Properties of Euclidean error measures for rigid body position are investigated. For two positions represented by 4 × 4 matrices A1 and A2, it is shown that matrices [A2 − A1] and [(A1)−1 A2] lead directly to desirable measures of rotational and translational errors, while the matrix [A2(A1)−1], although physically very meaningful, does not do so. With a proper choice of the origin of the body system, it is shown that the simple difference matrix [A2 − A1] leads to positional error measures which are meaningful both analytically and physically, and can be computed efficiently.

Issue Section:
Research Papers
Topics:
Errors
1.
Cheng
H.
, and
Gupta
K. C.
, “
A Study of Robot Inverse Kinematics Based Upon the Solution of Differential Equations
,”
J. Robotic Systems
, Vol.
8
, No.
2
, pp.
159
–
175
,
1991
.
2.
Gupta, K. C., and Kazerounian, K., “Improved Numerical Solutions of Inverse Kinematics of Robots,” Proc. IEEE Intl. Conf. on Robotics and Automation, St. Louis, 1985, pp. 743–748.
3.
Gupta
K. C.
, and
Singh
V. K.
, “
A Numerical Algorithm for Solving Robot Inverse Kinematics
,”
Robotica
, Vol.
7
, pp.
159
–
164
,
1989
.
4.
Kazerounian, K., and Rastegar, J., “A Class of Coordinate and Metric Independent Norms for Displacements,” Proc. ASME Mechanisms Conf., Scottsdale, 1992, DE47, pp. 271–275.
5.
McCarthy, J. M., Introduction to Theoretical Kinematics, MIT Press, 1990.
6.
Martinez
J. M. R.
, and
Duffy
J.
, “
On the Metrics of Rigid Body Displacements for Infinite and Finite Bodies
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, No.
1
, pp.
41
–
47
,
1995
.
7.
Park
F. C.
, “
Distance Metrics on the Rigid-Body Motions with Applications to Mechanical Design
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, No.
1
, pp.
48
–
54
,
1995
.
8.
Singh, V. K., and Gupta, K. C., “A Manipulator Jacobian Based Modified Newton-Raphson Algorithm (JMNR) for Robot Inverse Kinematics,” Proc. ASME Design Automation Conf., Montreal, 1989, Vol. 3, pp. 327–332.
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