Identification of standard dynamic parameters of robots with positive definite inertia matrix

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Abstract
For any rigid robot, a set of 14 standard parameters characterises the dynamics of each of its links and joints. Only a subset of these standard parameters: the base parameters have unique values identified with the Inverse Dynamic Identification Model and linear least squares techniques (IDIM-LS). Moreover, some of the base parameters are poorly identified when their effect on the joint torques is too small. They can be eliminated, leading to a new subset of essential (base) parameters. However, the consistency of the identified values of the base or the essential parameters cannot be guaranteed, regarding to the loss of the positive definiteness of the robot inertia matrix. The past methods proposed to verify the physical consistency of the identified parameters, relies on complicated, time consuming computations and even leads to non-optimal LS parameters. We propose a method that overcomes these drawbacks, calculating the set of optimal LS standard parameters closest to a set of a priori consistent dynamic parameters obtained through CAD data given by the robot manufacturers. This is a straightforward method, which relies on the use of the Singular Value Decomposition (SVD), the Cholesky factorization and the linear least squares techniques. The method is experimentally validated on a Stäubli TX-40, which is a 6 Degrees of Freedom (DoF) industrial robot. This example enlighten a strong result: the essential base parameters, which have significant identified values with respect to their small relative standard deviation, are consistent.