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Thomas Dehaeze 2020-02-18 13:58:08 +01:00
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@ -48,7 +48,7 @@ The global measurement and control schematic is shown in figure [[fig:control-sc
#+caption: Global Control Schematic for the Station
[[file:figs/control-schematic-nass.png]]
In this document, we develop and verify that the two green blocs are working.
In this document, are interesting by the "compute Sample Position w.r.t. Granite" bloc and we develop and verify that the two green blocs are working.
We suppose that we are able to measure perfectly the position of the sample with respect to the granite.
This means that we do not care about the bloc "Compute Sample Position w.r.t. Granite" that makes the transformation from the interferometer measurements to the position of the sample.
@ -57,6 +57,8 @@ This is actually done with a "transform sensor block" that outputs the x-y-z tra
Also, all the stages can be perfectly positioned.
First, in section [[sec:measurement_principle]], is explained how the measurement of the position of the sample with respect to the granite is performed (using Simscape blocs).
In section [[sec:compute_reference]], we verify that the function developed to compute the wanted pose (translation and orientation) of the sample with respect to the granite can be determined from the wanted position of each stage (translation stage, tilt stage, spindle and micro-hexapod). This corresponds to the bloc "Compute Wanted Sample Position w.r.t. Granite" in figure [[fig:control-schematic-nass]].
To do so, we impose a perfect displacement and all the stage, we perfectly measure the position of the sample with respect to the granite, and we verify that this measured position corresponds to the computed wanted pose of the sample.
@ -64,6 +66,20 @@ Then, in section [[sec:compute_pos_error]], we introduce some positioning error
The positioning error of the sample expressed with respect to the granite frame (the one measured) is expressed in a frame connected to the NASS top platform (corresponding to the green bloc "Compute Sample Position Error w.r.t. NASS" in figure [[fig:control-schematic-nass]]).
Then, we move the NASS such that it compensate for the positioning error that are expressed in the frame of the NASS, and we verify that the positioning error of the sample is well compensated.
* How do we measure the position of the sample with respect to the granite
<<sec:measurement_principle>>
A transform sensor block gives the translation and orientation of the follower frame with respect to the base frame.
The base frame is fixed to the granite and located at the initial sample location that defines the zero position.
The follower frame is attached to the sample (or more precisely to the reflector).
The outputs of the transform sensor are:
- the 3 translations x, y and z in meter
- the *rotation matrix* $\bm{R}$ that permits to rotate the base frame into the follower frame.
We can then determine extract other orientation conventions such that Euler angles or screw axis.
* Verify that the function to compute the reference pose is correct
<<sec:compute_reference>>
** Introduction :ignore: