Real-time Inverse Kinematics of (2n + 1) DOF hyper-redundant manipulator arm via a combined numerical and analytical approach

Abstract The task of solving Inverse Kinematics (IK) for redundant serial chain manipulators has been and still continues to be quite challenging in the field of robotics. Researchers from different fields have succeeded in solving the IK of different robot configurations for various applications. However, the challenge of computational efficiency still remains, in particular for complex robot configurations, to be used for real-time applications. This paper presents a novel, computationally efficient method of performing IK for general 2n + 1 (n is the number of joints) DOF manipulators with a spherical joint at the wrist. It uses the simplicity of analytical solutions to enhance the speed of numerical solvers that operate on each joint location individually. The problem of IK is approached as a constrained optimization, where obstacle avoidance and limit avoidance at joints are used as illustrations. The joint limitations are handled implicitly as boundary conditions for the numerical algorithm. The algorithm was executed and implemented on various paths for a 9 DOF arm and also simulated for a 13 DOF arm for generalization purposes.

[1]  Andreas Aristidou,et al.  FABRIK: A fast, iterative solver for the Inverse Kinematics problem , 2011, Graph. Model..

[2]  A. Liegeois,et al.  Automatic supervisory control of the configuration and behavior of multi-body mechanisms , 1977 .

[3]  Kazuhiro Kosuge,et al.  An Analytical Solution for a Redundant Manipulator with Seven Degrees of Freedom , 2012 .

[4]  Wang Yaonan,et al.  Inverse Kinematics Solution for Robot Manipulator based on Neural Network under Joint Subspace , 2014 .

[5]  Ning Xi,et al.  An online motion planning algorithm for a 7DOF redundant manipulator , 2010, 2010 IEEE International Conference on Robotics and Biomimetics.

[6]  Fumitoshi Matsuno,et al.  Control of redundant 3D snake robot based on kinematic model , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[7]  John M. Hollerbach,et al.  OPTIMUM KINEMATIC DESIGN FOR A SEVEN DEGREE OF FREEDOM MANIPULATOR. , 1985 .

[8]  Donald Sofge,et al.  Design, Implementation, and Cooperative Coevolution of an Autonomous/ Teleoperated Control System for a Serpentine Robotic Manipulator , 2007, ArXiv.

[9]  Bruno Siciliano,et al.  A solution algorithm to the inverse kinematic problem for redundant manipulators , 1988, IEEE J. Robotics Autom..

[10]  John M. Hollerbach,et al.  Redundancy resolution of manipulators through torque optimization , 1987, IEEE J. Robotics Autom..

[11]  Pei-Yan Zhang,et al.  RBF networks-based inverse kinematics of 6R manipulator , 2005 .

[12]  Zhao Zhang,et al.  Inverse kinematics of modular Cable-driven Snake-like Robots with flexible backbones , 2011, 2011 IEEE 5th International Conference on Robotics, Automation and Mechatronics (RAM).

[13]  Mahmoud Moghavvemi,et al.  Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics, path planning and workspace , 2011, Simul. Model. Pract. Theory.

[14]  Kazuhiro Kosuge,et al.  Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution , 2008, IEEE Transactions on Robotics.

[15]  Bruno Siciliano,et al.  Modeling and Control of Robot Manipulators , 1995 .

[16]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[17]  Raul Ordonez,et al.  Design and construction of 9-DOF hyper-redundant robotic arm , 2014, NAECON 2014 - IEEE National Aerospace and Electronics Conference.

[18]  Raúl Ordóñez,et al.  Real-time Inverse Kinematics of redundant manipulator using a hybrid (analytical and numerical) method , 2013, 2013 16th International Conference on Advanced Robotics (ICAR).

[19]  Bruno Siciliano,et al.  A closed-loop inverse kinematic scheme for on-line joint-based robot control , 1990, Robotica.

[20]  Wei-Qiang Song,et al.  A Fast Inverse Kinematics Algorithm for Joint Animation , 2011 .

[21]  Norman I. Badler,et al.  Real-Time Inverse Kinematics Techniques for Anthropomorphic Limbs , 2000, Graph. Model..

[22]  Chih-Cheng Chen,et al.  A combined optimization method for solving the inverse kinematics problems of mechanical manipulators , 1991, IEEE Trans. Robotics Autom..

[23]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .