP are often quite inecient in dealing with local minima which unavoidably arise in the potential eld. ....

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Workshop on the Algorithmic Foundations of Robotics, Houston, TX, 1998.

....nodes lie near to each other but no connection has been found between them. One can increase the number of samples in such areas. Another approach is to place addition samples near to edges and vertices of obstacles[1, 26] or to allow for samples inside obstacles and pushing them to the outside[30, 12]. Such methods though require more complicated geometric operations on the obstacles. An approach that avoids such geometric computations is the Gaussian sampling technique[7] The approach works as follows. Rather than one sample we take two samples where the distance between the two samples is ....

D. Hsu, L. Kavraki, J.C. Latombe, R. Motwani, S. Sorkin, On nding narrow passages with probabilistic roadmap planners, in: P.K. Agarwal, L.E. Kavraki, M.T. Mason (eds.), Robotics: The algorithmic perspective, A.K. Peters, Natick, 1998, pp. 141-154.

....of this space warrants randomized methods. However, a completely randomized approach would be ine ective since many important con gurations for the disassembly sequence will involve closely packed parts, i.e. the disassembly sequence will pass through narrow passages in the C space [15]. Our approach to the disassembly problem involves biasing the sampling based on the geometric characteristics of con gurations known to be reachable from the assembled con guration (the start) In particular, information based on the relative positions of the parts in one con guration is used to ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

....corridors, then the attraction sequence will be longer and each A i will be smaller. Our analysis indicates that the planning performance will signi cantly degrade in this case, which is consistent with analysis results obtained for randomized Rapidly Exploring Random Trees 7 holonomic planners [17]. Note that for kinodynamic planning, the choice of metric, can also greatly affect the attraction sequence, and ultimately the performance of the algorithm. Using to represent measure, let p be de ned as p = min i f (A i ) X free )g; which corresponds to a lower bound on the ....

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In et al. P. Agarwal, editor, Robotics: The Algorithmic Perspective, pages 141-154. A.K. Peters, Wellesley, MA, 1998.

....standard deviations (STDs) we use are f5 , 10 , 20 , 40 , 80 , 160 g. The small STDs capture the detail around the goal, and the larger STDs ensure adequate roadmap coverage of the conformation space. Similar biased sampling strategies have been applied successfully in robotics applications [2, 7, 16, 18, 20, 25, 41], where oversampling in and near narrow 1 We would like to remind the readers that the focus of the work presented here is not to predict native folds, but rather to study folding pathways and potential funnels leading to a known native fold. passages in C space is crucial for some problems. Our ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

....sampling will likely result in many con gurations there. In the connection phase, connections between con gurations can be made which correspond to a reasonable representation of the connectivity of the free space. Figure 10 and Figure 11 each give an example of the narrow passage problem [13, 35, 59, 67, 68]. In Figure 10, a two dimensional space is shown. All white areas are collision free for the point robot while all dark areas represent collision with either an obstacle or the workspace boundary. Random sampling in this workspace will easily discover the two large white areas. However, it is ....

....is used to retract randomly generated nodes to the medial axis using known properties of the generalized Voronoi diagram. This is done without 24 having to calculate the axis itself. This work, although preliminary, is appealing due to its strong theoretical foundation. 4. Dilated Space In [35], the free space is dilated during rst phase node generation and then in a second phase, nodes in the dilated free space but not in the real free space are pushed towards free space. Although this method widens narrow corridors so they are probabilistically more likely to be discovered by random ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin, \On nding narrow passages with probabilistic roadmap planners," in Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

....same time, these new applications served to point out some weaknesses in the prm approach. In particular, it was observed that there were some classes of problems for which prms did not yield ecient solutions. For example, problems where the solution path must traverse narrow passages in C space [12]. As a result, a number of prm variants speci cally targeted at this problem have been proposed, e.g. 1, 6, 12] Also, some novel approaches for improving prm eciency have shown promising results [5, 20] these methods do not address the narrow passage problem) Unfortunately, however, prm ....

