Optimal Matching of Three-Dimensional Features under Geometrical Constraints

This paper addresses the problem of determination of the displacement parameters (rigid rotation and translation) that bring an object set of three-dimensional features to match a template set, minimizing a measure of the mismatch error and satisfying an assigned set of geometrical constraints. This problem is encountered in many applications of computer vision, manufacturing processes (tolerance inspection of machined parts) and robotics, and has been widely treated in the literature in the unconstrained case. In this paper the solution of the unconstrained problem (least-squares solution via singular value decomposition) is reviewed, and an original solution method for the constrained problem is proposed, based on an efficient interior-point convex optimization algorithm. An example of application to the target pose determination of a robot end-effector for a precision positioning task is presented to illustrate the use of the proposed methodology