Robot calibration without scaling

Abstract

Many engineering problems are studied through numerical schemes that use large matrices to mathematically describe the systems being analyzed. Some of the problems require iterative algorithms. In many cases the matrices used in these numerical schemes are found to be "ill-conditioned", or close to singularity. The amount of ill-conditioning is measured with a condition number. 111-conditioned matrices significantly slow, and usually prevent, convergence toward a solution when using iterative methods. Scaling is a common way of improving the condition number for a matrix. Researchers in other fields have developed specific methods of scaling matrices to improve the condition number. However, robotics researchers have not specifically addressed, in robotics literature, their approaches to improving the condition of matrices that are used in kinematic parameter identification (calibration). A new calibration method was developed that uses matrices with significantly better condition numbers than matrices used in standard calibration methods, and scaling of the kinematic parameters describing the robot is not required. This method was tested on rotational joint robots only. The key feature of this new method is that it takes advantage of the rotational kinematic parameters' independence from the translational kinematic parameters. This feature is utilized as a constraint that simplifies the identification technique. The method is similar to standard methods in that it is iterative. There are two steps to each iteration. In the first step, the translational parameters are solved separately in a closed form solution. In the second step, the rotational parameters are estimated using a new type of Jacobian matrix. This new Jacobian has a condition number that is significantly better than those derived from standard methods. Furthermore, the new method is easy to understand and implement.