....it was observed that there were some classes of problems for which prms did not yield ecient solutions. For example, problems where the solution path must traverse narrow passages in C space [12] As a result, a number of prm variants speci cally targeted at this problem have been proposed, e.g. [1, 6, 12]. Also, some novel approaches for improving prm eciency have shown promising results [5, 20] these methods do not address the narrow passage problem) Unfortunately, however, prm solutions to many problems still take prohibitively long. Another shortcoming of prms is that while they are very ....

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D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

....Two of these were studied in [29] where in one case their approach failed to generate a con guration in the binding site. While our results are very encouraging, a fully automated approach su ers from the known 1 problems of prms. The most signi cant of which is the narrow passage problem [8], so called because it is dicult for the planner to sample important con gurations in a narrow C space region. In molecular docking, the narrow passage becomes a passage through high potential areas. Another challenge with prms is that it is hard for the user to visualize and understand the ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

....and convergence was not dependent on dimension. There are interesting parallels between later developments of specialized random sampling methods that improve performance for sharply peaked integrands [13, 14, 18] and the recent development of specialized sampling methods for path planning [1, 6, 11]. In practice, random sampling methods require the construction of deterministic, pseudo random samples. Thus, researchers began to question whether other deterministic samples could be designed which lead to better performance in numerical methods. The design of a good set of samples can be ....

....dicult to nd at random. Indeed, several planners have been developed to address this issue. Creating nodes in narrow passages has been the main motivation of the enhancement step in [15] the generation of nodes near the con guration space obstacles in [2] the penetration of obstacles in [11], the Gaussian sampling in [5] the retraction to the con guration space medial axis in [2] and the use of the workspace medial axis in [10] and [23] 3.2 Q PRM Overview Monte Carlo methods, like PRM and its uniform random sampling cousins for integration and optimization, have been adopted for ....

[Article contains additional citation context not shown here]

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In et al. P. Agarwal, editor, Robotics: The Algorithmic Perspective, pages 141-154. A.K. Peters, Wellesley, MA, 1998.

....models: a box and a periscope. The periscope has 11 degrees of freedom (11 joints) and the box has 12. However, for the box, the number of dof can be reduced to ve using symmetry arguments. Both foldings are non trivial, and in fact, correspond to what is known as narrow passage problems [19], which are thought to be the last major challenge for path planning of rigid bodies in static environments. We present results for two small proteins. Protein GB1 has 56 residues (112 dof) and consists of one alpha helix and two beta sheets. Its structure has been determined by both NMR and ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

.... of freedom (dof) 12] 16] For this reason, attention has focused on randomized methods, such as randomized potential eld methods (e.g. 5] Recently, a class of randomized motion planning methods, called probabilistic roadmap methods (prms) has gained much attention (see, e.g. 1] 4] [11], 14] 22] These methods use randomization during preprocessing to construct a graph in C space (a roadmap) Queries are processed by connecting the initial and goal con gurations to the roadmap, and then nding a path in the roadmap between these two connection points. prms have been shown to ....

.... objects in cluttered three dimensional workspaces typical, e.g. of virtual prototyping applications such as maintainability studies in mechanical CAD designs [7] Such applications present dicult motion planning problems which typically require navigating narrow passages in the con guration space [11]. We believe such problems are amenable to solution by prms but this will require a ne tuning of every prm component, including primitive operations such as distance computations and local planners. II. Distance Metrics Distance metrics are used in prms to determine which nodes one should ....

D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

....uniform random sampling is used to generate free nodes along with a 5 post connection roadmap enhancement heuristic designed improve connectivity of the roadmap. Intuitively, narrow corridors in con guration space may be characterized by their large surface area to volume ratio. The methods in [19] have exploited this idea. In [1, 5] nodes are sampled from the contact space, the set of con gurations for which the workpiece is in contact but not collision with an obstacle. In [19] preliminary con gurations are generated by allowing the workpiece to penetrate the obstacles by a small ....

