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#+TITLE : Simscape Model - Nano Active Stabilization System
:DRAWER:
#+LANGUAGE : en
#+EMAIL : dehaeze.thomas@gmail.com
#+AUTHOR : Dehaeze Thomas
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* Notes :noexport:
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** Notes
Prefix is =nass=
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The goals of this report are:
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- [X] ([[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning_error.org ][positioning_error ]]): Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
- [X] ([[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_experiment.org ][uncertainty_experiment ]]): Effect of experimental conditions on the plant (payload mass, Ry position, Rz position, Rz velocity, etc...)
- [ ] Determination of the *optimal stiffness* for the hexapod actuators:
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_optimal_stiffness.org ][uncertainty_optimal_stiffness ]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/optimal_stiffness_disturbances.org ][optimal_stiffness_disturbances ]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org ][state-of-thesis-2020 ]]
- [ ] [[file:/home/thomas/Cloud/meetings/group-meetings-me/2020-04-06-NASS-Design/2020-04-06-NASS-Design.org ][group-meeting-optimal-stiffness ]]
Should this be in this report? *This should be in chapter 2*
- [X] Explain why HAC-LAC strategy is nice (*It was already explained in uniaxial model* )
- [X] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control.org ][different control architectures ]]
- [X] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-vibration-isolation.org ][hexapod - vibration isolation ]]
- [X] How to apply/optimize IFF on an hexapod? ([[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control_active_damping.org ][control_active_damping ]], [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org ][active damping for stewart platforms ]])
- [X] ([[file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org ][decoupling-strategies ]]): Decoupling strategies for HAC? (maybe also in previous report)
*Will be in chapter 2*
- [X] Validation of the concept using simulations:
- [X] Find where this simulation in OL/CL is made (maybe for the conference?)
It was re-made for micro-station validation. Will just have to do the same simulation but with nano-hexapod in closed-loop
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- Tomography experiment (maybe also Ty scans)
- Open VS Closed loop results
- *Conclusion* : concept validation
nano hexapod architecture with APA
decentralized IFF + centralized HAC
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- In this section simple control (in the frame of the struts)
- Justify future used control architecture (control in the frame of the struts? Need to check what was done in ID31 tests)
- Table that compares different approaches (specify performances in different DoF, same plans on the diagonal, etc...)
- Literature review about Stewart platform control?
*In chapter 2: Special section about MIMO control, complementary filters, etc...*
** Outline
*** Control Kinematics
- Explain how the position error can be expressed in the frame of the nano-hexapod
- ([[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning_error.org ][positioning_error ]]): Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
- Control architecture, block diagram
*** LAC
- How to apply/optimize IFF on an hexapod? ([[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control_active_damping.org ][control_active_damping ]], [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org ][active damping for stewart platforms ]])
- Robustness to payload mass
- Root Locus
- Damping optimization
*** HAC
- ([[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_experiment.org ][uncertainty_experiment ]]): Effect of experimental conditions on the plant (payload mass, Ry position, Rz position, Rz velocity, etc...)
- Determination of the *optimal stiffness* for the hexapod actuators:
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_optimal_stiffness.org ][uncertainty_optimal_stiffness ]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/optimal_stiffness_disturbances.org ][optimal_stiffness_disturbances ]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org ][state-of-thesis-2020 ]]
- [ ] [[file:/home/thomas/Cloud/meetings/group-meetings-me/2020-04-06-NASS-Design/2020-04-06-NASS-Design.org ][group-meeting-optimal-stiffness ]]
- Effect of micro-station compliance
- Effect of IFF
- Effect of payload mass
- Decoupled plant
- Controller design
*** Simulations
- Take into account disturbances, metrology sensor noise. Maybe say here that we don't take in account other noise sources as they will be optimized latter (detail design phase)
- Tomography + lateral scans (same as what was done in open loop [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A4-simscape-micro-station/simscape-micro-station.org::*Simulation of Scientific Experiments ][here ]])
- Validation of concept
** DONE Old Outline
CLOSED: [2024-11-07 Thu 16:19]
*** Introduction :ignore:
Discussion of:
- Transformation matrices / control architecture (computation of the position error in the frame of the nano-hexapod)
- Control of parallel architectures
- Control in the frame of struts or cartesian?
- Effect of rotation on IFF? => APA
- HAC-LAC
- New noise budgeting?
*** Control Kinematics
- Explain how the position error can be expressed in the frame of the nano-hexapod
- block diagram
- Explain how to go from external metrology to the frame of the nano-hexapod
*** High Authority Control - Low Authority Control (HAC-LAC)
- general idea
- case for parallel manipulator: decentralized LAC + centralized HAC
*** Decoupling Strategies for parallel manipulators
[[file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org::+TITLE: Diagonal control using the SVD and the Jacobian Matrix ][study ]]
- Jacobian matrices, CoK, CoM, ...
- Discussion of cubic architecture
- SVD, Modal, ...
*** Decentralized Integral Force Feedback (LAC)
- Root Locus
- Damping optimization
*** Decoupled Dynamics
- Centralized HAC
- Control in the frame of the struts
- Effect of IFF
*** Centralized Position Controller (HAC)
- Decoupled plant
- Controller design
*** Time domain simulations
Goal: validation of the concept
- Take into account disturbances, sensor noise, etc...
- Tomography + lateral scans (same as what was done in open loop [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A4-simscape-micro-station/simscape-micro-station.org::*Simulation of Scientific Experiments ][here ]])
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** DONE [#A] Merge the micro-station model with the nano-hexapod model
CLOSED: [2025-02-12 Wed 12:10] SCHEDULED: <2025-02-12 Wed >
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- [X] *Start from the Simscape model of the ID31 tests*
=/home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/C5-test-bench-id31/matlab/nass_model_id31.slx=
- [X] Remove LION metrology to have perfect measurement
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- [X] Remove nano-hexapod model and add simplified model
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- [ ] Add "cylindrical" payloads (configurable in mass)
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** TODO [#B] Add payload configurable subsystem
SCHEDULED: <2025-02-12 Wed>
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** TODO [#B] Discuss the necessity of estimated Rz?
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One big advantage of doing the control in the cartesian plane, is that we don't need the estimation of nano-hexapod Rz, therefore we don't need the encoders anymore!
Maybe this should be done *here* .
Here it can be reminded when doing the control in the cartesian frame.
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** TODO [#B] Check if things are compatible to results of uniaxial model
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** CANC [#C] What performance metric can we use? :@christophe:
CLOSED: [2024-11-12 Tue 09:22]
- State "CANC" from "QUES" [2024-11-12 Tue 09:22]
This can be nice to have a (scalar) performance metric that can be used for optimization.
In cite:hauge04_sensor_contr_space_based_six, a (scalar) performance metric representing the 6dof transmissibility is used.
** DONE [#C] Identify the sensibility to disturbances without the nano-hexapod and save the results
CLOSED: [2024-11-07 Thu 09:20]
This can then be used to compare with obtained performance with the nano-hexapod.
This should be done in the ustation report (A4).
