Kinematic localization for world model calibration in off-line robot programming using Clifford algebra

The calibration of spatial relationships among CAD models of objects used in offline robot programming is discussed. An approach based on a Clifford algebra is used, and simple algorithms for this kinematic localization problem are developed. The position and orientation of each object in a workcell are represented by multivectors of different ranks and the localization problem is converted into that of solving a set of multivector equations. Given locations of points in two frames, an averaging process which yields the best orientation as the root of four linear equations and the best position as a linear combination of the best rotation and the centroids of two point systems is developed. If normal vectors are also sensed, the Clifford algebra representation facilitates definition of a measure of orientation error compatible with the position error