....corridors in con guration space may be characterized by their large surface area to volume ratio. The methods in [19] have exploited this idea. In [1, 5] nodes are sampled from the contact space, the set of con gurations for which the workpiece is in contact but not collision with an obstacle. In [19], preliminary con gurations are generated by allowing the workpiece to penetrate the obstacles by a small amount. The areas near these nodes are then re sampled to nd nearby collision free con gurations. The idea is that the allowed penetration dilates the free space by a small amount (albeit not ....

[Article contains additional citation context not shown here]

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin, On nding narrow passages with probabilistic roadmap planners, in Proc. Int. Workshop on Algorithmic Foundations of Robotics, P. K. Agarwal, L. E. Kavraki, and M. T. Mason, eds., A. K. Peters, Wellesley, MA, 1998, pp. 141-153.

....case, it might be preferable to allow any value for orientation, which generates a cylinder. Another reasonable alternative is to de ne rectangular neighborhoods, as opposed to spheres. Our method is expected to su er, along with other randomized planning methods, from the narrow passage problem [6]. Although our algorithm converges in volume to a covering of C free , it does not indicate the probability that the topology of B will follow the topology of C free . Randomized path planning techniques, such as probabilistic roadmaps [10] rapidly exploring random trees [15, 14] or even random ....

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In et al. P. Agarwal, editor, Robotics: The Algorithmic Perspective, pages 141-154. A.K. Peters, Wellesley, MA, 1998.

....have resulted in the successful application of these techniques to diverse domains, such as assembly planning, virtual prototyping, drug design, and computer animation. Much of the progress can be attributed to the introduction of probabilistic roadmap techniques [9] and their various extensions [1, 2, 7, 8, 15]. Despite these advances, however, some areas of application have still remained out of reach for automated planning algorithms. Applications requiring robots with many degrees of freedom to operate in highly dynamic and unpredictably changing environments fall into that category. To operate ....

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Workshop on the Alg. Found. of Robotics, pages 141-154. A K Peters, 1998.

....have resulted in the successful application of these techniques to diverse domains, such as assembly planning, virtual prototyping, drug design, and computer animation. Much of the progress can be attributed to the introduction of probabilistic roadmap techniques [8] and their various extentions [1, 2, 6, 7, 11, 13]. Despite these advances, however, some areas of application have still remained out of reach for automated planning algorithms. Applications requiring robots with many degrees of freedom to operate in highly dynamic and unpredictably changing environments fall into that category. To operate ....

David Hsu, Lydia E. Kavraki, Jean-Claude Latombe, Rajeev Motwani, and Stephen Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. of the Workshop on the Algorithmic Foundations of Robotics, pages 141-154. A K Peters, 1998.

....a local planner succeeds, the corresponding edge is inserted in the roadmap. This random exploration of the C space is often accompanied by a heuristic that adds extra nodes in dicult regions of the C space, to improve the performance in cases where the solution path goes through narrow passages [4, 8, 14]. Individual planning queries are solved by adding the start and goal con guration as nodes in the roadmap and then using graph search to nd a path connecting these nodes. The application of the PRM framework to manipulation planning was possible because of the introduction of fuzzy roadmaps. ....

D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. of the Workshop on Algorithmic Foundations of Robotics, March 1998.

....increase performance. We propose two simple variations of Lazy PRM for the cases of more cluttered con guration spaces and faster collision checking than in typical industrial applications. These cases are handled to a certain extent, but neither these cases nor the narrow passage problem (see [2, 8, 18]) are our main objectives. This paper extends the results presented in [7] and [6] Related ideas about lazy evaluation has been developed concurrently and independently in [37] Lazy PRM is described in detail in Section 3. Its performance is theoretically analyzed in Section 4, and ....

....of the roadmap, basic PRM still has weaknesses in nding paths through narrow passages in F . Several recent approaches are intended to improve basic PRM in this respect by using di erent sampling strategies. The underlying idea is to distribute nodes close to the boundary of F . The planner in [18] initially allows the robot to penetrate the obstacles to a certain extent. Small neighborhoods around the con gurations just in collision are then re sampled in order to place nodes close to the boundary of F . The Obstacle Based PRM (OBPRM) in [2] and [3] repeatedly determines a con guration in ....