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* Introduction :ignore:
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From last sections:
- Uniaxial: No stiff nano-hexapod (should also demonstrate that here)
- Rotating: No soft nano-hexapod, Decentralized IFF can be used robustly by adding parallel stiffness
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In this section:
- Take the model of the nano-hexapod with stiffness 1um/N
- Apply decentralized IFF
- Apply HAC-LAC
- Check robustness to payload change
- Simulation of experiments
* Control Kinematics
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:PROPERTIES:
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:HEADER-ARGS:matlab+: :tangle matlab/nass_1_kinematics.m
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:END:
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<<sec:nass_kinematics >>
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** Introduction :ignore:
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- Explain how the position error can be expressed in the frame of the nano-hexapod
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning_error.org ][positioning_error ]]: Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
- Control architecture, block diagram
- Schematic with micro-station + nass + metrology + control system
- Zoom in the control system with blocs
- Then explain all the blocs
- Say that there are many control strategies.
It will be the topic of chapter 2.3.
Here, we start with something simple: control in the frame of the struts
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** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir >>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init >>
#+end_src
#+begin_src matlab :tangle no :noweb yes
<<m-init-path >>
#+end_src
#+begin_src matlab :eval no :noweb yes
<<m-init-path-tangle >>
#+end_src
#+begin_src matlab :noweb yes
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<<m-init-simscape >>
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#+end_src
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#+begin_src matlab :noweb yes
<<m-init-other >>
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#+end_src
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** Micro Station Kinematics
- from ref:ssec:ustation_kinematics, computation of the wanted sample pose from the setpoint of each stage.
** Computation of the sample's pose error
From metrology (here supposed to be perfect 6-DoF), compute the sample's pose error.
Has to invert the homogeneous transformation.
** Position error in the frame of the nano-hexapod
Explain how to compute the errors in the frame of the struts (rotating)
* Decentralized Active Damping
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/nass_2_active_damping.m
:END:
<<sec:nass_active_damping >>
** Introduction :ignore:
- How to apply/optimize IFF on an hexapod? ()
- Robustness to payload mass
- Root Locus
- Damping optimization
- [ ][[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control_active_damping.org ][control_active_damping ]]
- [ ][[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org ][active damping for stewart platforms ]]
- [ ][[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org::*Vibration Control and Active Damping ][Vibration Control and Active Damping ]]
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** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir >>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init >>
#+end_src
#+begin_src matlab :tangle no :noweb yes
<<m-init-path >>
#+end_src
#+begin_src matlab :eval no :noweb yes
<<m-init-path-tangle >>
#+end_src
#+begin_src matlab :noweb yes
<<m-init-simscape >>
#+end_src
#+begin_src matlab :noweb yes
<<m-init-other >>
#+end_src
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** IFF Plant
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#+begin_src matlab
%% Identify the plant dynamics using the Simscape model
% Initialize each Simscape model elements
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeSimplifiedNanoHexapod();
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initializeSample('type', 'cylindrical');
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initializeSimscapeConfiguration('gravity', false);
initializeDisturbances('enable', false);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'open-loop');
initializeReferences();
% Input/Output definition
% clear io; io_i = 1;
% io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [V]
% io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vs'); io_i = io_i + 1; % Force Sensors voltages [V]
% io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Position Errors [m]
% % With no payload
% Gm = exp(-1e-4*s)*linearize(mdl, io);
% Gm.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
% Gm.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
% 'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
#+end_src
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- Show how it changes with the payload mass (1, 25, 50)
- Effect of rotation (1rpm, 60rpm)
** Controller Design
- Apply IFF
- Show Root Locus
- Choose optimal gain.
Here in MIMO, cannot have optimal damping for all modes. (there is a paper that tries to optimize that)
- Show robustness to change of payload (loci?)
- Reference to paper showing stability in MIMO for decentralized IFF
** Sensitivity to disturbances
- Compute transfer functions from spindle vertical error to sample vertical error with IFF (and compare without the NASS)
- Same for horizontal
- Maybe noise budgeting, but may be complex in MIMO...
* Centralized Active Vibration Control
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/nass_3_hac.m
:END:
<<sec:nass_hac >>
** Introduction :ignore:
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_experiment.org ][uncertainty_experiment ]]: Effect of experimental conditions on the plant (payload mass, Ry position, Rz position, Rz velocity, etc...)
- Effect of micro-station compliance
- Effect of IFF
- Effect of payload mass
- Decoupled plant
- Controller design
From control kinematics:
- Talk about issue of not estimating Rz from external metrology? (maybe could be nice to discuss that during the experiments!)
- Show what happens is Rz is not estimated (for instance supposed equaled to zero => increased coupling)
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** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir >>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init >>
#+end_src
#+begin_src matlab :tangle no :noweb yes
<<m-init-path >>
#+end_src
#+begin_src matlab :eval no :noweb yes
<<m-init-path-tangle >>
#+end_src
#+begin_src matlab :noweb yes
<<m-init-simscape >>
#+end_src
#+begin_src matlab :noweb yes
<<m-init-other >>
#+end_src
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** HAC Plant
- Compute transfer function from u to dL (with IFF applied)
** Effect of Payload mass
- Show effect of payload mass + rotation
** Controller design
- Show robustness with Loci
** Sensitivity to disturbances
- Compute transfer functions from spindle vertical error to sample vertical error with HAC-IFF
Compare without the NASS, and with just IFF
- Same for horizontal
- Maybe noise budgeting, but may be complex in MIMO...
