Kinematic Modeling of Robotic Manipulators

This paper presents the exhaustive review on the kinematic modeling of robotic manipulators in a systematic manner. A lot of techniques are available in the literature for kinematic modeling of robotic manipulators, however the ambiguity lies with the user to select the most appropriate method. This paper presents the comparative study of different kinematic modeling techniques in terms of complexity, applicability of the method to a particular class of robots and number of parameters or variables required to define the robot. Determination of the correct kinematic parameters, required to develop accurate kinematic models, using different methods has been demonstrated by considering the case study of a five degrees-of-freedom (DOFs) articulated manipulator. Moreover, a seven-DOFs manipulator is considered to highlight and address the inconsistencies of popular methods, while dealing with spatial hybrid manipulators. In this article, a review of 100 research papers is presented to investigate the kinematic study of robotic manipulators with a variety of modeling techniques, which are evolved or refined during the last sixty-odd years (1955–2016).

[1]  Maxime Gautier,et al.  Numerical calculation of the base inertial parameters of robots , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[2]  Bertold Bongardt.  CAD-2-SIM - Kinematic Modeling of Mechanisms Based on the Sheth-Uicker Convention , 2011, ICIRA.

[3]  Panagiotis K. Artemiadis,et al.  Quantifying anthropomorphism of robot hands , 2013, 2013 IEEE International Conference on Robotics and Automation.

[4]  Bruno Siciliano,et al.  An experimental study on compliance control for a redundant personal robot arm , 2003, Robotics Auton. Syst..

[5]  Guy Bessonnet,et al.  Optimal dynamics of actuated kinematic chains. Part 1: Dynamic modelling and symbolic differentiations , 2005 .

[6]  E. Study.  Geometrie der Dynamen : die Zusammensetzung von Kräften und verwandte Gegenstände der Geometrie , 1904 .

[7]  Raymond J. Cipra,et al.  The Kinematics of Open Loop Manipulators using IMP (Integrated Mechanisms Program) , 1984, 1984 American Control Conference.

[8]  Russell H. Taylor,et al.  On homogeneous transforms, quaternions, and computational efficiency , 1990, IEEE Trans. Robotics Autom..

[9]  You-Liang Gu.  Analysis of orientation representations by Lie algebra in robotics , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[10]  M. Kamel,et al.  Quaternions approach to solve the kinematic equation of rotation, A/sub a/A/sub x/=A/sub x/A/sub b/, of a sensor-mounted robotic manipulator , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[11]  Changbin Yu,et al.  Unit-Dual-Quaternion-Based PID Control Scheme for Rigid-Body Transformation , 2011 .

[12]  S. Qiao,et al.  Dual quaternion-based inverse kinematics of the general spatial 7R mechanism , 2008 .

[13]  Jon A. Webb,et al.  Quaternions in Computer Vision and Robotics , 1982 .

[14]  Frank Chongwoo Park,et al.  A recursive algorithm for robot dynamics using Lie groups , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[15]  John J. Craig,et al.  Introduction to Robotics Mechanics and Control , 1986 .

[16]  Carl D. Crane,et al.  Kinematic Analysis of Robot Manipulators , 1998 .

[17]  Kostas Daniilidis,et al.  Hand-Eye Calibration Using Dual Quaternions , 1999, Int. J. Robotics Res..

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

[19]  J. Michael McCarthy,et al.  Dual quaternion synthesis of constrained robotic systems , 2003 .

[20]  Fouad Bennis,et al.  Minimum inertial parameters of robots with parallelogram closed loops , 1991, IEEE Trans. Syst. Man Cybern..

[21]  A. T. Yang,et al.  Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators , 1985 .

[22]  Philippe Lemoine,et al.  Identification of the payload inertial parameters of industrial manipulators , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[23]  J. Michael McCarthy,et al.  Spatial rigid body dynamics using dual quaternion components , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[24]  Urbano Nunes,et al.  Lie algebra application to mobile robot control: a tutorial , 2003, Robotica.

[25]  Lorenzo Flückiger,et al.  A Robot Interface Using Virtual Reality and Automatic Kinematics Generator , 1998 .

[26]  Kevin Cleary,et al.  Kinematic analysis of a novel 6-DOF parallel manipulator , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[27]  Wisama Khalil,et al.  A new geometric notation for open and closed-loop robots , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[28]  Wisama Khalil,et al.  Calibration of the geometric parameters of robots without external sensors , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[29]  Joe Rooney,et al.  William Kingdon Clifford (1845-1879) , 2007 .

[30]  Ulrike Thomas,et al.  A Unified Notation for Serial, Parallel and Hybrid Kinematic Structures , 2011, Robotic Systems for Handling and Assembly.

[31]  J. Hervé.  Analyse structurelle des mcanismes par groupe des dplacements , 1978 .

[32]  Massimo Bergamasco,et al.  An arm exoskeleton system for teleoperation and virtual environments applications , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[33]  Frédéric Boyer,et al.  An efficient calculation of computed torque control of flexible manipulators , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[34]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[35]  Wisama Khalil,et al.  Inverse and direct dynamic modeling of Gough-Stewart robots , 2004, IEEE Transactions on Robotics.

[36]  F. Sparacino,et al.  Synthesis of parallel manipulators using Lie-groups Y-STAR and H-ROBOT , 1993, Proceedings of 1993 IEEE/Tsukuba International Workshop on Advanced Robotics.

