Configuration-Based Optimization for Six Degree-of-Freedom Haptic Rendering for Fine Manipulation

Six-degree-of-freedom (6-DOF) haptic rendering for fine manipulation in narrow space is a challenging topic because of frequent constraint changes caused by small tool movement and the requirement to preserve the feel of fine-features of objects. In this paper, we introduce a configuration-based constrained optimization method for solving this rendering problem. We represent an object using a hierarchy of spheres, i.e., a sphere tree, which allows faster detection of multiple contacts/collisions among objects than polygonal mesh and facilitates contact constraint formulation. Given a moving graphic tool as the avatar of the haptic tool in the virtual environment, we compute its quasi-static motion by solving a configuration-based optimization. The constraints in the 6D configuration space of the graphic tool is obtained and updated through online mapping of the nonpenetration constraint between the spheres of the graphic tool and those of the other objects in the three-dimensional physical space, based on the result of collision detection. This problem is further modeled as a quadratic programming optimization and solved by the classic active-set methods. Our algorithm has been implemented and interfaced with a 6-DOF Phantom Premium 3.0. We demonstrate its performance in several benchmarks involving complex, multiregion contacts. The experimental results show both the high efficiency and stability of haptic rendering by our method for complex scenarios. Nonpenetration between the graphic tool and the object is maintained under frequent contact switches. Update rate of the simulation loop including optimization and constraint identification is maintained at about 1 kHz.

[1]  Brian Mirtich,et al.  Impulse-based dynamic simulation of rigid body systems , 1996 .

[2]  Philip M. Hubbard,et al.  Approximating polyhedra with spheres for time-critical collision detection , 1996, TOGS.

[3]  John Kenneth Salisbury,et al.  Voxel-Based Haptic Rendering Using Implicit Sphere Trees , 2008, 2008 Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems.

[4]  Stephane Cotin,et al.  Interactive physically-based simulation of catheter and guidewire , 2006, Comput. Graph..

[5]  Carol O'Sullivan,et al.  Adaptive medial-axis approximation for sphere-tree construction , 2004, TOGS.

[6]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[7]  Ming C. Lin,et al.  A modular haptic rendering algorithm for stable and transparent 6-DOF manipulation , 2006, IEEE Transactions on Robotics.

[8]  Yuan-Shin Lee,et al.  Cutting on triangle mesh: local model-based haptic display for dental preparation surgery simulation , 2005, IEEE Transactions on Visualization and Computer Graphics.

[9]  Ge Yu,et al.  Six degree-of-freedom haptic simulation of sharp geometric features using a hybrid sphere-tree model , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Xin Zhang,et al.  Configuration-based optimization for six degree-of-freedom haptic rendering for fine manipulation. , 2013, IEEE transactions on haptics.

[11]  Liangjun Zhang,et al.  Efficient motion planning using generalized penetration depth computation , 2009 .

[12]  Rene Weller,et al.  A unified approach for physically-based simulations and haptic rendering , 2009, Sandbox@SIGGRAPH.

[13]  Abderrahmane Kheddar,et al.  Gauss' least constraints principle and rigid body simulations , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[14]  Dinesh Manocha,et al.  Fast distance queries with rectangular swept sphere volumes , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[15]  Jernej Barbic,et al.  Six-DoF Haptic Rendering of Contact Between Geometrically Complex Reduced Deformable Models , 2008, IEEE Transactions on Haptics.

[16]  Qi Luo,et al.  Haptic modeling of contact formations and compliant motion , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[17]  Xin Zhang,et al.  Six degree-of-freedom haptic simulation of periodontal pathological changes , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[18]  John Kenneth Salisbury,et al.  A constraint-based god-object method for haptic display , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[19]  Xin Zhang,et al.  Configuration-based optimization for six degree-of-freedom haptic rendering using sphere-trees , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[20]  N. Durlach,et al.  Manual discrimination of force using active finger motion , 1991, Perception & psychophysics.

[22]  Michael Ortega-Binderberger,et al.  A Six Degree-of-Freedom God-Object Method for Haptic Display of Rigid Bodies with Surface Properties , 2007, IEEE Transactions on Visualization and Computer Graphics.

[23]  Christian Duriez,et al.  Realistic haptic rendering of interacting deformable objects in virtual environments , 2008, IEEE Transactions on Visualization and Computer Graphics.

[24]  Markus H. Gross,et al.  Implicit Contact Handling for Deformable Objects , 2009, Comput. Graph. Forum.

[25]  David Baraff,et al.  Analytical methods for dynamic simulation of non-penetrating rigid bodies , 1989, SIGGRAPH.

[26]  Ming Wan,et al.  Quasi-Static Approximation for 6 Degrees-of-Freedom Haptic Rendering , 2003, IEEE Visualization.

[27]  Stéphane Redon,et al.  Fast continuous collision detection and handling for desktop virtual prototyping , 2004, Virtual Reality.

[28]  R. J. Irwin,et al.  Differential thresholds for limb movement measured using adaptive techniques , 1992, Perception & psychophysics.

[29]  Binh Nguyen,et al.  Modeling non-convex configuration space using linear complementarity problems , 2010, 2010 IEEE International Conference on Robotics and Automation.

[30]  Boeing Phantom,et al.  Voxel-Based 6-DOF Haptic Rendering Improvements , 2006 .

[31]  Ming Wan,et al.  Quasi-static approach approximation for 6 degrees-of-freedom haptic rendering , 2003, IEEE Visualization, 2003. VIS 2003..

[32]  Ming C. Lin,et al.  Haptic Rendering : Foundations, Algorithms, and Applications , 2008 .

[33]  Dinesh K. Pai,et al.  Post-stabilization for rigid body simulation with contact and constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[34]  Elaine Cohen,et al.  Six degree-of-freedom haptic rendering using spatialized normal cone search , 2005, IEEE Transactions on Visualization and Computer Graphics.

[35]  Xinyu Zhang,et al.  Interactive continuous collision detection for non-convex polyhedra , 2006, The Visual Computer.

[36]  Christian Duriez,et al.  Six Degree-of Freedom Haptic Rendering for Dental Implantology Simulation , 2010, ISMBS.

[37]  Xin Zhang,et al.  Six-degree-of-freedom haptic simulation of organ deformation in dental operations , 2012, 2012 IEEE International Conference on Robotics and Automation.

[38]  Yong Wang,et al.  Haptic rendering for dental training system , 2009, Science in China Series F: Information Sciences.

[39]  Dinesh Manocha,et al.  C2A: Controlled conservative advancement for continuous collision detection of polygonal models , 2009, 2009 IEEE International Conference on Robotics and Automation.

[40]  M A Srinivasan,et al.  Manual discrimination of compliance using active pinch grasp: The roles of force and work cues , 1995, Perception & psychophysics.