** Tomography experiment
- With HAC-IFF, perform tomography experiment, and compare with open-loop
- Take into account disturbances, metrology sensor noise. Maybe say here that we don't take in account other noise sources as they will be optimized latter (detail design phase)
- Tomography + lateral scans (same as what was done in open loop [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A4-simscape-micro-station/simscape-micro-station.org::*Simulation of Scientific Experiments ][here ]])
- Validation of concept
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* Conclusion
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<<sec:nass_conclusion >>
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* Bibliography :ignore:
#+latex : \printbibliography[heading=bibintoc,title={Bibliography}]
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* Matlab Functions :noexport:
** =initializeSimscapeConfiguration=: Simscape Configuration
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/initializeSimscapeConfiguration.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
*** Function description
#+begin_src matlab
function [] = initializeSimscapeConfiguration(args)
#+end_src
*** Optional Parameters
#+begin_src matlab
arguments
args.gravity logical {mustBeNumericOrLogical} = true
end
#+end_src
*** Structure initialization
#+begin_src matlab
conf_simscape = struct();
#+end_src
*** Add Type
#+begin_src matlab
if args.gravity
conf_simscape.type = 1;
else
conf_simscape.type = 2;
end
#+end_src
*** Save the Structure
#+begin_src matlab
if exist('./mat', 'dir')
if exist('./mat/nass_model_conf_simscape.mat', 'file')
save('mat/nass_model_conf_simscape.mat', 'conf_simscape', '-append');
else
save('mat/nass_model_conf_simscape.mat', 'conf_simscape');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_conf_simscape.mat', 'file')
save('matlab/mat/nass_model_conf_simscape.mat', 'conf_simscape', '-append');
else
save('matlab/mat/nass_model_conf_simscape.mat', 'conf_simscape');
end
end
#+end_src
** =initializeLoggingConfiguration=: Logging Configuration
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/initializeLoggingConfiguration.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
*** Function description
#+begin_src matlab
function [] = initializeLoggingConfiguration(args)
#+end_src
*** Optional Parameters
#+begin_src matlab
arguments
args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none'
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
end
#+end_src
*** Structure initialization
#+begin_src matlab
conf_log = struct();
#+end_src
*** Add Type
#+begin_src matlab
switch args.log
case 'none'
conf_log.type = 0;
case 'all'
conf_log.type = 1;
case 'forces'
conf_log.type = 2;
end
#+end_src
*** Sampling Time
#+begin_src matlab
conf_log.Ts = args.Ts;
#+end_src
*** Save the Structure
#+begin_src matlab
if exist('./mat', 'dir')
if exist('./mat/nass_model_conf_log.mat', 'file')
save('mat/nass_model_conf_log.mat', 'conf_log', '-append');
else
save('mat/nass_model_conf_log.mat', 'conf_log');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_conf_log.mat', 'file')
save('matlab/mat/nass_model_conf_log.mat', 'conf_log', '-append');
else
save('matlab/mat/nass_model_conf_log.mat', 'conf_log');
end
end
#+end_src
** =initializeReferences=: Generate Reference Signals
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/initializeReferences.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
*** Function Declaration and Documentation
#+begin_src matlab
function [ref] = initializeReferences(args)
#+end_src
*** Optional Parameters
#+begin_src matlab
arguments
% Sampling Frequency [s]
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
% Maximum simulation time [s]
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
% Either "constant" / "triangular" / "sinusoidal"
args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
% Amplitude of the displacement [m]
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the displacement [s]
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% Either "constant" / "triangular" / "sinusoidal"
args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
% Amplitude [rad]
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the displacement [s]
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% Either "constant" / "rotating"
args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating', 'rotating-not-filtered'})} = 'constant'
% Initial angle [rad]
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
% Period of the rotating [s]
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
% For now, only constant is implemented
args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
% For now, only constant is implemented
args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
% Initial position of the two masses
args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
% For now, only constant is implemented
args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
% Initial position [m,m,m,rad,rad,rad] of the top platform
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
end
#+end_src
*** Initialize Parameters
#+begin_src matlab
%% Set Sampling Time
Ts = args.Ts;
Tmax = args.Tmax;
%% Low Pass Filter to filter out the references
s = zpk('s');
w0 = 2*pi*10;
xi = 1;
H_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
#+end_src
*** Translation Stage
#+begin_src matlab
%% Translation stage - Dy
t = 0:Ts:Tmax; % Time Vector [s]
Dy = zeros(length(t), 1);
Dyd = zeros(length(t), 1);
Dydd = zeros(length(t), 1);
switch args.Dy_type
case 'constant'
Dy(:) = args.Dy_amplitude;
Dyd(:) = 0;
Dydd(:) = 0;
case 'triangular'
% This is done to unsure that we start with no displacement
Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2);
i0 = find(t>=args.Dy_period/4,1);
Dy(1:end-i0+1) = Dy_raw(i0:end);
Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value
% The signal is filtered out
Dy = lsim(H_lpf, Dy, t);
Dyd = lsim(H_lpf*s, Dy, t);
Dydd = lsim(H_lpf*s^2, Dy, t);
case 'sinusoidal'
Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t);
Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t);
Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t);
otherwise
warning('Dy_type is not set correctly');
end
Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd);
#+end_src
*** Tilt Stage
#+begin_src matlab
%% Tilt Stage - Ry
t = 0:Ts:Tmax; % Time Vector [s]
Ry = zeros(length(t), 1);
Ryd = zeros(length(t), 1);
Rydd = zeros(length(t), 1);
switch args.Ry_type
case 'constant'
Ry(:) = args.Ry_amplitude;
Ryd(:) = 0;
Rydd(:) = 0;
case 'triangular'
Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2);
i0 = find(t>=args.Ry_period/4,1);
Ry(1:end-i0+1) = Ry_raw(i0:end);
Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value
% The signal is filtered out
Ry = lsim(H_lpf, Ry, t);
Ryd = lsim(H_lpf*s, Ry, t);
Rydd = lsim(H_lpf*s^2, Ry, t);
case 'sinusoidal'
Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t);
Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t);
Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t);
otherwise
warning('Ry_type is not set correctly');
end
Ry = struct('time', t, 'signals', struct('values', Ry), 'deriv', Ryd, 'dderiv', Rydd);
#+end_src
*** Spindle
#+begin_src matlab
%% Spindle - Rz
t = 0:Ts:Tmax; % Time Vector [s]
Rz = zeros(length(t), 1);
Rzd = zeros(length(t), 1);
Rzdd = zeros(length(t), 1);
switch args.Rz_type
case 'constant'
Rz(:) = args.Rz_amplitude;
Rzd(:) = 0;
Rzdd(:) = 0;
case 'rotating-not-filtered'
Rz(:) = 2*pi/args.Rz_period*t;
% The signal is filtered out
Rz(:) = 2*pi/args.Rz_period*t;
Rzd(:) = 2*pi/args.Rz_period;
Rzdd(:) = 0;
% We add the angle offset
Rz = Rz + args.Rz_amplitude;
case 'rotating'
Rz(:) = 2*pi/args.Rz_period*t;
% The signal is filtered out
Rz = lsim(H_lpf, Rz, t);
Rzd = lsim(H_lpf*s, Rz, t);
