Basis functions for use in direct calibration techniques to determine part-in-hand location

A common difficulty in implementing flexible automation is the complexity and lack of robustness of the intercalibration of all the components of the workcell and the part itself.; A novel approach to the calibration problem, called Direct Calibration, calibrates the entire assembly system—the robot, the sensors, and the parts to be assembled—in a single procedure. The relationship between feature information in sensor coordinates and the part location in robot coordinates is determined in three steps: calibration data are generated by using the robot to move the part to be assembled under the view of the sensors by known amounts; the best-fit mapping representing this assembly process is calculated; and this mapping is used in production to estimate the part locations from the current sensor data.; While this approach has been demonstrated to work very well in its current application, this research establishes which basis functions should be used in the Direct Calibration mapping for optimal process performance. Furthermore, this work generates a better understanding of the significance of the basis functions for the process performance.; “Perfect” basis functions are developed for the most common classes of parts. These perfect basis functions are broken down into their elementary terms and compared to the basis function set that was found to be suited best for a general application of Direct Calibration.; The limits to performance improvement of the Direct Calibration technique due to changes in basis functions for certain classes of parts are established in simulation.; A set of basis functions for the general application of Direct Calibration is recommended. This basis function set is shown to have wide applicability and high accuracy.; The performance potential of higher-order basis functions is evaluated in simulation.; An empirical technique for finding the optimal part-specific basis functions, without the need for a model of the part, is presented. This technique uses methods from experimental design and statistics and maximizes the performance of Direct Calibration for a specific part.