Parameter Identification for Flexible Models Using Additional Sensors

The identification procedure of linear least squares used for the identification of rigid robot models assumes that the position signal of all degrees of freedom are known or can be measured. If the all degrees position of freedom including the corresponding velocities and accelerations are known, the dynamic model can be written as a linear set of equations with the dynamic parameters as unknowns. Generally only motor position and torque data is available. Therefore, measurements from freedom arising additional degrees from flexibilities are not readily available and consequently the linear least squares technique cannot be used for flexible robot models. Several authors suggest the application of additional sensors to measure the elastic deformations, e.g. link position, acceleration sensors, and/or velocity sensors or torque. First, an overview of identification techniques using these additional sensors will be given.

This presents an identification method for the dynamical parameters of simple mechanical systems with lumped elasticity. The parameters are calculated by using the solution of a weighted least squares system of an over determined system that is linear with regard to a minimal set of parameters and obtained by sampling the dynamic model along a trajectory. Two different cases are considered according the types of measurements available for identification. In the first case, it is assumed that measurements for the load and the motor position are available. In the second case, it is assumed that measurements for the load acceleration and the motor position are available.

Instead of the load position reconstruction by integration of the measured acceleration, they suggest differentiating the dynamic equations twice. However, problems come out for non-continuous terms like joint friction. The use chirp signal as excitation signal should decrease the influence of the dynamic behavior, which is represented by these non-differentiable terms, on the measured data.

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