Rzdd = lsim(H_lpf*s^2, Rz, t);
% We add the angle offset
Rz = Rz + args.Rz_amplitude;
otherwise
warning('Rz_type is not set correctly');
end
Rz = struct('time', t, 'signals', struct('values', Rz), 'deriv', Rzd, 'dderiv', Rzdd);
#+end_src
*** Micro Hexapod
#+begin_src matlab
%% Micro-Hexapod
t = [0, Ts];
Dh = zeros(length(t), 6);
Dhl = zeros(length(t), 6);
switch args.Dh_type
case 'constant'
Dh = [args.Dh_pos, args.Dh_pos];
load('nass_model_stages.mat', 'micro_hexapod');
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
tx = args.Dh_pos(4);
ty = args.Dh_pos(5);
tz = args.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] = inverseKinematics(micro_hexapod, 'AP', AP, 'ARB', 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));
#+end_src
*** Save the Structure
#+begin_src matlab
if exist('./mat', 'dir')
if exist('./mat/nass_model_references.mat', 'file')
save('mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts', '-append');
else
save('mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_references.mat', 'file')
save('matlab/mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts', '-append');
else
save('matlab/mat/nass_model_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'args', 'Ts');
end
end
#+end_src
** =initializeDisturbances=: Initialize Disturbances
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/initializeDisturbances.m
:header-args:matlab+: :comments none :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
*** Function Declaration and Documentation
#+begin_src matlab
function [] = initializeDisturbances(args)
% initializeDisturbances - Initialize the disturbances
%
% Syntax: [] = initializeDisturbances(args)
%
% Inputs:
% - args -
#+end_src
*** Optional Parameters
#+begin_src matlab
arguments
% Global parameter to enable or disable the disturbances
args.enable logical {mustBeNumericOrLogical} = true
% Ground Motion - X direction
args.Dw_x logical {mustBeNumericOrLogical} = true
% Ground Motion - Y direction
args.Dw_y logical {mustBeNumericOrLogical} = true
% Ground Motion - Z direction
args.Dw_z logical {mustBeNumericOrLogical} = true
% Translation Stage - X direction
args.Fdy_x logical {mustBeNumericOrLogical} = true
% Translation Stage - Z direction
args.Fdy_z logical {mustBeNumericOrLogical} = true
% Spindle - X direction
args.Frz_x logical {mustBeNumericOrLogical} = true
% Spindle - Y direction
args.Frz_y logical {mustBeNumericOrLogical} = true
% Spindle - Z direction
args.Frz_z logical {mustBeNumericOrLogical} = true
end
#+end_src
#+begin_src matlab
% Initialization of random numbers
rng("shuffle");
#+end_src
*** Ground Motion
#+begin_src matlab
%% Ground Motion
if args.enable
% Load the PSD of disturbance
load('ustation_disturbance_psd.mat', 'gm_dist')
% Frequency Data
Dw.f = gm_dist.f;
Dw.psd_x = gm_dist.pxx_x;
Dw.psd_y = gm_dist.pxx_y;
Dw.psd_z = gm_dist.pxx_z;
% Time data
Fs = 2*Dw.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
N = 2*length(Dw.f); % Number of Samples match the one of the wanted PSD
T0 = N/Fs; % Signal Duration [s]
Dw.t = linspace(0, T0, N+1)'; % Time Vector [s]
% ASD representation of the ground motion
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(Dw.psd_x(i)/T0);
end
if args.Dw_x
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Dw.x = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m]
else
Dw.x = zeros(length(Dw.t), 1);
end
if args.Dw_y
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Dw.y = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m]
else
Dw.y = zeros(length(Dw.t), 1);
end
if args.Dw_y
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Dw.z = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m]
else
Dw.z = zeros(length(Dw.t), 1);
end
else
Dw.t = [0,1]; % Time Vector [s]
Dw.x = [0,0]; % Ground Motion - X [m]
Dw.y = [0,0]; % Ground Motion - Y [m]
Dw.z = [0,0]; % Ground Motion - Z [m]
end
#+end_src
*** Translation stage
#+begin_src matlab
%% Translation stage
if args.enable
% Load the PSD of disturbance
load('ustation_disturbance_psd.mat', 'dy_dist')
% Frequency Data
Dy.f = dy_dist.f;
Dy.psd_x = dy_dist.pxx_fx;
Dy.psd_z = dy_dist.pxx_fz;
% Time data
Fs = 2*Dy.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
N = 2*length(Dy.f); % Number of Samples match the one of the wanted PSD
T0 = N/Fs; % Signal Duration [s]
Dy.t = linspace(0, T0, N+1)'; % Time Vector [s]
% ASD representation of the disturbance voice
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(Dy.psd_x(i)/T0);
end
if args.Fdy_x
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Dy.x = N/sqrt(2)*ifft(Cx); % Translation stage disturbances - X direction [N]
else
Dy.x = zeros(length(Dy.t), 1);
end
if args.Fdy_z
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Dy.z = N/sqrt(2)*ifft(Cx); % Translation stage disturbances - Z direction [N]
else
Dy.z = zeros(length(Dy.t), 1);
end
else
Dy.t = [0,1]; % Time Vector [s]
Dy.x = [0,0]; % Translation Stage disturbances - X [N]
Dy.z = [0,0]; % Translation Stage disturbances - Z [N]
end
#+end_src
*** Spindle
#+begin_src matlab
%% Spindle
if args.enable
% Load the PSD of disturbance
load('ustation_disturbance_psd.mat', 'rz_dist')
% Frequency Data
Rz.f = rz_dist.f;
Rz.psd_x = rz_dist.pxx_fx;
Rz.psd_y = rz_dist.pxx_fy;
Rz.psd_z = rz_dist.pxx_fz;
% Time data
Fs = 2*Rz.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
N = 2*length(Rz.f); % Number of Samples match the one of the wanted PSD
T0 = N/Fs; % Signal Duration [s]
Rz.t = linspace(0, T0, N+1)'; % Time Vector [s]
% ASD representation of the disturbance voice
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(Rz.psd_x(i)/T0);
end
if args.Frz_x
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Rz.x = N/sqrt(2)*ifft(Cx); % spindle disturbances - X direction [N]
else
Rz.x = zeros(length(Rz.t), 1);
end
if args.Frz_y
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Rz.y = N/sqrt(2)*ifft(Cx); % spindle disturbances - Y direction [N]
else
Rz.y = zeros(length(Rz.t), 1);
end
if args.Frz_z
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
Cx = [Cx; flipud(conj(Cx(2:end)))];;
Rz.z = N/sqrt(2)*ifft(Cx); % spindle disturbances - Z direction [N]
else
Rz.z = zeros(length(Rz.t), 1);
end
else
Rz.t = [0,1]; % Time Vector [s]
Rz.x = [0,0]; % Spindle disturbances - X [N]
Rz.y = [0,0]; % Spindle disturbances - X [N]
Rz.z = [0,0]; % Spindle disturbances - Z [N]
end
#+end_src
*** Direct Forces
#+begin_src matlab
u = zeros(100, 6);
Fd = u;
#+end_src
*** Set initial value to zero
#+begin_src matlab
Dw.x = Dw.x - Dw.x(1);
Dw.y = Dw.y - Dw.y(1);
Dw.z = Dw.z - Dw.z(1);
Dy.x = Dy.x - Dy.x(1);
Dy.z = Dy.z - Dy.z(1);
Rz.x = Rz.x - Rz.x(1);
Rz.y = Rz.y - Rz.y(1);
Rz.z = Rz.z - Rz.z(1);
#+end_src
*** Save the Structure
#+begin_src matlab
if exist('./mat', 'dir')
save('mat/nass_model_disturbances.mat', 'Dw', 'Dy', 'Rz', 'Fd', 'args');
elseif exist('./matlab', 'dir')
save('matlab/mat/nass_model_disturbances.mat', 'Dw', 'Dy', 'Rz', 'Fd', 'args');
end
#+end_src
** =initializeController=: Initialize Controller
#+begin_src matlab :tangle matlab/src/initializeController.m :comments none :mkdirp yes :eval no
function [] = initializeController(args)
arguments
args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
end
controller = struct();
switch args.type
case 'open-loop'
controller.type = 1;
controller.name = 'Open-Loop';
case 'dvf'
controller.type = 2;
controller.name = 'Decentralized Direct Velocity Feedback';
case 'iff'
controller.type = 3;
controller.name = 'Decentralized Integral Force Feedback';
case 'hac-dvf'
controller.type = 4;
controller.name = 'HAC-DVF';
case 'ref-track-L'
controller.type = 5;
controller.name = 'Reference Tracking in the frame of the legs';
case 'ref-track-iff-L'
controller.type = 6;
controller.name = 'Reference Tracking in the frame of the legs + IFF';
case 'cascade-hac-lac'
controller.type = 7;
