COMPUTATION OF SPATIAL DISPLACEMENTS FROM REDUNDANT GEOMETRIC FEATURES

This paper follows a previous one on the computation of spatial displa cements (Ravani and Ge, 1993). The first paper dealt with the problem of computing spatial displacements from a minimum number of simple fea tures of points, lines, planes, and their combinations. The present pa per deals with the same problem using a redundant set of the simple ge ometric features. The problem for redundant information is formulated as a least squares problem which includes all simple features. A Cliff ord algebra is used to unify the handling of various feature informati on. An algorithm for determining the best orientation is developed whi ch involves finding the eigenvector associated with the least eigenval ue of a 4 x 4 symmetric matrix. The best translation is found to be a rational cubic function of the best orientation. Special cases are dis cussed which yield the best orientation in closed form. In addition, s imple algorithms ave provided for automatic generation of body-fixed c oordinate frames from various feature information. The results have ap plications in robot and world model calibration for off-line programmi ng and computer vision.