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This paper presents a design methodology of a path following feedback control system using parametric curves for a cooperative transportation system with two car-like mobile robots. Specifically, the authors first present a numerical method for transforming the position and the orientation of the cooperative transportation system in the Cartesian coordinate system into those in a new coordinate system in which a parametric curve path is an axis and a straight line perpendicular to the tangent of the path is another axis. Especially, the kinematical equation of the cooperative transportation system is convertible to chained form in the new coordinate system. The authors secondly present a numerical method for calculating the second differential of the curvature of the parametric curve path which is much faster than an analytical method. These two numerical methods are embedded in the path following feedback control system, and it is possible to execute the two numerical methods in an effective control period for the path following feedback control system. The authors design a path following feedback control system using a parametric curve path, e.g., a twelve-order bezier path, for driving an experimental system developed, e.g., a cooperative transportation system with two tricycle mobile robots kinematically equivalent to the car-like mobile robots, into a garage in which clearance is tight. Such driving motion is reproduced with high reliability. Therefore, the validity of the designed path following feedback control system is verified experimentally.

Design of a Path Following Feedback Control System Using Parametric Curves for a Cooperative Transportation System with Two Car-like Mobile Robots