controller.name = 'Cascade Control + HAC-LAC';
case 'hac-iff'
controller.type = 8;
controller.name = 'HAC-IFF';
case 'stabilizing'
controller.type = 9;
controller.name = 'Stabilizing Controller';
end
if exist('./mat', 'dir')
save('mat/nass_model_controller.mat', 'controller');
elseif exist('./matlab', 'dir')
save('matlab/mat/nass_model_controller.mat', 'controller');
end
end
#+end_src
** =describeMicroStationSetup=
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/describeMicroStationSetup.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
*** Function description
#+begin_src matlab
function [] = describeMicroStationSetup()
% describeMicroStationSetup -
%
% Syntax: [] = describeMicroStationSetup()
%
% Inputs:
% - -
%
% Outputs:
% - -
#+end_src
*** Simscape Configuration
#+begin_src matlab
load('./mat/nass_model_conf_simscape.mat', 'conf_simscape');
#+end_src
#+begin_src matlab
fprintf('Simscape Configuration:\n');
if conf_simscape.type == 1
fprintf('- Gravity is included\n');
else
fprintf('- Gravity is not included\n');
end
fprintf('\n');
#+end_src
*** Disturbances
#+begin_src matlab
load('./mat/nass_model_disturbances.mat', 'args');
#+end_src
#+begin_src matlab
fprintf('Disturbances:\n');
if ~args.enable
fprintf('- No disturbance is included\n');
else
if args.Dwx && args.Dwy && args.Dwz
fprintf('- Ground motion\n');
end
if args.Fdy_x && args.Fdy_z
fprintf('- Vibrations of the Translation Stage\n');
end
if args.Frz_z
fprintf('- Vibrations of the Spindle\n');
end
end
fprintf('\n');
#+end_src
*** References
#+begin_src matlab
load('./mat/nass_model_references.mat', 'args');
#+end_src
#+begin_src matlab
fprintf('Reference Tracking:\n');
fprintf('- Translation Stage:\n');
switch args.Dy_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Dy = %.0f [mm]\n', args.Dy_amplitude*1e3);
case 'triangular'
fprintf(' - Triangular Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Dy_period);
case 'sinusoidal'
fprintf(' - Sinusoidal Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Dy_period);
end
fprintf('- Tilt Stage:\n');
switch args.Ry_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Ry = %.0f [mm]\n', args.Ry_amplitude*1e3);
case 'triangular'
fprintf(' - Triangular Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Ry_period);
case 'sinusoidal'
fprintf(' - Sinusoidal Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Ry_period);
end
fprintf('- Spindle:\n');
switch args.Rz_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Rz = %.0f [deg]\n', 180/pi*args.Rz_amplitude);
case { 'rotating', 'rotating-not-filtered' }
fprintf(' - Rotating\n');
fprintf(' - Speed = %.0f [rpm]\n', 60/args.Rz_period);
end
fprintf('- Micro Hexapod:\n');
switch args.Dh_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Dh = %.0f, %.0f, %.0f [mm]\n', args.Dh_pos(1), args.Dh_pos(2), args.Dh_pos(3));
fprintf(' - Rh = %.0f, %.0f, %.0f [deg]\n', args.Dh_pos(4), args.Dh_pos(5), args.Dh_pos(6));
end
fprintf('\n');
#+end_src
*** Micro-Station
#+begin_src matlab
load('./mat/nass_model_stages.mat', 'ground', 'granite', 'ty', 'ry', 'rz', 'micro_hexapod', 'axisc');
#+end_src
#+begin_src matlab
fprintf('Micro Station:\n');
if granite.type == 1 && ...
ty.type == 1 && ...
ry.type == 1 && ...
rz.type == 1 && ...
micro_hexapod.type == 1;
fprintf('- All stages are rigid\n');
elseif granite.type == 2 && ...
ty.type == 2 && ...
ry.type == 2 && ...
rz.type == 2 && ...
micro_hexapod.type == 2;
fprintf('- All stages are flexible\n');
else
if granite.type == 1 || granite.type = = 4
fprintf('- Granite is rigid\n');
else
fprintf('- Granite is flexible\n');
end
if ty.type == 1 || ty.type = = 4
fprintf('- Translation Stage is rigid\n');
else
fprintf('- Translation Stage is flexible\n');
end
if ry.type == 1 || ry.type = = 4
fprintf('- Tilt Stage is rigid\n');
else
fprintf('- Tilt Stage is flexible\n');
end
if rz.type == 1 || rz.type = = 4
fprintf('- Spindle is rigid\n');
else
fprintf('- Spindle is flexible\n');
end
if micro_hexapod.type == 1 || micro_hexapod.type = = 4
fprintf('- Micro Hexapod is rigid\n');
else
fprintf('- Micro Hexapod is flexible\n');
end
end
fprintf('\n');
#+end_src
** =computeReferencePose=
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/computeReferencePose.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
#+begin_src matlab
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, Dn)
%
% Inputs:
% - 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 -
%% Translation Stage
Rty = [1 0 0 0;
0 1 0 Dy;
0 0 1 0;
0 0 0 1];
%% Tilt Stage - Pure rotating aligned with Ob
Rry = [ cos(Ry) 0 sin(Ry) 0;
0 1 0 0;
-sin(Ry) 0 cos(Ry) 0;
0 0 0 1];
%% Spindle - Rotation along the Z axis
Rrz = [cos(Rz) -sin(Rz) 0 0 ;
sin(Rz) cos(Rz) 0 0 ;
0 0 1 0 ;
0 0 0 1 ];
%% Micro-Hexapod
Rhx = [1 0 0;
0 cos(Dh(4)) -sin(Dh(4));
0 sin(Dh(4)) cos(Dh(4))];
Rhy = [ cos(Dh(5)) 0 sin(Dh(5));
0 1 0;
-sin(Dh(5)) 0 cos(Dh(5))];
Rhz = [cos(Dh(6)) -sin(Dh(6)) 0;
sin(Dh(6)) cos(Dh(6)) 0;
0 0 1];
Rh = [1 0 0 Dh(1) ;
0 1 0 Dh(2) ;
0 0 1 Dh(3) ;
0 0 0 1 ];
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) = Rnz*Rny*Rnx;
%% Total Homogeneous transformation
WTr = Rty*Rry*Rrz*Rh*Rn;
end
#+end_src
** =circlefit=
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/circlefit.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
#+begin_src matlab
function [xc,yc,R,a] = circlefit(x,y)
%
% [xc yx R] = circfit(x,y)
%
% fits a circle in x,y plane in a more accurate
% (less prone to ill condition )
% procedure than circfit2 but using more memory
% x,y are column vector where (x(i),y(i)) is a measured point
%
% result is center point (yc,xc) and radius R
% an optional output is the vector of coeficient a
% describing the circle's equation
%
% x^2+y^2+a(1)*x+a(2)*y+a(3)=0
%
% By: Izhak bucher 25/oct /1991,
x=x(:); y=y(:);
a=[x y ones(size(x))]\[-(x.^2+y.^2)];
xc = -.5*a(1);
yc = -.5*a(2);
R = sqrt((a(1)^2+a(2)^2)/4-a(3));
#+end_src
** Initialize Micro-Station Stages
*** =initializeGround=: Ground
#+begin_src matlab :tangle matlab/src/initializeGround.m :comments none :mkdirp yes :eval no
function [ground] = initializeGround(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid'})} = 'rigid'
args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) % Rotation point for the ground motion [m]
end
ground = struct();
switch args.type
case 'none'
ground.type = 0;
case 'rigid'
ground.type = 1;
end
ground.shape = [2, 2, 0.5]; % [m]
ground.density = 2800; % [kg/m3]
ground.rot_point = args.rot_point;
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'ground', '-append');
else
save('mat/nass_model_stages.mat', 'ground');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'ground', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'ground');
end
end
end
#+end_src
*** =initializeGranite=: Granite
#+begin_src matlab :tangle matlab/src/initializeGranite.m :comments none :mkdirp yes :eval no
function [granite] = initializeGranite(args)
arguments
args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none'})} = 'flexible'
args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3]
args.K (6,1) double {mustBeNumeric, mustBeNonnegative} = [5e9; 5e9; 5e9; 2.5e7; 2.5e7; 1e7] % [N/m]
args.C (6,1) double {mustBeNumeric, mustBeNonnegative} = [4.0e5; 1.1e5; 9.0e5; 2e4; 2e4; 1e4] % [N/(m/s)]
args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m]
args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m]
args.z0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Z direction [m]
args.sample_pos (1,1) double {mustBeNumeric} = 0.775 % Height of the measurment point [m]
end
granite = struct();
switch args.type
case 'none'
granite.type = 0;
case 'rigid'
granite.type = 1;
case 'flexible'
granite.type = 2;
end
granite.density = args.density; % [kg/m3]
granite.STEP = 'granite.STEP';
% Z-offset for the initial position of the sample with respect to the granite top surface.
