Caging and Path Non-existence: A Deterministic Sampling-Based Verification Algorithm

Caging restricts the mobility of an object without necessarily immobilizing it completely. The object is caged if it cannot move arbitrarily far from its initial position. Apart from its common applications to grasping and manipulation, caging can also be considered as a problem dual to motion planning: an object is caged when it is isolated within a bounded connected component of its configuration space and is disconnected from the rest of the latter. In this paper, we address the problem of caging and path non-existence verification in 2D and 3D workspaces by representing a subset of the collision space as a simplicial complex and analyzing the connectivity of its complement. Since configuration spaces of 2D and 3D rigid objects are three-dimensional and six-dimensional respectively, it is computationally expensive to reconstruct them explicitly. Thus, we represent the object’s collision space as a union of a finite set of ‘slices’, corresponding to small intervals of the object’s orientation coordinates.

[1]  A. Frank van der Stappen,et al.  Caging Polygons with Two and Three Fingers , 2006, WAFR.

[2]  Danica Kragic,et al.  Integrated motion and clasp planning with virtual linking , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[3]  Vijay Kumar,et al.  Decentralized Algorithms for Multi-Robot Manipulation via Caging , 2004, Int. J. Robotics Res..

[4]  Andrew Blake,et al.  Caging Planar Bodies by One-Parameter Two-Fingered Gripping Systems , 1999, Int. J. Robotics Res..

[5]  Danica Kragic,et al.  A Decomposition-Based Approach to Reasoning about Free Space Path-Connectivity for Rigid Objects in 2D , 2017, ArXiv.

[6]  Danica Kragic,et al.  Caging Grasps of Rigid and Partially Deformable 3-D Objects With Double Fork and Neck Features , 2016, IEEE Transactions on Robotics.

[7]  Danica Kragic,et al.  Grasping objects with holes: A topological approach , 2013, 2013 IEEE International Conference on Robotics and Automation.

[8]  Herbert Edelsbrunner,et al.  Computational Topology - an Introduction , 2009 .

[9]  Attawith Sudsang,et al.  Two-finger caging of concave polygon , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[10]  Siddhartha S. Srinivasa,et al.  CHOMP: Gradient optimization techniques for efficient motion planning , 2009, 2009 IEEE International Conference on Robotics and Automation.

[11]  Dinesh Manocha,et al.  Efficient Cell Labelling and Path Non-existence Computation using C-obstacle Query , 2008, Int. J. Robotics Res..

[12]  Kenneth Y. Goldberg,et al.  Energy-Bounded Caging: Formal Definition and 2-D Energy Lower Bound Algorithm Based on Weighted Alpha Shapes , 2016, IEEE Robotics and Automation Letters.

[13]  Lydia E. Kavraki,et al.  A Random Sampling Scheme for Path Planning , 1997, Int. J. Robotics Res..

[14]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[15]  Satoshi Makita,et al.  3D multifingered caging: Basic formulation and planning , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  Satoshi Makita,et al.  3D two-fingered caging for two types of objects: sufficient conditions and planning , 2013, Int. J. Mechatronics Autom..

[17]  Alberto Rodriguez,et al.  From caging to grasping , 2011, Int. J. Robotics Res..

[18]  Timothy Bretl,et al.  Proving path non-existence using sampling and alpha shapes , 2012, 2012 IEEE International Conference on Robotics and Automation.

[19]  Danica Kragic,et al.  A topology-based object representation for clasping, latching and hooking , 2013, 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids).

[20]  Attawith Sudsang,et al.  Two-Finger Caging of Nonconvex Polytopes , 2011, IEEE Transactions on Robotics.

[21]  Leonidas J. Guibas,et al.  Disconnection proofs for motion planning , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).