From b3e630459a1f57df174b2f8e62004859290bb4df Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Wed, 11 Dec 2019 09:33:46 +0100 Subject: [PATCH] Update the way the micro-hexapod is initialize (pitch-roll-yaw) Next verified that the function to compute the wanted sample position is working => yes --- metrology/index.html | 313 +++++++++++------- metrology/index.org | 78 +++-- simscape/index.org | 103 ++++-- simscape/sim_nano_station_disp.slx | Bin 35116 -> 34891 bytes simscape/sim_nano_station_metrology.slx | Bin 35552 -> 35899 bytes simscape_subsystems/hexapod_leg.slx | Bin 26042 -> 26789 bytes .../micro_hexapod_rigid_simple.slx | Bin 56835 -> 56839 bytes simscape_subsystems/nass_references.slx | Bin 29882 -> 31205 bytes src/computeReferencePose.m | 34 +- src/initializeMicroHexapod.m | 24 +- src/initializeReferences.m | 49 ++- 11 files changed, 380 insertions(+), 221 deletions(-) diff --git a/metrology/index.html b/metrology/index.html index 45057fb..5292ab0 100644 --- a/metrology/index.html +++ b/metrology/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Metrology @@ -262,7 +262,10 @@ for the JavaScript code in this tag. TeX: { equationNumbers: {autoNumber: "AMS"}, MultLineWidth: "85%", TagSide: "right", - TagIndent: ".8em" + TagIndent: ".8em", + Macros: { + bm: ["{\\boldsymbol #1}",1], + } } }); @@ -280,24 +283,25 @@ for the JavaScript code in this tag.

Table of Contents

@@ -310,29 +314,63 @@ Also, all the stages can be perfectly positioned.

-In section 1, 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). +First, in section 1, is explained how the measurement of the position of the sample with respect to the granite is performed. +

+ +

+In section 2, 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). 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.

-Then, in section 2, we introduce some positioning error in the position stages. +Then, in section 3, we introduce some positioning error in the position stages. 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. Finally, 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.

-
-

1 Verify that the function to compute the reference pose is correct

+
+

1 How do we measure the position of the sample with respect to the granite

- + +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. +

+
+
+ +
+

2 Verify that the function to compute the reference pose is correct

+
+

+

The goal here is to perfectly move the station and verify that there is no mismatch between the metrology measurement and the computation of the reference pose.

-
-

1.1 Prepare the Simulation

-
+
+

2.1 Prepare the Simulation

+

We load the configuration.

@@ -349,6 +387,23 @@ We set a small StopTime.
+

+We initialize all the stages. +

+
+
initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+initializeNanoHexapod(struct('actuator', 'piezo'));
+initializeSample(struct('mass', 50));
+
+
+

We setup the reference path to be constant.

@@ -359,17 +414,17 @@ We setup the reference path to be constant. 'Dy_amplitude', 5e-3, ... % Amplitude of the displacement [m] 'Dy_period', 1, ... % Period of the displacement [s] 'Ry_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal" - 'Ry_amplitude', -1, ... % Amplitude [deg] + 'Ry_amplitude', -1*pi/180, ... % Amplitude [rad] 'Ry_period', 10, ... % Period of the displacement [s] 'Rz_type', 'constant', ... % Either "constant" / "rotating" - 'Rz_amplitude', -135, ... % Initial angle [deg] + 'Rz_amplitude', -135*pi/180, ... % Initial angle [rad] 'Rz_period', 1, ... % Period of the rotating [s] 'Dh_type', 'constant', ... % For now, only constant is implemented - 'Dh_pos', [0; 0; 0; -3; 1; 3], ... % Initial position [m,m,m,deg,deg,deg] of the top platform + 'Dh_pos', [0.01; 0.02; -0.03; -3*pi/180; 1*pi/180; 3*pi/180], ... % Initial position [m,m,m,rad,rad,rad] of the top platform 'Rm_type', 'constant', ... % For now, only constant is implemented 'Rm_pos', [0, pi]', ... % Initial position of the two masses 'Dn_type', 'constant', ... % For now, only constant is implemented - 'Dn_pos', [0; 0; 0; 0; 0; 0] ... % Initial position [m,m,m,deg,deg,deg] of the top platform + 'Dn_pos', [1e-3; 2e-3; 3e-3; 1*pi/180; 0; 1*pi/180] ... % Initial position [m,m,m,rad,rad,rad] of the top platform ); initializeReferences(opts); @@ -384,6 +439,7 @@ No position error for now (perfect positioning). Rye = 0; % [rad] Rze = 0; % [rad] Dhe = zeros(6,1); % [m,rad] +Dne = zeros(6,1); % [m,rad]
@@ -397,9 +453,9 @@ And we run the simulation.
-
-

1.2 Verify that the pose of the sample is the same as the computed one

-
+
+

2.2 Verify that the pose of the sample is the same as the computed one

+

Let's denote:

@@ -413,8 +469,8 @@ Let's denote: We have then computed:

    -
  • \({}^W\boldsymbol{T}_R\) which corresponds to the wanted pose of the sample with respect to the granite
    • -
  • \({}^W\boldsymbol{T}_M\) which corresponds to the measured pose of the sample with respect to the granite
    • +
  • \({}^W\bm{T}_R\) which corresponds to the wanted pose of the sample with respect to the granite
    • +
  • \({}^W\bm{T}_M\) which corresponds to the measured pose of the sample with respect to the granite

@@ -422,10 +478,9 @@ We load the reference and we compute the desired trajectory of the sample in the 

n = length(Dref.Dy.Time);
-
 WTr = zeros(4, 4, n);
 for i = 1:n
-  WTr(:, :, i) = computeReferencePose(Dref.Dy.Data(i), Dref.Ry.Data(i), Dref.Rz.Data(i), Dref.Dh.Data(i,:));
+  WTr(:, :, i) = computeReferencePose(Dref.Dy.Data(i), Dref.Ry.Data(i), Dref.Rz.Data(i), Dref.Dh.Data(i,:), Dref.Dn.Data(i,:));
 end
@@ -445,13 +500,13 @@ WTm( @@ -463,21 +518,21 @@ WTr( WTr(1:3, 4, end)-WTm(1:3, 4, end) ans = - 5.38287405101034e-15 - 9.42822209193395e-15 - -7.25141518012618e-16 + 1.8027246362351e-14 + 1.40408518145563e-14 + 6.93889390390723e-17 WTr(1:3, 1:3, end)'*WTm(1:3, 1:3, end)-eye(3) ans = - 1.53210777398272e-14 -1.60173523749974e-14 -7.42461647718073e-16 - 1.60683098771042e-14 1.53210777398272e-14 -2.33146835171283e-15 - -3.95516952522712e-16 -1.72084568816899e-15 9.2370555648813e-14 + 1.59872115546023e-14 -1.56629266848118e-14 -3.71230823859037e-16 + 1.56742023874057e-14 1.59872115546023e-14 -2.12330153459561e-15 + -1.14144804719274e-15 -5.51642065360625e-16 9.28146448586631e-14
-
-

