A Fast and Practical Algorithm for Generalized Penetration Depth Computation

Zhang, Liangjun; Kim, Young J; Manocha, Dinesh

doi:10.15607/rss.2007.iii.034

Cited by 30 publications

(22 citation statements)

References 37 publications

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“…The penetration depth (PD) is a proper metric to quantify the amount of overlap between A and B. In the literature, different types of penetration depth are known [26] and in our case, we use pointwise penetration depth [24] since it is computationally cheaper to compute as compared to other penetration measures.…”

Section: Penetration Depthmentioning

confidence: 99%

CCQ: Efficient Local Planning Using Connection Collision Query

Tang

Kim

Manocha

2010

Springer Tracts in Advanced Robotics

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We introduce a novel proximity query, called connection collision query (CCQ), and use it for efficient and exact local planning in sampling-based motion planners. Given two collision-free configurations, CCQ checks whether these configurations can be connected by a given continuous path that either lies completely in the free space or penetrates any obstacle by at most ε, a given threshold. Our approach is general, robust, and can handle different continuous path formulations. We have integrated the CCQ algorithm with sampling-based motion planners and can perform reliable local planning queries with little performance degradation, as compared to prior methods. Moreover, the CCQ-based exact local planner is about an order of magnitude faster than prior exact local planning algorithms.

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Section: Penetration Depthmentioning

confidence: 99%

CCQ: Efficient Local Planning Using Connection Collision Query

Tang

Kim

Manocha

2010

Springer Tracts in Advanced Robotics

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“…For example, computing the closest boundary point for an incolliding configuration boils down to penetration depth computation, which has high complexity [30]. Other algorithms use heuristics to compute samples near the boundary of CObstacle space or near approximate medial axis [1], [23], [28].…”

Section: Retraction-based Planningmentioning

confidence: 99%

Retraction-based RRT planner for articulated models

Pan

Zhang

Manocha

2010

2010 IEEE International Conference on Robotics and Automation

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Abstract-We present a new retraction algorithm for high DOF articulated models and use our algorithm to improve the performance of RRT planners in narrow passages. The retraction step is formulated as a constrained optimization problem and performs iterative refinement on the boundary of CObstacle space. We also combine the retraction algorithm with decomposition planners to handle very high DOF articulated models. The performance of our approach is analyzed using Voronoi diagrams and we show that our retraction algorithm provides a good approximation to the ideal RRT-extension in constrained environments. We have implemented our algorithm and tested its performance on robots with more than 40 DOFs in complex environments. In practice, we observe significant performance (2-80X) improvement over prior RRT planners on challenging scenarios with narrow passages.

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“…To the best of our knowledge, the papers of Zhang et al (2006Zhang et al ( ,2007 are the only works on P D computation. A key issue for the definition of P D is the choice of the distance metric on SE(3), because there exists no naturally introduced metric as in the case of P D t .…”

Section: Prior Workmentioning

confidence: 99%

“…Recently, Zhang et al (2007) also presented an optimization-based algorithm for P D computation with respect to the so called DIST-metric, which is more suitable for computation than the above mentioned one.…”

Section: Prior Workmentioning

confidence: 99%

Generalized penetration depth computation based on kinematical geometry

Nawratil

Pottmann

Ravani

2009

Computer Aided Geometric Design

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The generalized penetration depth P D of two overlapping bodies X and Y is the distance between the given colliding position of X and the closest collision-free Euclidean copy X ε to X according to a distance metric. We present geometric optimization algorithms for the computation of P D with respect to an object-oriented metric S which takes the mass distribution of the moving body X into consideration. We use a kinematic mapping which maps rigid body displacements to points of a 6-dimensional manifold M 6 in the 12-dimensional space R 12 of affine mappings equipped with S. We formulate P D as the solution of the constrained minimization problem of finding the closest point on the boundary of the set of all points of M 6 which correspond to colliding configurations. Based on the theory of gliding motions, the closest point with respect to the metric S (⇒ P D S ) can be computed with an adapted projected gradient algorithm. We also present an algorithm for the computation of the closest point with respect to the geodesic metric G of M 6 induced by S (⇒ P D G ). Moreover we introduce two methods for the computation of a collision-free initial guess and give a physical interpretation of P D S and P D G .

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A Fast and Practical Algorithm for Generalized Penetration Depth Computation

Cited by 30 publications

References 37 publications

CCQ: Efficient Local Planning Using Connection Collision Query

CCQ: Efficient Local Planning Using Connection Collision Query

Retraction-based RRT planner for articulated models

Generalized penetration depth computation based on kinematical geometry

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