granite.sample_pos = args.sample_pos; % [m]
granite.K = args.K; % [N/m]
granite.C = args.C; % [N/(m/s)]
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'granite', '-append');
else
save('mat/nass_model_stages.mat', 'granite');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'granite', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'granite');
end
end
end
#+end_src
*** =initializeTy=: Translation Stage
#+begin_src matlab :tangle matlab/src/initializeTy.m :comments none :mkdirp yes :eval no
function [ty] = initializeTy(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
end
ty = struct();
switch args.type
case 'none'
ty.type = 0;
case 'rigid'
ty.type = 1;
case 'flexible'
ty.type = 2;
end
% Ty Granite frame
ty.granite_frame.density = 7800; % [kg/m3] = > 43kg
ty.granite_frame.STEP = 'Ty_Granite_Frame.STEP';
% Guide Translation Ty
ty.guide.density = 7800; % [kg/m3] = > 76kg
ty.guide.STEP = 'Ty_Guide.STEP';
% Ty - Guide_Translation12
ty.guide12.density = 7800; % [kg/m3]
ty.guide12.STEP = 'Ty_Guide_12.STEP';
% Ty - Guide_Translation11
ty.guide11.density = 7800; % [kg/m3]
ty.guide11.STEP = 'Ty_Guide_11.STEP';
% Ty - Guide_Translation22
ty.guide22.density = 7800; % [kg/m3]
ty.guide22.STEP = 'Ty_Guide_22.STEP';
% Ty - Guide_Translation21
ty.guide21.density = 7800; % [kg/m3]
ty.guide21.STEP = 'Ty_Guide_21.STEP';
% Ty - Plateau translation
ty.frame.density = 7800; % [kg/m3]
ty.frame.STEP = 'Ty_Stage.STEP';
% Ty Stator Part
ty.stator.density = 5400; % [kg/m3]
ty.stator.STEP = 'Ty_Motor_Stator.STEP';
% Ty Rotor Part
ty.rotor.density = 5400; % [kg/m3]
ty.rotor.STEP = 'Ty_Motor_Rotor.STEP';
ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; % [N/m, N*m/rad]
ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 1e4]; % [N/(m/s), N*m/ (rad/s)]
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'ty', '-append');
else
save('mat/nass_model_stages.mat', 'ty');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'ty', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'ty');
end
end
end
#+end_src
*** =initializeRy=: Tilt Stage
#+begin_src matlab :tangle matlab/src/initializeRy.m :comments none :mkdirp yes :eval no
function [ry] = initializeRy(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
args.Ry_init (1,1) double {mustBeNumeric} = 0
end
ry = struct();
switch args.type
case 'none'
ry.type = 0;
case 'rigid'
ry.type = 1;
case 'flexible'
ry.type = 2;
end
% Ry - Guide for the tilt stage
ry.guide.density = 7800; % [kg/m3]
ry.guide.STEP = 'Tilt_Guide.STEP';
% Ry - Rotor of the motor
ry.rotor.density = 2400; % [kg/m3]
ry.rotor.STEP = 'Tilt_Motor_Axis.STEP';
% Ry - Motor
ry.motor.density = 3200; % [kg/m3]
ry.motor.STEP = 'Tilt_Motor.STEP';
% Ry - Plateau Tilt
ry.stage.density = 7800; % [kg/m3]
ry.stage.STEP = 'Tilt_Stage.STEP';
% Z-Offset so that the center of rotation matches the sample center;
ry.z_offset = 0.58178; % [m]
ry.Ry_init = args.Ry_init; % [rad]
ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8];
ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4];
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'ry', '-append');
else
save('mat/nass_model_stages.mat', 'ry');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'ry', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'ry');
end
end
end
#+end_src
*** =initializeRz=: Spindle
#+begin_src matlab :tangle matlab/src/initializeRz.m :comments none :mkdirp yes :eval no
function [rz] = initializeRz(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
end
rz = struct();
switch args.type
case 'none'
rz.type = 0;
case 'rigid'
rz.type = 1;
case 'flexible'
rz.type = 2;
end
% Spindle - Slip Ring
rz.slipring.density = 7800; % [kg/m3]
rz.slipring.STEP = 'Spindle_Slip_Ring.STEP';
% Spindle - Rotor
rz.rotor.density = 7800; % [kg/m3]
rz.rotor.STEP = 'Spindle_Rotor.STEP';
% Spindle - Stator
rz.stator.density = 7800; % [kg/m3]
rz.stator.STEP = 'Spindle_Stator.STEP';
rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7];
rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4];
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'rz', '-append');
else
save('mat/nass_model_stages.mat', 'rz');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'rz', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'rz');
end
end
end
#+end_src
*** =initializeMicroHexapod=: Micro Hexapod
#+begin_src matlab :tangle matlab/src/initializeMicroHexapod.m :comments none :mkdirp yes :eval no
function [micro_hexapod] = initializeMicroHexapod(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
% initializeFramesPositions
args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3
args.MO_B (1,1) double {mustBeNumeric} = 270e-3
% generateGeneralConfiguration
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 175.5e-3
args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180)
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 45e-3
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 118e-3
args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180)
% initializeStrutDynamics
args.Ki (1,1) double {mustBeNumeric, mustBeNonnegative} = 2e7
args.Ci (1,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3
% initializeCylindricalPlatforms
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 10
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 207.5e-3
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 10
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3
% initializeCylindricalStruts
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
% inverseKinematics
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, ...
'H', args.H, ...
'MO_B', args.MO_B);
stewart = generateGeneralConfiguration(stewart, ...
'FH', args.FH, ...
'FR', args.FR, ...
'FTh', args.FTh, ...
'MH', args.MH, ...
'MR', args.MR, ...
'MTh', args.MTh);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, ...
'k', args.Ki, ...
'c', args.Ci);
stewart = initializeJointDynamics(stewart, ...
'type_F', '2dof', ...
'type_M', '3dof');
stewart = initializeCylindricalPlatforms(stewart, ...
'Fpm', args.Fpm, ...
'Fph', args.Fph, ...
'Fpr', args.Fpr, ...
