Genericity and singularities of robot manipulators

The kinematic singularities of robot manipulators are studied from the point of view of the theory of singularities. The notion of a 'generic' kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator, is examined. For three-joint robots, an equivalent algebraic condition for genericity using the Jacobian determinants is derived. This condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. Orientation and translation singularities of manipulators are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation singularities of the eight possible topologies of three-joint robots are studied and the conditions on the link parameters for nongenericity are determined. >

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

[2]  Richard P. Paul,et al.  Kinematics of Robot Wrists , 1983 .

[3]  K. Sugimoto,et al.  Determination of Extreme Distances of a Robot Hand—Part 1: A General Theory , 1981 .

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

[5]  Alain Liégeois,et al.  A study of multiple manipulator inverse kinematic solutions with applications to trajectory planning and workspace determination , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[6]  T. Shamir,et al.  The Singularities of Redundant Robot Arms , 1990, Int. J. Robotics Res..

[7]  K. C. Gupta,et al.  Design Considerations for Manipulator Workspace , 1982 .

[8]  K. Waldron,et al.  A Study of the Jacobian Matrix of Serial Manipulators , 1985 .

[9]  J. Spanos,et al.  Workspace Analysis of Mechanical Manipulators Using Polynomial Discriminants , 1985 .

[10]  H. Whitney.  On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane , 1955 .

[11]  Joseph Duffy,et al.  Special configurations of spatial mechanisms and robot arms , 1982 .

[12]  D. Kohli,et al.  Boundary Surfaces, Limit Surfaces, Crossable and Noncrossable Surfaces in Workspace of Mechanical Manipulators , 1988 .

[13]  Beno Benhabib,et al.  A complete generalized solution to the inverse kinematics of robots , 1985, IEEE J. Robotics Autom..

[14]  D. E. Whitney,et al.  The mathematics of coordinated control of prosthetic arms and manipulators. , 1972 .

[15]  Faydor L. Litvin,et al.  Singularities in Motion and Displacement Functions of Constrained Mechanical Systems , 1989, Int. J. Robotics Res..

[16]  R. J. Walker.  Algebraic curves , 1950 .

[17]  L. Wang,et al.  Recursive computations of kinematic and dynamic equations for mechanical manipulators , 1985, IEEE J. Robotics Autom..

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

[19]  Shih-Liang Wang,et al.  A Study of the Singular Configurations of Serial Manipulators , 1987 .

[20]  J. M. Boardman.  Singularties of differentiable maps , 1967 .

[21]  Bradley Evan Paden,et al.  Kinematics and Control of Robot Manipulators , 1985 .