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9 PARAMETER ESTIMATION
To simulate a Delta-3 robot in Simulink one needs to choose parameters so the model becomes
as close as possible to the real robot. Therefore it is good to divide the parameters into different
parts for the different equipment used to control the robot. P1, P2, P3 and P4 contain the
parameters used in the different parts shown in Figure 9.1.
Figure 9.1, P1, P2, P3 and P4 are the parameterization for the
different blocks. Where “d” is the robot dynamics.
The parameters in P1 are given from the robot manufacture and are depending on the robots
physically structure such as the upper arms, forearms, base plate and the travelling plate. These
parameters are needed to be able to calculate the inverse and forward kinematics for the robot.
The parameters in P2 are given from the drive unit MC-4 which ELAU GmbH use to control
their motors. The configurations of these parameters are the same as the configuration in the
real MC-4s which are used at the real robot. P3 contains values given from the real robot
structure such as the weight of the different parts of the robot. P3 also contains the parameters
given in P1 and the torques given to the motors. The parameters in P3 are used in chapter 4.8.3
to be able to obtain the coupling effect between the arms which is given in Eq. 4.31.
The parameters in P4 are given from the motor model which is used to simulate the motors
which ELAU GmbH is using. The parameters are given from the data sheets from the motor
which is used on the real robot.
The parameters in P4 are also estimated with the Matlab function lsqnonlin to try to obtain
better dynamics in the Simulink motor model. lsqnonlin is used to solve nonlinear least-squares
curve fitting problems. In this case the curve fitting problem is between the Simulink model
output and the real robots output. Matlab tries to estimate the parameters which the user has
given as initial value so the curve fitting problem becomes minimized. But this function in
Matlab can’t find any better values for the parameters in P4 to be able to include more of the
dynamics from the real motor. The Matlab function only returns the same values as the initial
value. This could depend on that the nonlinear least-square curve fitting problem already is in a
minimum. And when Matlab tries to change the parameters it only finds values which makes
the non-linear curve fitting problem bigger instead of smaller.
Table 9-1 shows an overview of the parameters which are included in the different
parameterization parameters P1 (Kinematics), P2 (drive unit MC4), P3 (dynamic for real robot)
and P4 (Motor parameters).
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Public Report ELAU GmbH, Marktheidenfeld
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