Nonlinear programming method for 3D localization of mobile robots

This paper presents a system, which is composed of a laser range finder and four artificial reflectors, for the three-dimensional (3D) localization of a mobile robot. In this system, it will be proved that the position and the heading angle of a mobile robot in a 3D space with respect to a reference frame can be determined provided that the four artificial reflectors are not installed in the same plane. Since the artificial reflectors cannot be treated as points in practice, the proposed localization procedure will be formulated as a nonlinear programming problem to account for the actual sizes of the artificial reflectors. To show the feasibility of the proposed method, experiments will be given for illustration.