Closed-Form Inverse Kinematics for Continuum Manipulators

This paper presents a novel, analytical approach to solving inverse kinematics for multi-section continuum robots, defined as robots composed of a continuously bendable backbone. The problem is decomposed into several simpler subproblems. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming endpoints for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for the resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a prototype continuum robot are presented and possible applications discussed.

[1]  Guy Immega,et al.  The KSI tentacle manipulator , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[2]  Hideyuki Tsukagoshi,et al.  Active Hose: an artificial elephant's nose with maneuverability for rescue operation , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[3]  Kai Xu,et al.  An Investigation of the Intrinsic Force Sensing Capabilities of Continuum Robots , 2008, IEEE Transactions on Robotics.

[4]  Ian D. Walker,et al.  Field trials and testing of the OctArm continuum manipulator , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[5]  Pierre E. Dupont,et al.  A Steerable Needle Technology Using Curved Concentric Tubes , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[6]  Ian D. Walker,et al.  Soft robotics: Biological inspiration, state of the art, and future research , 2008 .

[7]  W. Kier,et al.  Tongues, tentacles and trunks: the biomechanics of movement in muscular‐hydrostats , 1985 .

[8]  Li Han,et al.  Inverse Kinematics for a Serial Chain with Joints Under Distance Constraints , 2006, Robotics: Science and Systems.

[9]  Takeshi Aoki,et al.  Design of Slim Slime Robot II (SSR-II) with Bridle Bellows , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Robert J. Webster,et al.  Toward Active Cannulas: Miniature Snake-Like Surgical Robots , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  John Kenneth Salisbury,et al.  Mechanics Modeling of Tendon-Driven Continuum Manipulators , 2008, IEEE Transactions on Robotics.

[12]  Pål Liljebäck,et al.  A survey on snake robot modeling and locomotion , 2009, Robotica.

[13]  Rob Buckingham,et al.  Snake arm robots , 2002 .

[14]  Ian D. Walker,et al.  Large deflection dynamics and control for planar continuum robots , 2001 .

[15]  Hiromi Mochiyama,et al.  Whole-arm impedance of a serial-chain manipulator , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[16]  David M. Lane,et al.  The AMADEUS dextrous subsea hand: design, modeling, and sensor processing , 1999 .

[17]  J. Bruce C. Davies,et al.  Continuum robots - a state of the art , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[18]  Ian D. Walker,et al.  Design and implementation of a multi-section continuum robot: Air-Octor , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  Bruno Siciliano,et al.  Kinematic control of redundant robot manipulators: A tutorial , 1990, J. Intell. Robotic Syst..

[20]  Ian D. Walker,et al.  User interfaces for continuum robot arms , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[21]  Ian D. Walker,et al.  Kinematics and the Implementation of an Elephant's Trunk Manipulator and Other Continuum Style Robots , 2003, J. Field Robotics.

[22]  Yacine Amirat,et al.  Modeling and Control of a Hybrid Continuum Active Catheter for Aortic Aneurysm Treatment , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[23]  Ian D. Walker,et al.  Three-Dimensional Modeling and Display of Continuum Robots , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[24]  Ian D. Walker,et al.  Kinematics for multisection continuum robots , 2006, IEEE Transactions on Robotics.

[25]  Dragomir N. Nenchev,et al.  Redundancy resolution through local optimization: A review , 1989, J. Field Robotics.

[26]  Masakatsu G. Fujie,et al.  Bending Laser Manipulator for Intrauterine Surgery and Viscoelastic Model of Fetal Rat Tissue , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[27]  M. Spong,et al.  Robot Modeling and Control , 2005 .

[28]  Shuichi Wakimoto,et al.  A miniature inspection robot negotiating pipes of widely varying diameter , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[29]  Srinivas Neppalli,et al.  Design, construction, and analysis of a continuum robot , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[30]  Robert J. Webster,et al.  Mechanics of Precurved-Tube Continuum Robots , 2009, IEEE Transactions on Robotics.

[31]  Li Han,et al.  A Unified Geometric Approach for Inverse Kinematics of a Spatial Chain with Spherical Joints , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.