A new objective function for robot calibration

Abstract

When using a robot, the operator usually desires to locate the tool accurately. To accomplish this, the operator should measure the tool position then use feedback to "drive" the manipulator in such a way that the tool position error becomes small. Unfortunately, with the current state of the art, position is difficult to measure. Sensors for making the required measurements are typically expensive and complex; hence, they cause the robot to run slowly and make robots economically unfeasible to use. To increase the robot's economic viability, they must be positioned accurately without the use of a tool position sensor. With current applications and teaching methods, robot accuracy is usually satisfactory; however, as robots attempt to be used where tight manufacturing tolerances are required and when off-line programming is desired, their open-loop position accuracy must be improved. In the present state of the art, tool position is determined by measuring the position of joint actuator motors and calculating where the tool must be given these measurements. The equations relating tool position to motor positions is called a model. When open-loop position accuracy is required, the model must be accurate. Unfortunately, modeling errors have been measured to be in excess of one inch. To improve the accuracy of the model, researchers use calibration. Calibration measures a small number of tool positions and their related motor positions then determines a "best fit" model to the measured data. Many researchers show that simple model identification procedures can reduce modeling errors significantly. The conventional calibration method used in nearly all research minimizes a least squares objective function representing model error. To date, little attention has been placed on the choice of objective function used in the calibration. This research points out some inherent problems of the conventional objective function and demonstrates that a better objective function exists that can improve the overall manipulator performance.