1.3 Conclusion

-
+
+

2.3 Conclusion

+

We are able to compute the wanted position and orientation of the sample. @@ -489,11 +544,11 @@ Both the measurement and the theory gives the same result.

-
-

2 Verify that the function to convert the position error in the frame fixed to the nano-hexapod is working

-
+
+

3 Verify that the function to convert the position error in the frame fixed to the nano-hexapod is working

+

- +

We now introduce some positioning error in the stage. @@ -504,9 +559,9 @@ This will induce a global positioning error of the sample with respect to the de We want to verify that we are able to measure this positioning error and convert it in the frame attached to the Nano-hexapod.

-
-

2.1 Prepare the Simulation

-
+
+

3.1 Prepare the Simulation

+

We load the configuration.

@@ -532,15 +587,15 @@ We setup the reference path to be constant. 'Dy_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal" 'Dy_amplitude', 0, ... % Amplitude of the displacement [m] 'Ry_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal" - 'Ry_amplitude', 0, ... % Amplitude [deg] + 'Ry_amplitude', 0, ... % Amplitude [rad] 'Rz_type', 'constant', ... % Either "constant" / "rotating" - 'Rz_amplitude', 180, ... % Initial angle [deg] + 'Rz_amplitude', 0*pi/180, ... % Initial angle [rad] 'Dh_type', 'constant', ... % For now, only constant is implemented - 'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,deg,deg,deg] of the top platform + 'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,rad,rad,rad] of the top platform 'Rm_type', 'constant', ... % For now, only constant is implemented 'Rm_pos', [0, pi]', ... % Initial position of the two masses 'Dn_type', 'constant', ... % For now, only constant is implemented - 'Dn_pos', [0; 0; 0; 0; 0; 0] ... % Initial position [m,m,m,deg,deg,deg] of the top platform + 'Dn_pos', [0; 0; 0; 0; 0; 0] ... % Initial position [m,m,m,rad,rad,rad] of the top platform ); initializeReferences(opts); @@ -554,7 +609,10 @@ Now we introduce some positioning error. 
Dye = 0; % [m]
 Rye = 0; % [rad]
 Rze = 0; % [rad]
-Dhe = [1e-3 ; 3e-3 ; 2e-3 ; 1e-3 ; 2e-3 ; 3e-3]; % [m,rad]
+Dhe = [1e-3 ; 0 ; 2e-3 ; 1e-3 ; 0 ; 3e-3]; % [m,rad]
+% Dhe = zeros(6,1);
+% Dne = [1e-3 ; 0 ; 2e-3 ; 0 ; 3e-3 ; 1e-3]; % [m,rad]
+Dne = zeros(6,1);
@@ -568,45 +626,44 @@ And we run the simulation.
-
-

2.2 Compute the wanted pose of the sample in the NASS Base from the metrology and the reference

-
+
+

3.2 Compute the wanted pose of the sample in the NASS Base from the metrology and the reference

+

Now that we have introduced some positioning error, the computed wanted pose and the measured pose will not be the same.

-We would like to compute \({}^M\boldsymbol{T}_R\) which corresponds to the wanted pose of the sample expressed in a frame attached to the top platform of the nano-hexapod (frame \(\{M\}\)). +We would like to compute \({}^M\bm{T}_R\) which corresponds to the wanted pose of the sample expressed in a frame attached to the top platform of the nano-hexapod (frame \(\{M\}\)).

We have:

\begin{align} - {}^M\boldsymbol{T}_R &= {}^M\boldsymbol{T}_W \cdot {}^W\boldsymbol{T}_R \\ - &= {}^W{\boldsymbol{T}_M}^{-1} \cdot {}^W\boldsymbol{T}_R + {}^M\bm{T}_R &= {}^M\bm{T}_W \cdot {}^W\bm{T}_R \\ + &= {}^W{\bm{T}_M}^{-1} \cdot {}^W\bm{T}_R \end{align}

-The top platform of the nano-hexapod is considered to be rigidly connected to the sample, thus, \({}^M\boldsymbol{T}_R\) corresponds to the pose error of the sample with respect to the nano-hexapod platform. +The top platform of the nano-hexapod is considered to be rigidly connected to the sample, thus, \({}^M\bm{T}_R\) corresponds to the pose error of the sample with respect to the nano-hexapod platform.

-We load the reference and we compute the desired trajectory of the sample in the form of an homogeneous transformation matrix \({}^W\boldsymbol{T}_R\). +We load the reference and we compute the desired trajectory of the sample in the form of an homogeneous transformation matrix \({}^W\bm{T}_R\). 

n = length(Dref.Dy.Time);
-
 WTr = zeros(4, 4, n);
 for i = 1:n
-  WTr(:, :, i) = computeReferencePose(Dref.Dy.Data(i), Dref.Ry.Data(i), Dref.Rz.Data(i), Dref.Dh.Data(i,:));
+  WTr(:, :, i) = computeReferencePose(Dref.Dy.Data(i), Dref.Ry.Data(i), Dref.Rz.Data(i), Dref.Dh.Data(i,:), Dref.Dn.Data(i,:));
 end

We also measure in simulation the pose of the sample with respect to the granite. -From that we can compute the homogeneous transformation matrix \({}^W\boldsymbol{T}_M\). +From that we can compute the homogeneous transformation matrix \({}^W\bm{T}_M\). 

n = length(Dsm.R.Time);
@@ -620,18 +677,19 @@ WTm(
 
MTr = zeros(4, 4, n);
@@ -644,6 +702,22 @@ Finally, we compute \({}^M\boldsymbol{T}_R\).
 

