Measures of Positional Error for a Rigid Body

Abstract

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.