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## Online Identification of Dynamical Robot Parameters

### Project Description

To achieve maximum accuracy and performance in robot control, mathematical models are used to predict dynamic coupling effects and nonlinearities of the robot. We have developed an on-line parameter identification scheme, and tested the algorithms with an experimental direct drive arm as well as with a geared driven industrial robot. In order to be able to apply the same algorithms to any industrial robot, we constrained ourselves to measured joint positions as the only sensor information.

The model of robot dynamics actually is linear in the parameters, where the parameters themselves are linear combinations of the physical parameters. The data functions, exciting the identification model, in general are nonlinear functions of the measured values.

The model of robot dynamics actually is linear in the parameters, where the parameters themselves are linear combinations of the physical parameters. The data functions, exciting the identification model, in general are nonlinear functions of the measured values.

Identification scheme.

Experimental direct drive arm EDDA.

When objects are grabbed, moved and released, parameter changes occur. Also friction may change with time, due to aging lubricants. Due to the linearity in the parameters, a simple model can be derived. The model error, which results from mismatched parameters (and from measurement noise or modelling errors) can be used as criterion for parameter adjustment.

One main problem can be seen in the next plot, where measured position, numerically derived velocity and acceleration signal are shown. It has been shown that the bias in identification, produced by noise can drasticly be reduced. It should be pointed out, that simply filtering the acceleration signal implies a change to the model equation. It yields an equation, which is -in a mathematical sense- not equivalent to the original model equation.

One main problem can be seen in the next plot, where measured position, numerically derived velocity and acceleration signal are shown. It has been shown that the bias in identification, produced by noise can drasticly be reduced. It should be pointed out, that simply filtering the acceleration signal implies a change to the model equation. It yields an equation, which is -in a mathematical sense- not equivalent to the original model equation.

Position and velocity.

Unfiltered acceleration.

Filtered acceleration.

The consequence of the disturbed acceleration signal can be seen in the next plots. The left one shows recursive least squares estimates in comparison to a reference method, which gives optimal estimates. Actually, the least squares method takes the measurement noise as a part of the information signal. The correct identification was done by applying a lowpass filter to the complete model.

Recursive least squares method.

Recursive instrumental variables method.

We have worked with both a differential model, as well as with an integral model, suggested by Gautier and Khalil, based on the energy in the system. This approach avoids the problems caused by the noisy acceleration signal, because the energy in a system only depends on the position and the velocity.

Since we do not intend to use online identification only during specially designed test movements but also during normal operation, it cannot be assumed, that identifiability conditions will always be optimal. On the contrary, it is much more likely, that good identifiability conditions will be the exception during normal operation. Therefore we are working on automatic selection of submodels to be identified, while the other parameters, not affected by the robot movement, are fixed to their former values.

Since we do not intend to use online identification only during specially designed test movements but also during normal operation, it cannot be assumed, that identifiability conditions will always be optimal. On the contrary, it is much more likely, that good identifiability conditions will be the exception during normal operation. Therefore we are working on automatic selection of submodels to be identified, while the other parameters, not affected by the robot movement, are fixed to their former values.

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