 Verify that the pose error corresponds to the positioning error of the stages.
 

+

+
MTr(1:3, 1:3, end)
+Rx = [1 0       0;
+      0 cos(Erx) -sin(Erx);
+      0 sin(Erx)  cos(Erx)];
+
+Ry = [ cos(Ery) 0 sin(Ery);
+      0      1 0;
+      -sin(Ery) 0 cos(Ery)];
+
+Rz = [cos(Erz) -sin(Erz) 0;
+      sin(Erz)  cos(Erz) 0;
+      0       0      1];
+

+

+
 
 
 
@@ -677,10 +751,10 @@ Verify that the pose error corresponds to the positioning error of the stages.
 
-
+
-
+
@@ -688,14 +762,14 @@ Verify that the pose error corresponds to the positioning error of the stages.
 
 
-

-
2.3 Verify that be imposing the error motion on the nano-hexapod, we indeed have zero error at the end

-

+

+
3.3 Verify that be imposing the error motion on the nano-hexapod, we indeed have zero error at the end

+

 

-We now impose a displacement of the nano hexapod corresponding to the measured position error.
+We now keep the wanted pose but we impose a displacement of the nano hexapod corresponding to the measured position error.
 

 

-
opts.Dn_pos = [Edx, Edy, Edz, 180/pi*Erx, 180/pi*Ery, 180/pi*Erz]';
+
opts.Dn_pos = [Edx, Edy, Edz, Erx, Ery, Erz]';
 initializeReferences(opts);
 

 

@@ -709,21 +783,12 @@ And we run the simulation.
 

 
 

-We load the reference and we compute the desired trajectory of the sample in the form of an homogeneous transformation matrix \({}^WT_R\).
+We keep the old computed computed reference pose \({}^W\bm{T}_r\) even though we have change the nano hexapod reference, but this is not a real wanted reference but rather a adaptation to reject the positioning errors.
 

-

-
n = length(Dref.Dy.Time);
-
-WTr = zeros(4, 4, n);
-for i = 1:n
-  WTr(:, :, i) = computeReferencePose(Dref.Dy.Data(i), Dref.Ry.Data(i), Dref.Rz.Data(i), Dref.Dh.Data(i,:));
-end
-

-

 
 

 As the displacement is perfect, we also measure in simulation the pose of the sample with respect to the granite.
-From that we can compute the homogeneous transformation matrix \({}^WT_M\).
+From that we can compute the homogeneous transformation matrix \({}^W\bm{T}_M\).
 

 

 
n = length(Dsm.R.Time);
@@ -735,7 +800,7 @@ WTm(
 
MTr = zeros(4, 4, n);
@@ -780,21 +845,21 @@ Verify that the pose error is small.
 

-
-
-
-
-
-
+
+
+
+
+
+

 Error
 -1.0e-03-3.0e-031.0e-06
 -2.0e-03
 -1.0e-03-2.0e-033.0e-06
 -3.0e-03
 

 
 
 

 Error1.2e-163.3e-162.3e-16-6.2e-171.1e-162.2e-16-3.0e-09-1.0e-093.0e-092.0e-09-1.0e-093.0e-09
-
-

2.4 Conclusion

-
+
+

3.4 Conclusion

+

Indeed, we are able to convert the position error in the frame of the NASS and then compensate these errors with the NASS. @@ -805,15 +870,15 @@ Indeed, we are able to convert the position error in the frame of the NASS and t

-
-

3 Functions

-
+
+

4 Functions

+
-
-

3.1 computeReferencePose

-
+
+

4.1 computeReferencePose

+

- +

@@ -821,13 +886,17 @@ This Matlab function is accessible here

-
function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh)
+
function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
 % computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample
 %
-% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh)
+% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
 %
 % Inputs:
-%    - Dy, Ry, Rz, Dh -
+%    - Dy - Reference of the Translation Stage [m]
+%    - Ry - Reference of the Tilt Stage [rad]
+%    - Rz - Reference of the Spindle [rad]
+%    - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad]
+%    - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad]
 %
 % Outputs:
 %    - WTr -
@@ -869,10 +938,30 @@ This Matlab function is accessible here
         0 0 1 Dh(3) ;
         0 0 0 1 ];
 
-  Rh(1:3, 1:3) = Rhx*Rhy*Rhz;
+  Rh(1:3, 1:3) = Rhz*Rhy*Rhx;
+
+  %% Nano-Hexapod
+  Rnx = [1 0           0;
+         0 cos(Dn(4)) -sin(Dn(4));
+         0 sin(Dn(4))  cos(Dn(4))];
+
+  Rny = [ cos(Dn(5)) 0 sin(Dn(5));
+         0           1 0;
+         -sin(Dn(5)) 0 cos(Dn(5))];
+
+  Rnz = [cos(Dn(6)) -sin(Dn(6)) 0;
+         sin(Dn(6))  cos(Dn(6)) 0;
+         0           0          1];
+
+  Rn = [1 0 0 Dn(1) ;
+        0 1 0 Dn(2) ;
+        0 0 1 Dn(3) ;
+        0 0 0 1 ];
+
+  Rn(1:3, 1:3) = Rnx*Rny*Rnz;
 
   %% Total Homogeneous transformation
-  WTr = Rty*Rry*Rrz*Rh;
+  WTr = Rty*Rry*Rrz*Rh*Rn;
 end
@@ -882,7 +971,7 @@ This Matlab function is accessible here

