Computationally Efficient Kinematics for Manipulators with Spherical Wrists Based on the Homogeneous Transformation Representation

Abstract

Most manipulators in use today are kinematically simple, and closed-form symbolic equations are the most efficient means of expressing their kinematics. The analysis presented in this paper is based on the use of homogeneous transforma tions to describe position and orientation. Using these methods, kinematic equations are obtained directly in a form suitable for computer implementation. The equations are numerically stable and are obtained almost automatically. The resulting equations involve the minimum number of mathematical operations.

Get full access to this article

View all access options for this article.

References

Elgazzar, S. 1985. Efficient kinematic transformations for the PUMA 560 robot IEEE J. Robotics and Automation. RA-1 3 (September 1983), 142-151.

Featherstone, R. 1983

(summer). Position and velocity transformations between robot end-effector coordinates and joint angles

Robotics Research 2(2):35-45.

Hartenberg, R.S. , and Denavit, J. 1964. Kinematic synthesis of linkages New York: McGraw-Hill.

Hollerbach, J.M. , and Sahar, G. 1983

(winter). Wrist-partitioned, inverse kinematic accelerations and manipulator dynamics

Robotics Research 2(4):61-76.

Orin, D. , and Schrader, W.W. 1984. Efficient Jacobian determination for robot manipulators. Proc. 1 st Symp. of Robotics Research Cambridge: MIT Press.

Paul, R.P. 1981. Robot manipulators: mathematics, programming, and control Cambridge: MIT Press.

Paul, R.P. , Renaud, M. , and Stevenson, C.N. 1984. A systematic approach for obtaining the kinematics of recursive manipulators based on homogeneous transformations Proc. 1st Symp. of Robotics Research. Cambridge: MIT Press.

Pieper, D.L. 1968. The kinematics of manipulators under computer control. AIM-72 Stanford, Calif.: Stanford University Artificial Intelligence Laboratory.

Renaud, M. 1981 (Tokyo, Japan). Geometric and kinematic models of a robot manipulator: calculation of the Jacobian matrix and its inverse Proc. 11th ISIR.

10.

Roberts, L.G. 1965. Homogeneous matrix representation and manipulation of n-dimensional constructs Lincoln Laboratory, Massachusetts Institute of Technology, Document No. MS 1045.