Computational Advances in Robot Kinematics

This paper presents an overview of the current state-of-the-art in solving the sets of nonlinear equations which arise in robot kinematics. It reviews some recent results and the history and fundamental concepts of the most widely used computational methods. The paper deals mainly with equations with numerical coefficients, since for such equations methods have been developed which, in principle, will allow for the determination of all solutions.

[1]  B. Roth,et al.  Synthesis of Path-Generating Mechanisms by Numerical Methods , 1963 .

[2]  B. Roth,et al.  Structural Parameters Which Reduce the Number of Manipulator Configurations , 1994 .

[3]  Joseph Duffy,et al.  Analysis of mechanisms and robot manipulators , 1980 .

[4]  B. Roth Computations in Kinematics , 1993 .

[5]  Joseph James Duffy,et al.  A displacement analysis of the general spatial 7-link, mechanism , 1980 .

[6]  M. Raghavan The Stewart platform of general geometry has 40 configurations , 1993 .

[7]  D. Lazard,et al.  On the Representation of Rigid-Body Motions and its Application to Generalized Platform Manipulators , 1993 .

[8]  Bernhard Roth,et al.  A closed-form solution of the forward displacement analysis of a class of in-parallel mechanisms , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[9]  K. H. Hunt,et al.  Assembly configurations of some in-parallel-actuated manipulators , 1993 .

[10]  Masoud Ghazvini,et al.  Reducing the Inverse Kinematics of Manipulators to the Solution of a Generalized Eigenproblem , 1993 .

[11]  Leo Joskowicz,et al.  Computational Kinematics , 1991, Artif. Intell..

[12]  Jean-Pierre Merlet,et al.  The (true) Stewart platform has 12 configurations , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[13]  Wei Lin,et al.  Forward Displacement Analyses of the 4-4 Stewart Platforms , 1992 .

[14]  Milton A. Chace Vector Analysis of Linkages , 1963 .

[15]  B. Kutzler,et al.  On the Application of Buchberger's Algorithm to Automated Geometry Theorem Proving , 1986, J. Symb. Comput..

[16]  A. Morgan,et al.  Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods , 1985 .

[17]  Carlo Innocenti,et al.  Direct position analysis of the Stewart platform mechanism , 1990 .

[18]  Kenneth J. Waldron,et al.  Kinematics of a Hybrid Series-Parallel Manipulation System , 1989 .

[19]  H. Hironaka Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II , 1964 .

[20]  C. Innocenti,et al.  Closed-Form Direct Position Analysis of a 5–5 Parallel Mechanism , 1993 .

[21]  Donald R. Flugrad,et al.  Five-Bar Path Generation Synthesis by Continuation Methods , 1993 .

[22]  B. Roth,et al.  Inverse Kinematics of the General 6R Manipulator and Related Linkages , 1993 .

[23]  B. Buchberger,et al.  Grobner Bases : An Algorithmic Method in Polynomial Ideal Theory , 1985 .

[24]  Madhusudan Raghavan,et al.  On the design of manipulators for applying wrenches , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[25]  Dinesh Manocha,et al.  A fast algorithm and system for the inverse kinematics of general serial manipulators , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[26]  Kok-Meng Lee,et al.  Dynamic analysis of a three-degrees-of-freedom in-parallel actuated manipulator , 1988, IEEE J. Robotics Autom..

[27]  Deepak Kapur,et al.  Using Gröbner Bases to Reason About Geometry Problems , 1986, J. Symb. Comput..

[28]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[29]  Jürgen Weiss,et al.  Resultant Methods for the Inverse Kinematics Problem , 1993 .

[30]  J. Jouanolou,et al.  Singularites Rationnelles Du Resultant , 1979 .

[31]  Jorge Angeles,et al.  The Semigraphical Solution of the Direct Kinematics of General Platform-Type Parallel Manipulators , 1993 .

[32]  Dinesh Manocha,et al.  Real time inverse kinematics for general 6R manipulators , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[33]  Bernard Roth,et al.  Kinematic analysis of the 6R manipulator of general geometry , 1991 .

[34]  Donald Lee Pieper The kinematics of manipulators under computer control , 1968 .

[35]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[36]  Hong Y. Lee,et al.  Displacement analysis of the general spatial 7-link 7R mechanism , 1988 .