Author: Dehaeze Thomas

-

Created: 2019-12-06 ven. 12:02

+

Created: 2019-12-11 mer. 09:33

Validate

diff --git a/metrology/index.org b/metrology/index.org index 243325e..45f9388 100644 --- a/metrology/index.org +++ b/metrology/index.org @@ -64,7 +64,7 @@ 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 $\boldsymbol{R}$ that permits to rotate the base frame into the follower frame. +- 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. @@ -101,6 +101,20 @@ We set a small =StopTime=. set_param(conf_simscape, 'StopTime', '0.5'); #+end_src +We initialize all the stages. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); + initializeNanoHexapod(struct('actuator', 'piezo')); + initializeSample(struct('mass', 50)); +#+end_src + We setup the reference path to be constant. #+begin_src matlab opts = struct( ... @@ -115,11 +129,11 @@ We setup the reference path to be constant. 'Rz_amplitude', -135*pi/180, ... % Initial angle [rad] 'Rz_period', 1, ... % Period of the rotating [s] 'Dh_type', 'constant', ... % For now, only constant is implemented - 'Dh_pos', [0; 0; 0; -3*pi/180; 1*pi/180; 3*pi/180], ... % Initial position [m,m,m,rad,rad,rad] of the top platform + 'Dh_pos', [0.01; 0.02; -0.03; -3*pi/180; 1*pi/180; 3*pi/180], ... % Initial position [m,m,m,rad,rad,rad] of the top platform 'Rm_type', 'constant', ... % For now, only constant is implemented 'Rm_pos', [0, pi]', ... % Initial position of the two masses 'Dn_type', 'constant', ... % For now, only constant is implemented - 'Dn_pos', [1e-3; 0; 0; 1*pi/180; 0; 1*pi/180] ... % Initial position [m,m,m,rad,rad,rad] of the top platform + 'Dn_pos', [1e-3; 2e-3; 3e-3; 1*pi/180; 0; 1*pi/180] ... % Initial position [m,m,m,rad,rad,rad] of the top platform ); initializeReferences(opts); @@ -146,8 +160,8 @@ Let's denote: - $\{M\}$ the frame corresponding to the measured pose of the sample We have then computed: -- ${}^W\boldsymbol{T}_R$ which corresponds to the wanted pose of the sample with respect to the granite -- ${}^W\boldsymbol{T}_M$ which corresponds to the measured pose of the sample with respect to the granite +- ${}^W\bm{T}_R$ which corresponds to the wanted pose of the sample with respect to the granite +- ${}^W\bm{T}_M$ which corresponds to the measured pose of the sample with respect to the granite We load the reference and we compute the desired trajectory of the sample in the form of an homogeneous transformation matrix ${}^WT_R$. #+begin_src matlab @@ -169,11 +183,11 @@ From that we can compute the homogeneous transformation matrix ${}^WT_M$. #+end_src As the simulation is perfect (no measurement error and no motion error), we should have that -\[ {}^W\boldsymbol{T}_R = {}^W\boldsymbol{T}_M \] +\[ {}^W\bm{T}_R = {}^W\bm{T}_M \] Or are least: -\[ {}^W\boldsymbol{T}_R(1:3, 4) = {}^W\boldsymbol{T}_M(1:3, 4) \] -\[ {}^W\boldsymbol{R}_R^t \cdot {}^W\boldsymbol{R}_M = \boldsymbol{I}_3 \] +\[ {}^W\bm{T}_R(1:3, 4) = {}^W\bm{T}_M(1:3, 4) \] +\[ {}^W\bm{R}_R^t \cdot {}^W\bm{R}_M = \bm{I}_3 \] #+begin_src matlab :results output replace WTr(1:3, 4, end)-WTm(1:3, 4, end) @@ -184,14 +198,14 @@ Or are least: #+begin_example WTr(1:3, 4, end)-WTm(1:3, 4, end) ans = - -8.47173893536723e-15 - -1.38430933382949e-15 - -8.88361324636402e-16 + 1.8027246362351e-14 + 1.40408518145563e-14 + 6.93889390390723e-17 WTr(1:3, 1:3, end)'*WTm(1:3, 1:3, end)-eye(3) ans = - 2.66453525910038e-15 1.19459143341844e-15 -1.07098845850834e-17 - -1.185456383777e-15 2.66453525910038e-15 2.9392720896082e-16 - 1.07732002978906e-17 -2.9392720896082e-16 2.88657986402541e-15 + 1.59872115546023e-14 -1.56629266848118e-14 -3.71230823859037e-16 + 1.56742023874057e-14 1.59872115546023e-14 -2.12330153459561e-15 + -1.14144804719274e-15 -5.51642065360625e-16 9.28146448586631e-14 #+end_example ** Conclusion @@ -276,17 +290,17 @@ And we run the simulation. ** Compute the wanted pose of the sample in the NASS Base from the metrology and the reference Now that we have introduced some positioning error, the computed wanted pose and the measured pose will not be the same. -We would like to compute ${}^M\boldsymbol{T}_R$ which corresponds to the wanted pose of the sample expressed in a frame attached to the top platform of the nano-hexapod (frame $\{M\}$). +We would like to compute ${}^M\bm{T}_R$ which corresponds to the wanted pose of the sample expressed in a frame attached to the top platform of the nano-hexapod (frame $\{M\}$). We have: \begin{align} - {}^M\boldsymbol{T}_R &= {}^M\boldsymbol{T}_W \cdot {}^W\boldsymbol{T}_R \\ - &= {}^W{\boldsymbol{T}_M}^{-1} \cdot {}^W\boldsymbol{T}_R + {}^M\bm{T}_R &= {}^M\bm{T}_W \cdot {}^W\bm{T}_R \\ + &= {}^W{\bm{T}_M}^{-1} \cdot {}^W\bm{T}_R \end{align} -The top platform of the nano-hexapod is considered to be rigidly connected to the sample, thus, ${}^M\boldsymbol{T}_R$ corresponds to the pose error of the sample with respect to the nano-hexapod platform. +The top platform of the nano-hexapod is considered to be rigidly connected to the sample, thus, ${}^M\bm{T}_R$ corresponds to the pose error of the sample with respect to the nano-hexapod platform. -We load the reference and we compute the desired trajectory of the sample in the form of an homogeneous transformation matrix ${}^W\boldsymbol{T}_R$. +We load the reference and we compute the desired trajectory of the sample in the form of an homogeneous transformation matrix ${}^W\bm{T}_R$. #+begin_src matlab n = length(Dref.Dy.Time); WTr = zeros(4, 4, n); @@ -296,7 +310,7 @@ We load the reference and we compute the desired trajectory of the sample in the #+end_src We also measure in simulation the pose of the sample with respect to the granite. -From that we can compute the homogeneous transformation matrix ${}^W\boldsymbol{T}_M$. +From that we can compute the homogeneous transformation matrix ${}^W\bm{T}_M$. #+begin_src matlab n = length(Dsm.R.Time); WTm = zeros(4, 4, n); @@ -307,17 +321,17 @@ From that we can compute the homogeneous transformation matrix ${}^W\boldsymbol{ The *inverse of the transformation matrix* can be obtain by (it is less computation intensive than doing a full inverse) \begin{equation} - {}^B\boldsymbol{T}_A = {}^A\boldsymbol{T}_B^{-1} = + {}^B\bm{T}_A = {}^A\bm{T}_B^{-1} = \left[ \begin{array}{ccc|c} & & & \\ - & {}^A\boldsymbol{R}_B^T & & -{}^A \boldsymbol{R}_B^T {}^A\boldsymbol{P}_{O_B} \\ + & {}^A\bm{R}_B^T & & -{}^A \bm{R}_B^T {}^A\bm{P}_{O_B} \\ & & & \\ \hline 0 & 0 & 0 & 1 \\ \end{array} \right] \end{equation} -Finally, we compute ${}^M\boldsymbol{T}_R$. +Finally, we compute ${}^M\bm{T}_R$. #+begin_src matlab MTr = zeros(4, 4, n); for i = 1:n @@ -372,10 +386,10 @@ And we run the simulation. sim('simscape/sim_nano_station_metrology.slx'); #+end_src -We keep the old computed computed reference pose ${}^W\boldsymbol{T}_r$ even though we have change the nano hexapod reference, but this is not a real wanted reference but rather a adaptation to reject the positioning errors. +We keep the old computed computed reference pose ${}^W\bm{T}_r$ even though we have change the nano hexapod reference, but this is not a real wanted reference but rather a adaptation to reject the positioning errors. As the displacement is perfect, we also measure in simulation the pose of the sample with respect to the granite. -From that we can compute the homogeneous transformation matrix ${}^W\boldsymbol{T}_M$. +From that we can compute the homogeneous transformation matrix ${}^W\bm{T}_M$. #+begin_src matlab n = length(Dsm.R.Time); WTm = zeros(4, 4, n); @@ -384,7 +398,7 @@ From that we can compute the homogeneous transformation matrix ${}^W\boldsymbol{ WTm(4, 4, :) = 1; #+end_src -Finally, we compute ${}^M\boldsymbol{T}_R$. +Finally, we compute ${}^M\bm{T}_R$. #+begin_src matlab MTr = zeros(4, 4, n); for i = 1:n @@ -437,7 +451,7 @@ This Matlab function is accessible [[file:src/computeReferencePose.m][here]]. % - Dy - Reference of the Translation Stage [m] % - Ry - Reference of the Tilt Stage [rad] % - Rz - Reference of the Spindle [rad] - % - Dh - Reference of the Micro Hexapod [m, m, m, rad, rad, rad] + % - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad] % - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad] % % Outputs: @@ -480,7 +494,7 @@ This Matlab function is accessible [[file:src/computeReferencePose.m][here]]. 0 0 1 Dh(3) ; 0 0 0 1 ]; - Rh(1:3, 1:3) = Rhx*Rhy*Rhz; + Rh(1:3, 1:3) = Rhz*Rhy*Rhx; %% Nano-Hexapod Rnx = [1 0 0; @@ -534,8 +548,8 @@ Let's define the following frames: The origin of $T$ is $O_T$ and is the wanted position of the sample. Thus: -- the *measurement* of the position of the sample corresponds to ${}^W O_S = \begin{bmatrix} {}^WP_{x,m} & {}^WP_{y,m} & {}^WP_{z,m} \end{bmatrix}^T$ in translation and to $\theta_m {}^W\boldsymbol{s}_m = \theta_m \cdot \begin{bmatrix} {}^Ws_{x,m} & {}^Ws_{y,m} & {}^Ws_{z,m} \end{bmatrix}^T$ in rotations -- the *wanted position* of the sample expressed w.r.t. the granite is ${}^W O_T = \begin{bmatrix} {}^WP_{x,r} & {}^WP_{y,r} & {}^WP_{z,r} \end{bmatrix}^T$ in translation and to $\theta_r {}^W\boldsymbol{s}_r = \theta_r \cdot \begin{bmatrix} {}^Ws_{x,r} & {}^Ws_{y,r} & {}^Ws_{z,r} \end{bmatrix}^T$ in rotations +- the *measurement* of the position of the sample corresponds to ${}^W O_S = \begin{bmatrix} {}^WP_{x,m} & {}^WP_{y,m} & {}^WP_{z,m} \end{bmatrix}^T$ in translation and to $\theta_m {}^W\bm{s}_m = \theta_m \cdot \begin{bmatrix} {}^Ws_{x,m} & {}^Ws_{y,m} & {}^Ws_{z,m} \end{bmatrix}^T$ in rotations +- the *wanted position* of the sample expressed w.r.t. the granite is ${}^W O_T = \begin{bmatrix} {}^WP_{x,r} & {}^WP_{y,r} & {}^WP_{z,r} \end{bmatrix}^T$ in translation and to $\theta_r {}^W\bm{s}_r = \theta_r \cdot \begin{bmatrix} {}^Ws_{x,r} & {}^Ws_{y,r} & {}^Ws_{z,r} \end{bmatrix}^T$ in rotations ** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) @@ -655,7 +669,7 @@ Let's compute the corresponding orientation using screw axis. We then obtain the orientation measurement in the form of screw coordinate $\theta_m ({}^Ws_{x,m},\ {}^Ws_{y,m},\ {}^Ws_{z,m})^T$ where: - $\theta_m = \cos^{-1} \frac{\text{Tr}(R) - 1}{2}$ -- ${}^W\boldsymbol{s}_m$ is the eigen vector of the rotation matrix $R$ corresponding to the eigen value $\lambda = 1$ +- ${}^W\bm{s}_m$ is the eigen vector of the rotation matrix $R$ corresponding to the eigen value $\lambda = 1$ #+begin_src matlab thetam = acos((trace(STw(1:3, 1:3))-1)/2); % [rad] @@ -675,7 +689,7 @@ We then obtain the orientation measurement in the form of screw coordinate $\the The wanted position expressed with respect to the granite is ${}^WO_T$ and the measured position with respect to the granite is ${}^WO_S$, thus the *position error* expressed in $\{W\}$ is \[ {}^W E = {}^W O_T - {}^W O_S \] The same is true for rotations: -\[ \theta_\epsilon {}^W\boldsymbol{s}_\epsilon = \theta_r {}^W\boldsymbol{s}_r - \theta_m {}^W\boldsymbol{s}_m \] +\[ \theta_\epsilon {}^W\bm{s}_\epsilon = \theta_r {}^W\bm{s}_r - \theta_m {}^W\bm{s}_m \] #+begin_src matlab WPe = WPr - WPm; diff --git a/simscape/index.org b/simscape/index.org index 7909dc4..ee72cb4 100644 --- a/simscape/index.org +++ b/simscape/index.org @@ -755,8 +755,7 @@ This Matlab function is accessible [[file:../src/runSimulation.m][here]]. 'time', 'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', 'K'); end #+end_src -* Initialize Elements -<> +* Helping Functions ** Experiment :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeExperiment.m @@ -797,7 +796,6 @@ This Matlab function is accessible [[file:../src/initializeExperiment.m][here]]. :header-args:matlab+: :comments org :mkdirp yes :header-args:matlab+: :eval no :results none :END: - <> This Matlab function is accessible [[file:../src/initializeInputs.m][here]]. @@ -817,7 +815,7 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]]. 'Rz_amplitude', 0, ... % Initial angle [rad] 'Rz_period', 1, ... % Period of the rotating [s] 'Dh_type', 'constant', ... % For now, only constant is implemented - 'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,rad,rad,rad] of the top platform + 'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles) 'Rm_type', 'constant', ... % For now, only constant is implemented 'Rm_pos', [0; pi], ... % Initial position of the two masses 'Dn_type', 'constant', ... % For now, only constant is implemented @@ -887,14 +885,37 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]]. %% Micro-Hexapod t = [0, Ts]; Dh = zeros(length(t), 6); + Dhl = zeros(length(t), 6); switch opts.Dh_type case 'constant' Dh = [opts.Dh_pos, opts.Dh_pos]; + + load('./mat/stages.mat', 'micro_hexapod'); + + AP = [opts.Dh_pos(1) ; opts.Dh_pos(2) ; opts.Dh_pos(3)]; + + tx = opts.Dh_pos(4); + ty = opts.Dh_pos(5); + tz = opts.Dh_pos(6); + + ARB = [cos(tz) -sin(tz) 0; + sin(tz) cos(tz) 0; + 0 0 1]*... + [ cos(ty) 0 sin(ty); + 0 1 0; + -sin(ty) 0 cos(ty)]*... + [1 0 0; + 0 cos(tx) -sin(tx); + 0 sin(tx) cos(tx)]; + + [Dhl] = inverseKinematicsHexapod(micro_hexapod, AP, ARB); + Dhl = [Dhl, Dhl]; otherwise warning('Dh_type is not set correctly'); end Dh = struct('time', t, 'signals', struct('values', Dh)); + Dhl = struct('time', t, 'signals', struct('values', Dhl)); %% Axis Compensation - Rm t = [0, Ts]; @@ -914,7 +935,7 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]]. Dn = struct('time', t, 'signals', struct('values', Dn)); %% Save - save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Rm', 'Dn', 'Ts'); + save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts'); end #+end_src @@ -1108,6 +1129,42 @@ This Matlab function is accessible [[file:../src/initializeInputs.m][here]]. end #+end_src +** Inverse Kinematics of the Hexapod +:PROPERTIES: +:header-args:matlab+: :tangle ../src/inverseKinematicsHexapod.m +:header-args:matlab+: :comments org :mkdirp yes +:header-args:matlab+: :eval no :results none +:END: +<> + +This Matlab function is accessible [[file:src/inverseKinematicsHexapod.m][here]]. + +#+begin_src matlab + function [L] = inverseKinematicsHexapod(hexapod, AP, ARB) + % inverseKinematicsHexapod - Compute the initial position of each leg to have the wanted Hexapod's position + % + % Syntax: inverseKinematicsHexapod(hexapod, AP, ARB) + % + % Inputs: + % - hexapod - Hexapod object containing the geometry of the hexapod + % - AP - Position vector of point OB expressed in frame {A} in [m] + % - ARB - Rotation Matrix expressed in frame {A} + + % Wanted Length of the hexapod's legs [m] + L = zeros(6, 1); + + for i = 1:length(L) + Bbi = hexapod.pos_top_tranform(i, :)' - 1e-3*[0 ; 0 ; hexapod.TP.thickness+hexapod.Leg.sphere.top+hexapod.SP.thickness.top+hexapod.jacobian]; % [m] + Aai = hexapod.pos_base(i, :)' + 1e-3*[0 ; 0 ; hexapod.BP.thickness+hexapod.Leg.sphere.bottom+hexapod.SP.thickness.bottom-hexapod.h-hexapod.jacobian]; % [m] + + L(i) = sqrt(AP'*AP + Bbi'*Bbi + Aai'*Aai - 2*AP'*Aai + 2*AP'*(ARB*Bbi) - 2*(ARB*Bbi)'*Aai); + end + end +#+end_src + + +* Initialize Elements +<> ** Ground :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeGround.m @@ -1420,19 +1477,19 @@ This Matlab function is accessible [[file:../src/initializeRz.m][here]]. ** Initialize Hexapod legs' length :PROPERTIES: -:header-args:matlab+: :tangle ../src/initializeHexapodPosition.m +:header-args:matlab+: :tangle ../src/inverseKinematicsHexapod.m :header-args:matlab+: :comments org :mkdirp yes :header-args:matlab+: :eval no :results none :END: -<> +<> -This Matlab function is accessible [[file:../src/initializeHexapodPosition.m][here]]. +This Matlab function is accessible [[file:../src/inverseKinematicsHexapod.m][here]]. #+begin_src matlab - function [hexapod] = initializeHexapodPosition(hexapod, AP, ARB) - % initializeHexapodPosition - + function [hexapod] = inverseKinematicsHexapod(hexapod, AP, ARB) + % inverseKinematicsHexapod - % - % Syntax: initializeHexapodPosition(hexapod, AP, ARB) + % Syntax: inverseKinematicsHexapod(hexapod, AP, ARB) % % Inputs: % - hexapod - Hexapod object containing the geometry of the hexapod @@ -1563,7 +1620,7 @@ This Matlab function is accessible [[file:../src/initializeMicroHexapod.m][here] micro_hexapod = initializeParameters(micro_hexapod); %% Setup equilibrium position of each leg - micro_hexapod.L0 = initializeHexapodPosition(micro_hexapod, opts.AP, opts.ARB); + micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, opts.AP, opts.ARB); %% Save save('./mat/stages.mat', 'micro_hexapod', '-append'); @@ -1666,28 +1723,6 @@ This Matlab function is accessible [[file:../src/initializeMicroHexapod.m][here] J(:, 1:3) = RM'; J(:, 4:6) = cross(M_pos_base, RM)'; end - - %% - function [L] = initializeHexapodPosition(hexapod, AP, ARB) - % initializeHexapodPosition - Compute the initial position of each leg to have the wanted Hexapod's position - % - % Syntax: initializeHexapodPosition(hexapod, AP, ARB) - % - % Inputs: - % - hexapod - Hexapod object containing the geometry of the hexapod - % - AP - Position vector of point OB expressed in frame {A} in [m] - % - ARB - Rotation Matrix expressed in frame {A} - - % Wanted Length of the hexapod's legs [m] - L = zeros(6, 1); - - for i = 1:length(L) - Bbi = hexapod.pos_top_tranform(i, :)' - 1e-3*[0 ; 0 ; hexapod.TP.thickness+hexapod.Leg.sphere.top+hexapod.SP.thickness.top+hexapod.jacobian]; % [m] - Aai = hexapod.pos_base(i, :)' + 1e-3*[0 ; 0 ; hexapod.BP.thickness+hexapod.Leg.sphere.bottom+hexapod.SP.thickness.bottom-micro_hexapod.h-hexapod.jacobian]; % [m] - - L(i) = sqrt(AP'*AP + Bbi'*Bbi + Aai'*Aai - 2*AP'*Aai + 2*AP'*(ARB*Bbi) - 2*(ARB*Bbi)'*Aai); - end - end end #+end_src diff --git a/simscape/sim_nano_station_disp.slx b/simscape/sim_nano_station_disp.slx index 99a295cd50037986140a94f0bde42c46a78068ea..97ea0d68f2a40ea8351d05c1581b39a5efb0bdf4 100644 GIT binary patch delta 13512 zcmZX51yCMMvo03g-QC^Y-QC^YT>>xe{z7nfcZcBa?k>RzP9VU|m+#zj?tku7bv?5^ z&-TpDY)#MBc2_5ZO(udND9eFEpo4&bK!Ys%M>ik{f`R|RCPlDHQ0PAuC5enXgk%U> zfa3r$`g>~lGv?d~O$Em~W}aoEJ)_>!$X?|%EPG$|^#zm$pVidPUiM%|gr5`3W(Dth zut(~=nmAi9>fFGXY+c!@1&`7wwM(wuxLuJ+^wXX)D;?ZCvk5)F?qc90MmssS&8Rq= z1l|o^cmo=q@|J~20eAylU5#J<;95r6V{9!@Ra+V^qYo1~RlXXVtvY;{?j%CPPB9TbuB&WH z%&H*r#Q^OQEe&s~I4~YTvjqp*nJ{pmKpE;j#D1lzi=Wp4JW|Jjb1t%XDajN#05)0d zjBc!#1Alh@>^O!rR8IWwB$d9*l$9O#G0dA9U+z4OUgKcy&w>q@{rNqHK4!UO&WKNn 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[WTr] = computeReferencePose(Dy, Ry, Rz, Dh) +function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn) % computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample % -% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh) +% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn) % % Inputs: -% - Dy, Ry, Rz, Dh - +% - Dy - Reference of the Translation Stage [m] +% - Ry - Reference of the Tilt Stage [rad] +% - Rz - Reference of the Spindle [rad] +% - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad] +% - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad] % % Outputs: % - WTr - @@ -57,8 +61,28 @@ function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh) 0 0 1 Dh(3) ; 0 0 0 1 ]; - Rh(1:3, 1:3) = Rhx*Rhy*Rhz; + Rh(1:3, 1:3) = Rhz*Rhy*Rhx; + + %% Nano-Hexapod + Rnx = [1 0 0; + 0 cos(Dn(4)) -sin(Dn(4)); + 0 sin(Dn(4)) cos(Dn(4))]; + + Rny = [ cos(Dn(5)) 0 sin(Dn(5)); + 0 1 0; + -sin(Dn(5)) 0 cos(Dn(5))]; + + Rnz = [cos(Dn(6)) -sin(Dn(6)) 0; + sin(Dn(6)) cos(Dn(6)) 0; + 0 0 1]; + + Rn = [1 0 0 Dn(1) ; + 0 1 0 Dn(2) ; + 0 0 1 Dn(3) ; + 0 0 0 1 ]; + + Rn(1:3, 1:3) = Rnx*Rny*Rnz; %% Total Homogeneous transformation - WTr = Rty*Rry*Rrz*Rh; + WTr = Rty*Rry*Rrz*Rh*Rn; end diff --git a/src/initializeMicroHexapod.m b/src/initializeMicroHexapod.m index eeeb604..96df29c 100644 --- a/src/initializeMicroHexapod.m +++ b/src/initializeMicroHexapod.m @@ -109,7 +109,7 @@ function [micro_hexapod] = initializeMicroHexapod(opts_param) micro_hexapod = initializeParameters(micro_hexapod); %% Setup equilibrium position of each leg - micro_hexapod.L0 = initializeHexapodPosition(micro_hexapod, opts.AP, opts.ARB); + micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, opts.AP, opts.ARB); %% Save save('./mat/stages.mat', 'micro_hexapod', '-append'); @@ -212,26 +212,4 @@ function [micro_hexapod] = initializeMicroHexapod(opts_param) J(:, 1:3) = RM'; J(:, 4:6) = cross(M_pos_base, RM)'; end - - %% - function [L] = initializeHexapodPosition(hexapod, AP, ARB) - % initializeHexapodPosition - Compute the initial position of each leg to have the wanted Hexapod's position - % - % Syntax: initializeHexapodPosition(hexapod, AP, ARB) - % - % Inputs: - % - hexapod - Hexapod object containing the geometry of the hexapod - % - AP - Position vector of point OB expressed in frame {A} in [m] - % - ARB - Rotation Matrix expressed in frame {A} - - % Wanted Length of the hexapod's legs [m] - L = zeros(6, 1); - - for i = 1:length(L) - Bbi = hexapod.pos_top_tranform(i, :)' - 1e-3*[0 ; 0 ; hexapod.TP.thickness+hexapod.Leg.sphere.top+hexapod.SP.thickness.top+hexapod.jacobian]; % [m] - Aai = hexapod.pos_base(i, :)' + 1e-3*[0 ; 0 ; hexapod.BP.thickness+hexapod.Leg.sphere.bottom+hexapod.SP.thickness.bottom-micro_hexapod.h-hexapod.jacobian]; % [m] - - L(i) = sqrt(AP'*AP + Bbi'*Bbi + Aai'*Aai - 2*AP'*Aai + 2*AP'*(ARB*Bbi) - 2*(ARB*Bbi)'*Aai); - end - end end diff --git a/src/initializeReferences.m b/src/initializeReferences.m index 4bfc4d4..3606c4b 100644 --- a/src/initializeReferences.m +++ b/src/initializeReferences.m @@ -17,13 +17,13 @@ function [ref] = initializeReferences(opts_param) 'Dy_amplitude', 0, ... % Amplitude of the displacement [m] 'Dy_period', 1, ... % Period of the displacement [s] 'Ry_type', 'constant', ... % Either "constant" / "triangular" / "sinusoidal" - 'Ry_amplitude', 0, ... % Amplitude [deg] + 'Ry_amplitude', 0, ... % Amplitude [rad] 'Ry_period', 10, ... % Period of the displacement [s] 'Rz_type', 'constant', ... % Either "constant" / "rotating" - 'Rz_amplitude', 0, ... % Initial angle [deg] + 'Rz_amplitude', 0, ... % Initial angle [rad] 'Rz_period', 1, ... % Period of the rotating [s] 'Dh_type', 'constant', ... % For now, only constant is implemented - 'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,rad,rad,rad] of the top platform + 'Dh_pos', [0; 0; 0; 0; 0; 0], ... % Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles) 'Rm_type', 'constant', ... % For now, only constant is implemented 'Rm_pos', [0; pi], ... % Initial position of the two masses 'Dn_type', 'constant', ... % For now, only constant is implemented @@ -64,13 +64,13 @@ function [ref] = initializeReferences(opts_param) switch opts.Ry_type case 'constant' - Ry(:) = pi/180*opts.Ry_amplitude; + Ry(:) = opts.Ry_amplitude; case 'triangular' - Ry(:) = -4*(pi/180*opts.Ry_amplitude) + 4*(pi/180*opts.Ry_amplitude)/opts.Ry_period*t; - Ry(t<0.75*opts.Ry_period) = 2*(pi/180*opts.Ry_amplitude) - 4*(pi/180*opts.Ry_amplitude)/opts.Ry_period*t(t<0.75*opts.Ry_period); - Ry(t<0.25*opts.Ry_period) = 4*(pi/180*opts.Ry_amplitude)/opts.Ry_period*t(t<0.25*opts.Ry_period); + Ry(:) = -4*opts.Ry_amplitude + 4*opts.Ry_amplitude/opts.Ry_period*t; + Ry(t<0.75*opts.Ry_period) = 2*opts.Ry_amplitude - 4*opts.Ry_amplitude/opts.Ry_period*t(t<0.75*opts.Ry_period); + Ry(t<0.25*opts.Ry_period) = 4*opts.Ry_amplitude/opts.Ry_period*t(t<0.25*opts.Ry_period); case 'sinusoidal' - Ry(:) = opts.Ry_amplitude*sin(2*pi/opts.Ry_period*t); + otherwise warning('Ry_type is not set correctly'); end @@ -82,9 +82,9 @@ function [ref] = initializeReferences(opts_param) switch opts.Rz_type case 'constant' - Rz(:) = pi/180*opts.Rz_amplitude; + Rz(:) = opts.Rz_amplitude; case 'rotating' - Rz(:) = pi/180*opts.Rz_amplitude+2*pi/opts.Rz_period*t; + Rz(:) = opts.Rz_amplitude+2*pi/opts.Rz_period*t; otherwise warning('Rz_type is not set correctly'); end @@ -93,16 +93,37 @@ function [ref] = initializeReferences(opts_param) %% Micro-Hexapod t = [0, Ts]; Dh = zeros(length(t), 6); - - opts.Dh_pos(4:6) = pi/180*opts.Dh_pos(4:6); % convert from [deg] to [rad] + Dhl = zeros(length(t), 6); switch opts.Dh_type case 'constant' Dh = [opts.Dh_pos, opts.Dh_pos]; + + load('./mat/stages.mat', 'micro_hexapod'); + + AP = [opts.Dh_pos(1) ; opts.Dh_pos(2) ; opts.Dh_pos(3)]; + + tx = opts.Dh_pos(4); + ty = opts.Dh_pos(5); + tz = opts.Dh_pos(6); + + ARB = [cos(tz) -sin(tz) 0; + sin(tz) cos(tz) 0; + 0 0 1]*... + [ cos(ty) 0 sin(ty); + 0 1 0; + -sin(ty) 0 cos(ty)]*... + [1 0 0; + 0 cos(tx) -sin(tx); + 0 sin(tx) cos(tx)]; + + [Dhl] = inverseKinematicsHexapod(micro_hexapod, AP, ARB); + Dhl = [Dhl, Dhl]; otherwise warning('Dh_type is not set correctly'); end Dh = struct('time', t, 'signals', struct('values', Dh)); + Dhl = struct('time', t, 'signals', struct('values', Dhl)); %% Axis Compensation - Rm t = [0, Ts]; @@ -113,8 +134,6 @@ function [ref] = initializeReferences(opts_param) t = [0, Ts]; Dn = zeros(length(t), 6); - opts.Dn_pos(4:6) = pi/180*opts.Dn_pos(4:6); % convert from [deg] to [rad] - switch opts.Dn_type case 'constant' Dn = [opts.Dn_pos, opts.Dn_pos]; @@ -124,5 +143,5 @@ function [ref] = initializeReferences(opts_param) Dn = struct('time', t, 'signals', struct('values', Dn)); %% Save - save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Rm', 'Dn', 'Ts'); + save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts'); end