'Mpm', args.Mpm, ...
'Mph', args.Mph, ...
'Mpr', args.Mpr);
stewart = initializeCylindricalStruts(stewart, ...
'Fsm', args.Fsm, ...
'Fsh', args.Fsh, ...
'Fsr', args.Fsr, ...
'Msm', args.Msm, ...
'Msh', args.Msh, ...
'Msr', args.Msr);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart, ...
'AP', args.AP, ...
'ARB', args.ARB);
stewart = initializeInertialSensor(stewart, 'type', 'none');
switch args.type
case 'none'
stewart.type = 0;
case 'rigid'
stewart.type = 1;
case 'flexible'
stewart.type = 2;
end
micro_hexapod = stewart;
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'micro_hexapod', '-append');
else
save('mat/nass_model_stages.mat', 'micro_hexapod');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'micro_hexapod', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'micro_hexapod');
end
end
end
#+end_src
*** =initializeSimplifiedNanoHexapod=: Nano Hexapod
#+begin_src matlab :tangle matlab/src/initializeSimplifiedNanoHexapod.m :comments none :mkdirp yes :eval no
function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
arguments
%% initializeFramesPositions
args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3 % Height of the nano-hexapod [m]
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
%% generateGeneralConfiguration
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3 % Height of fixed joints [m]
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 120e-3 % Radius of fixed joints [m]
args.FTh (6,1) double {mustBeNumeric} = [220, 320, 340, 80, 100, 200]*(pi/180) % Angles of fixed joints [rad]
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3 % Height of mobile joints [m]
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 110e-3 % Radius of mobile joints [m]
args.MTh (6,1) double {mustBeNumeric} = [255, 285, 15, 45, 135, 165]*(pi/180) % Angles of fixed joints [rad]
%% Actuators
args.actuator_type char {mustBeMember(args.actuator_type,{'1dof', '2dof', 'flexible'})} = '1dof'
args.actuator_k (1,1) double {mustBeNumeric, mustBePositive} = 1e6
args.actuator_kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e4
args.actuator_ke (1,1) double {mustBeNumeric, mustBePositive} = 4952605
args.actuator_ka (1,1) double {mustBeNumeric, mustBePositive} = 2476302
args.actuator_c (1,1) double {mustBeNumeric, mustBePositive} = 50
args.actuator_cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.actuator_ce (1,1) double {mustBeNumeric, mustBePositive} = 100
args.actuator_ca (1,1) double {mustBeNumeric, mustBePositive} = 50
%% initializeCylindricalPlatforms
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 5 % Mass of the fixed plate [kg]
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3 % Thickness of the fixed plate [m]
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3 % Radius of the fixed plate [m]
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 5 % Mass of the mobile plate [kg]
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3 % Thickness of the mobile plate [m]
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3 % Radius of the mobile plate [m]
%% initializeCylindricalStruts
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % Mass of the fixed part of the strut [kg]
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 60e-3 % Length of the fixed part of the struts [m]
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3 % Radius of the fixed part of the struts [m]
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % Mass of the mobile part of the strut [kg]
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 60e-3 % Length of the mobile part of the struts [m]
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3 % Radius of the fixed part of the struts [m]
%% Bottom and Top Flexible Joints
args.flex_type_F char {mustBeMember(args.flex_type_F,{'2dof', '3dof', '4dof', '6dof', 'flexible'})} = '2dof'
args.flex_type_M char {mustBeMember(args.flex_type_M,{'2dof', '3dof', '4dof', '6dof', 'flexible'})} = '3dof'
args.Kf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kt_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ct_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kt_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ct_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ka_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ca_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ka_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ca_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
%% inverseKinematics
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, ...
'H', args.H, ...
'MO_B', args.MO_B);
stewart = generateGeneralConfiguration(stewart, ...
'FH', args.FH, ...
'FR', args.FR, ...
'FTh', args.FTh, ...
'MH', args.MH, ...
'MR', args.MR, ...
'MTh', args.MTh);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, ...
'type', args.actuator_type, ...
'k', args.actuator_k, ...
'kp', args.actuator_kp, ...
'ke', args.actuator_ke, ...
'ka', args.actuator_ka, ...
'c', args.actuator_c, ...
'cp', args.actuator_cp, ...
'ce', args.actuator_ce, ...
'ca', args.actuator_ca);
stewart = initializeJointDynamics(stewart, ...
'type_F', args.flex_type_F, ...
'type_M', args.flex_type_M, ...
'Kf_M', args.Kf_M, ...
'Cf_M', args.Cf_M, ...
'Kt_M', args.Kt_M, ...
'Ct_M', args.Ct_M, ...
'Kf_F', args.Kf_F, ...
'Cf_F', args.Cf_F, ...
'Kt_F', args.Kt_F, ...
'Ct_F', args.Ct_F, ...
'Ka_F', args.Ka_F, ...
'Ca_F', args.Ca_F, ...
'Kr_F', args.Kr_F, ...
'Cr_F', args.Cr_F, ...
'Ka_M', args.Ka_M, ...
'Ca_M', args.Ca_M, ...
'Kr_M', args.Kr_M, ...
'Cr_M', args.Cr_M);
stewart = initializeCylindricalPlatforms(stewart, ...
'Fpm', args.Fpm, ...
'Fph', args.Fph, ...
'Fpr', args.Fpr, ...
'Mpm', args.Mpm, ...
'Mph', args.Mph, ...
'Mpr', args.Mpr);
stewart = initializeCylindricalStruts(stewart, ...
'Fsm', args.Fsm, ...
'Fsh', args.Fsh, ...
'Fsr', args.Fsr, ...
'Msm', args.Msm, ...
'Msh', args.Msh, ...
'Msr', args.Msr);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart, ...
'AP', args.AP, ...