[Article contains additional citation context not shown here]

D. Hsu, L.E. Kavraki, J.C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In P. Agarwal, L. Kavraki, and M. Mason, editors, Robotics: The Algorithmic Perspective, pages 141-154. A K Peters, 1998.

....from workspace geometry to select samples in con guration space to address this problem. Using these extensions, sampling can be performed more eciently in areas of high or low complexity. In areas of high complexity knowledge about the workspace obstacles can be used to guide the sampling process [1, 12, 13, 25]. The computation of such knowledge, however, tends to be costly. In areas of low complexity the amount of computation can be reduced by discarding redundant samples [21, 28] Latter approaches require a mapping of workspace information into the con guration space. In high dimensional con guration ....

....con guration space of the robot, as it must represent a valid motion. As was noted in Section 1, probabilistic methods have successfully traded completeness for eciency, by replacing the notion of completeness with probabilistic completeness. As a result, the narrow passage problem arose [11, 13], referring to the diculty of probabilistic methods to nd solution paths through narrow passages of the con guration space. Decompositionbased planning performs a tradeo similar to probabilistic methods, giving up completeness for eciency by decomposing the planning problem into two subproblems. ....

David Hsu, Lydia E. Kavraki, Jean-Claude Latombe, Rajeev Motwani, and Stephen Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proceedings of the Workshop on the Algorithmic Foundations of Robotics, pages 141-154. A K Peters, 1998.

....of the total number of collision checks are actually performed on the returned collision free paths, and are therefore inevitable. Solutions for the cases of cluttered con guration spaces and fast collision checking are also proposed, but neither these cases nor the narrow passage problem (see [2, 6, 12]) are our main objectives. Our algorithm, called Lazy PRM, is described in detail in Section 3, and experimentally evaluated in Section 4 using a real industrial environment. 2 Probabilistic Techniques The path planning problem has been extensively studied in the last two decades, and a number ....

....PRM has a weakness in nding paths through narrow passages in F . The node enhancement step in [17] was developed in an e ort to address this issue. Other e orts have been made; one is to distribute nodes close to the boundary of F , and has led to several new sampling strategies. The planner in [12] initially allows the robot to penetrate the obstacles to a certain extent. Small neighborhoods around the con gurations just in collision are then re sampled in order to place nodes close to the boundary of F . The Obstacle Based PRM (OBPRM) in [2, 3] determines con gurations in collision to be ....

D. Hsu, L.E. Kavraki, J.C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In P. Agarwal, L. Kavraki, and M. Mason, editors, Robotics: The Algorithmic Perspective, pages 141-154. A K Peters, 1998.

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D. HSU, L. E. KAVRAKI, J.-C. LATOMBE, R. MOTWANI, and S. SORKIN: On nding narrow passages with probabilistic roadmap planners. P. Agarwal, editor, Robotics: The Algorithmic Perspective, A.K. Peters, Wellesley, MA, 1998, 141 154.

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D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In et al. P. Agarwal, editor, Robotics: The Algorithmic Perspective, pages 141-154. A.K. Peters, Wellesley, MA, 1998. 33

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D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

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D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), 1998.

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D. Hsu, L. E. Kavraki, J.-C. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Alg. Found. Rob., Wellesley, MA, 1998. A. K. Peters.

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D. Hsu, L.E. Kavraki, J.C. Latombe, R. Motwani, and S. Sorkin. On #nding narrow passages with probabilistic roadmap planners. In Proceedings of the 1998 Workshop on Algorithmic Foundations of Robotics, Houston, TX, March 1998.

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D. Hsu, L. Kavraki, J. Latombe, R. Motwani, and S. Sorkin. On nding narrow passages with probabilistic roadmap planners. Proc. of 3rd Workshop on Algorithmic Foundations of Robotics, 1998.

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