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.