Theory of kinematic modelling and numerical procedures for robot calibration

A robot calibration procedure is used to model, measure and identify the kinematic, actuator and static-mechanical characteristics of robots constructed of a sequence of rotary and prismatic joints. The chapter presents methods to build and determine optimal robot models for calibration. These methods are necessary not only because model parameters must be computed but also because there is a need for information about the reliability and significance of computed parameter values. Results from two different fields of research which are related to two different fields of mathematics are presented: A) First is a new approach to kinematic modeling which satisfies the requirements of completeness, minimality and model-continuity for all combinations of revolute and prismatic joints. It also allows the integration of an elastic deformation model. Joint transformations are selected from a set of 17 parametrizations: for each of them, model-continuity within their individual application range s has been shown by means of differential geometry. B) If actuator and elastic deformation models are included in the kinematic model for calibration, the numerical parameter identificaton problem must be modified in order to obtain usable und reliable results. Besides necessary scaling, a decision procedure has been developed allowing a reduced model to be selected which is optimized with respect to its numerical characteristics. The decision procedure uses singular value decomposition of the identification problem and sensitivity parameters which are derived from the covariance matrix.