[37]  J. M. Hervé,et al.  Structural synthesis of 'parallel' robots generating spatial translation , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[38]  Bernard Roth,et al.  The Near-Minimum-Time Control Of Open-Loop Articulated Kinematic Chains , 1971 .

[39]  Nikos A. Aspragathos,et al.  Computer graphics representation and transformation of geometric entities using dual unit vectors and line transformations , 2001, Comput. Graph..

[40]  J. Keat.  Analysis of Least-Squares Attitude Determination Routine DOAO , 1977 .

[41]  Robert J. Schilling,et al.  Fundamentals of robotics - analysis and control , 1990 .

[42]  Carme Torras,et al.  A group-theoretic approach to the computation of symbolic part relations , 1988, IEEE J. Robotics Autom..

[43]  Carlos Rodrigues Rocha,et al.  A comparison between the Denavit-Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators , 2011 .

[44]  Russell H. Taylor,et al.  Planning and execution of straight line manipulator trajectories , 1979 .

[45]  Wisama Khalil,et al.  General Solution for the Dynamic Modeling of Parallel Robots , 2007, J. Intell. Robotic Syst..

[46]  Bibhuti Bhusan Biswal,et al.  A Novel Method for Representing Robot Kinematics using Quaternion Theory , 2008 .

[47]  Wisama Khalil,et al.  A direct determination of minimum inertial parameters of robots , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[48]  C. Chevallereau,et al.  An efficient algorithm for the dynamic control of robots in the cartesian space , 1987, 26th IEEE Conference on Decision and Control.

[49]  Amit K. Sanyal,et al.  A Lie group variational integrator for rigid body motion in SE(3) with applications to underwater vehicle dynamics , 2010, 49th IEEE Conference on Decision and Control (CDC).

[50]  Harvey Lipkin,et al.  A Note on Denavit-Hartenberg Notation in Robotics , 2005 .

[51]  Philippe C. Cattin,et al.  Cinegen: a Rapid Prototyping Tool for Robot Manipulators , 1998 .

[52]  A. Quaid,et al.  Identifying robot parameters using partial pose information , 1993, IEEE Control Systems.

[53]  Wisama Khalil,et al.  Modeling, simulation and control of high speed machine tools using robotics formalism , 2002 .

[54]  Nikos A. Aspragathos,et al.  A comparative study of three methods for robot kinematics , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[55]  Christine Chevallereau,et al.  Calculation of the direct dynamic model of walking robots: comparison between two methods , 1997, Proceedings of International Conference on Robotics and Automation.

[56]  Andrea Maria Zanchettin,et al.  Kinematic analysis and synthesis of the human arm motion during a manipulation task , 2011, 2011 IEEE International Conference on Robotics and Automation.

[57]  D. Hu,et al.  Strapdown inertial navigation system algorithms based on dual quaternions , 2005 .

[58]  Richard A. Volz,et al.  Estimating 3-D location parameters using dual number quaternions , 1991, CVGIP Image Underst..

[59]  Nicola Pio Belfiore,et al.  Connectivity and Redundancy in Spatial Robots , 2000, Int. J. Robotics Res..

[60]  Said M. Megahed,et al.  Efficient robot arm modeling for computer control , 1993, J. Field Robotics.

[61]  Charles P. Neuman,et al.  Kinematic modeling of wheeled mobile robots , 1987, J. Field Robotics.

[62]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[63]  Wisama Khalil,et al.  Dynamic Modeling of Robots Using Newton-Euler Formulation , 2010, ICINCO.

[64]  Jaime Gallardo-Alvarado,et al.  Lie Algebra and the Mobility of Kinematic Chains , 2003, J. Field Robotics.

[65]  Amanpreet Singh,et al.  D-H parameters augmented with dummy frames for serial manipulators containing spatial links , 2014, The 23rd IEEE International Symposium on Robot and Human Interactive Communication.

[66]  Wisama Khalil,et al.  Minimum operations and minimum parameters of the dynamic models of tree structure robots , 1987, IEEE Journal on Robotics and Automation.

[67]  Wei Zhang,et al.  Multi-objective optimisation method for posture prediction and analysis with consideration of fatigue effect and its application case , 2009, Comput. Ind. Eng..

[68]  J. J. Uicker,et al.  A Generalized Symbolic Notation for Mechanisms , 1971 .

[69]  Maxime Gautier,et al.  Identification of joint stiffness with bandpass filtering , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[70]  Peter I. Corke,et al.  A Simple and Systematic Approach to Assigning Denavit–Hartenberg Parameters , 2007, IEEE Transactions on Robotics.

[71]  Robert Gilmore,et al.  Lie Groups, Physics, and Geometry: Frontmatter , 2008 .

[72]  A. Iserles,et al.  Lie-group methods , 2000, Acta Numerica.

[73]  Jonghoon Park,et al.  Geometric integration on Euclidean group with application to articulated multibody systems , 2005, IEEE Transactions on Robotics.

[74]  Ashish Singla,et al.  Extension of D-H parameter method to hybrid manipulators used in robot-assisted surgery , 2015, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[75]  Wisama Khalil,et al.  An efficient algorithm for the calculation of the filtered dynamic model of robots , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[76]  R. Paul.  Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[77]  Mahmoud Gouasmi.  Robot Kinematics, using Dual Quaternions , 2012, ICRA 2012.

[78]  Philippe Lemoine,et al.  Identification of the dynamic parameters of the Orthoglide , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[79]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[80]  A. T. Yang,et al.  Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms , 1964 .