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This paper presents a new approach to identify the minimum dynamic parameters of robots using least squares techniques (LS) and a power model. Theoretical analysis is carried out from a filtering point of view and clearly shows the superiority of the power model over the energy one and over the dynamic identification model which has been used to carry out a classical ordinary LS estimation and a new weighted LS estimation. These results are checked from comparing experimental identification of the dynamic parameters of a planar scara prototype robot.

Offline robot dynamic identification methods are mostly based on the use of the inverse dynamic model, which is linear with respect to the dynamic parameters. This model is sampled while the robot is tracking reference trajectories that excite the system dynamics. This allows using linear least-squares techniques to estimate the parameters. The efficiency of this method has been proved through the experimental identification of many prototypes and industrial robots. However, this method requires the joint force/torque and position measurements and the estimate of the joint velocity and acceleration, through the bandpass filtering of the joint position at high sampling rates. The proposed new method called DIDIM requires only the joint force/torque measurement, which avoids the calculation of the velocity and acceleration by bandpass filtering of the measured position. It is a closed-loop output error method where the usual joint position output is replaced by the joint force/torque. It is based on a closed-loop simulation of the robot using the direct dynamic model, the same structure of the control law, and the same reference trajectory for both the actual and the simulated robot. The optimal parameters minimize the 2-norm of the error between the actual force/torque and the simulated force/torque. This is a nonlinear least-squares problem which is dramatically simplified using the inverse dynamic model to obtain an analytical expression of the simulated force/torque, linear in the parameters. A validation experiment on a two degree-of-freedom direct drive rigid robot shows that the new method is efficient

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This paper presents a new approach to the problem of determining the minimum set of inertial parameters of robots.The calculation is based on numerical QR and SVD factorizations and on scaling procedure of matrices. It proceeds in two steps : -at fmt the number of base parameters is determined, -then a set of base parameters is determined by eliminating some standard parameters which are regrouped to some others in linear relations.Different models, linear in the inertial parameters are used: a complete dynamic model, a simplified dynamic model and an energy model. The method is general, it can be applied to open loop, or graph structured robots. The algorithms are easy to implement. An application for the PUMA 560 robot is given.Exact dynamic model of robot is required to control or simulate its motion. The model is characterized by ten inertial parameters per link, which are called the standard inertial parameters.Because of the redundancy of this representation, there is an infinite sets of standard parameters which satisfies the dynamic model. In order to reduce the computational cost of the dynamic model and to facilitate the identification process, a minimum set of inertial parameters, which are called also base parameters, must be used to determine the dynamic model [l,. . .,a, Dynamic model, using Newton Euler or Lagrange, or energy formulation model, linear in the inertial parameters, can be used to study this problem. From a linear algebra point of view, this problem appears to be a rank deficiency problem.The study is carried out in two steps: -find the rank of a linear system, this gives the number of base parameters.-choose the base parameters from the standard ones by eliminating some of them which are regrouped to the others in linear relations, in this step the regrouping relations will be determined. Previous work;Several authors have studied the problem using two principal approaches: i-Symbolic approach:-In [l, 2, 3, 41 a case by case method using the symbolic expression of the dynamic model have been presented, -In [5, 61, we have presented a general and direct method to aetermine most of the set of minimum inertial parametemof serial or tree structured robots, using the energy formulation. -At the same time similar results concerning the special case of robots whose successive axes are perpendicular or parallel have been given by Mayeda et al.[7,8].ii-Numerical approach: -Atkenson et all [9] used ridge regression and singular value decomposition, SVD, to solve the rank deficiency problem. The dynamic model using Newton Euler formulation was used.-Sheu and Walker [lo] used SVD also on the energy model.These two methods did not give explicitely the minimum set of inertial parameters, nor the linear relations which define them. In this paper we propose to use the QR decomposition, which serve equally well as the SVD and at less cost [l 1, pl l-231, and the SVD itself to solve the deficiency problem. We find the number of base parameters and we give a method to define them. Then we give an algor...

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