'ARB', args.ARB);
nano_hexapod = stewart;
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'nano_hexapod', '-append');
else
save('mat/nass_model_stages.mat', 'nano_hexapod');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'nano_hexapod', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'nano_hexapod');
end
end
end
#+end_src
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*** =initializeSample=: Sample
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#+begin_src matlab :tangle matlab/src/initializeSample.m :comments none :mkdirp yes :eval no
function [sample] = initializeSample(args)
arguments
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args.type char {mustBeMember(args.type,{'none', 'cylindrical'})} = 'none'
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args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3 % Height [m]
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args.R (1,1) double {mustBeNumeric, mustBePositive} = 110e-3 % Radius [m]
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args.m (1,1) double {mustBeNumeric, mustBePositive} = 1 % Mass [kg]
end
sample = struct();
switch args.type
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case 'none'
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sample.type = 0;
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sample.m = 0;
case 'cylindrical'
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sample.type = 1;
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sample.H = args.H;
sample.R = args.R;
sample.m = args.m;
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end
if exist('./mat', 'dir')
if exist('./mat/nass_model_stages.mat', 'file')
save('mat/nass_model_stages.mat', 'sample', '-append');
else
save('mat/nass_model_stages.mat', 'sample');
end
elseif exist('./matlab', 'dir')
if exist('./matlab/mat/nass_model_stages.mat', 'file')
save('matlab/mat/nass_model_stages.mat', 'sample', '-append');
else
save('matlab/mat/nass_model_stages.mat', 'sample');
end
end
end
#+end_src
** Initialize Nano-Hexapod
*** =initializeStewartPlatform=: Initialize the Stewart Platform structure
#+begin_src matlab :tangle matlab/src/initializeStewartPlatform.m :comments none :mkdirp yes :eval no
function [stewart] = initializeStewartPlatform()
% initializeStewartPlatform - Initialize the stewart structure
%
% Syntax: [stewart] = initializeStewartPlatform(args)
%
% Outputs:
% - stewart - A structure with the following sub-structures:
% - platform_F -
% - platform_M -
% - joints_F -
% - joints_M -
% - struts_F -
% - struts_M -
% - actuators -
% - geometry -
% - properties -
stewart = struct();
stewart.platform_F = struct();
stewart.platform_M = struct();
stewart.joints_F = struct();
stewart.joints_M = struct();
stewart.struts_F = struct();
stewart.struts_M = struct();
stewart.actuators = struct();
stewart.sensors = struct();
stewart.sensors.inertial = struct();
stewart.sensors.force = struct();
stewart.sensors.relative = struct();
stewart.geometry = struct();
stewart.kinematics = struct();
end
#+end_src
*** =initializeFramesPositions=: Initialize the positions of frames {A}, {B}, {F} and {M}
#+begin_src matlab :tangle matlab/src/initializeFramesPositions.m :comments none :mkdirp yes :eval no
function [stewart] = initializeFramesPositions(stewart, args)
% initializeFramesPositions - Initialize the positions of frames {A}, {B}, {F} and {M}
%
% Syntax: [stewart] = initializeFramesPositions(stewart, args)
%
% Inputs:
% - args - Can have the following fields:
% - H [1x1] - Total Height of the Stewart Platform (height from {F} to {M}) [m]
% - MO_B [1x1] - Height of the frame {B} with respect to {M} [m]
%
% Outputs:
% - stewart - A structure with the following fields:
% - geometry.H [1x1] - Total Height of the Stewart Platform [m]
% - geometry.FO_M [3x1] - Position of {M} with respect to {F} [m]
% - platform_M.MO_B [3x1] - Position of {B} with respect to {M} [m]
% - platform_F.FO_A [3x1] - Position of {A} with respect to {F} [m]
arguments
stewart
args.H (1,1) double {mustBeNumeric, mustBePositive} = 90e-3
args.MO_B (1,1) double {mustBeNumeric} = 50e-3
end
H = args.H; % Total Height of the Stewart Platform [m]
FO_M = [0; 0; H]; % Position of {M} with respect to {F} [m]
MO_B = [0; 0; args.MO_B]; % Position of {B} with respect to {M} [m]
FO_A = MO_B + FO_M; % Position of {A} with respect to {F} [m]
stewart.geometry.H = H;
stewart.geometry.FO_M = FO_M;
stewart.platform_M.MO_B = MO_B;
stewart.platform_F.FO_A = FO_A;
end
#+end_src
*** =generateGeneralConfiguration=: Generate a Very General Configuration
#+begin_src matlab :tangle matlab/src/generateGeneralConfiguration.m :comments none :mkdirp yes :eval no
function [stewart] = generateGeneralConfiguration(stewart, args)
% generateGeneralConfiguration - Generate a Very General Configuration
%
% Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
%
% Inputs:
% - args - Can have the following fields:
% - FH [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m]
% - FR [1x1] - Radius of the position of the fixed joints in the X-Y [m]
% - FTh [6x1] - Angles of the fixed joints in the X-Y plane with respect to the X axis [rad]
% - MH [1x1] - Height of the position of the mobile joints with respect to the frame {M} [m]
% - FR [1x1] - Radius of the position of the mobile joints in the X-Y [m]
% - MTh [6x1] - Angles of the mobile joints in the X-Y plane with respect to the X axis [rad]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
arguments
stewart
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 115e-3;
args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180);
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e-3;
args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180);
end
Fa = zeros(3,6);
Mb = zeros(3,6);
for i = 1:6
Fa(:,i) = [args.FR*cos(args.FTh(i)); args.FR*sin(args.FTh(i)); args.FH];
Mb(:,i) = [args.MR*cos(args.MTh(i)); args.MR*sin(args.MTh(i)); -args.MH];
end
stewart.platform_F.Fa = Fa;
stewart.platform_M.Mb = Mb;
end
#+end_src
*** =computeJointsPose=: Compute the Pose of the Joints
#+begin_src matlab :tangle matlab/src/computeJointsPose.m :comments none :mkdirp yes :eval no
function [stewart] = computeJointsPose(stewart)
% computeJointsPose -
%
% Syntax: [stewart] = computeJointsPose(stewart)
%
% Inputs:
% - stewart - A structure with the following fields
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
% - platform_F.FO_A [3x1] - Position of {A} with respect to {F}
% - platform_M.MO_B [3x1] - Position of {B} with respect to {M}
% - geometry.FO_M [3x1] - Position of {M} with respect to {F}
%
% Outputs:
% - stewart - A structure with the following added fields
% - geometry.Aa [3x6] - The i'th column is the position of ai with respect to {A}
% - geometry.Ab [3x6] - The i'th column is the position of bi with respect to {A}
% - geometry.Ba [3x6] - The i'th column is the position of ai with respect to {B}
% - geometry.Bb [3x6] - The i'th column is the position of bi with respect to {B}
% - geometry.l [6x1] - The i'th element is the initial length of strut i
% - geometry.As [3x6] - The i'th column is the unit vector of strut i expressed in {A}
% - geometry.Bs [3x6] - The i'th column is the unit vector of strut i expressed in {B}
% - struts_F.l [6x1] - Length of the Fixed part of the i'th strut
% - struts_M.l [6x1] - Length of the Mobile part of the i'th strut
% - platform_F.FRa [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the bottom of the i'th strut from {F}
% - platform_M.MRb [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the top of the i'th strut from {M}
assert(isfield(stewart.platform_F, 'Fa'), 'stewart.platform_F should have attribute Fa')
Fa = stewart.platform_F.Fa;
assert(isfield(stewart.platform_M, 'Mb'), 'stewart.platform_M should have attribute Mb')
Mb = stewart.platform_M.Mb;
assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
FO_A = stewart.platform_F.FO_A;
assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
MO_B = stewart.platform_M.MO_B;
assert(isfield(stewart.geometry, 'FO_M'), 'stewart.geometry should have attribute FO_M')
FO_M = stewart.geometry.FO_M;
Aa = Fa - repmat(FO_A, [1, 6]);
Bb = Mb - repmat(MO_B, [1, 6]);
Ab = Bb - repmat(-MO_B-FO_M+FO_A, [1, 6]);
Ba = Aa - repmat( MO_B+FO_M-FO_A, [1, 6]);
As = (Ab - Aa)./vecnorm(Ab - Aa); % As_i is the i'th vector of As
l = vecnorm(Ab - Aa)';
Bs = (Bb - Ba)./vecnorm(Bb - Ba);
FRa = zeros(3,3,6);
MRb = zeros(3,3,6);
for i = 1:6
FRa(:,:,i) = [cross([0;1;0], As(:,i)) , cross(As(:,i), cross([0;1;0], As(:,i))) , As(:,i)];
FRa(:,:,i) = FRa(:,:,i)./vecnorm(FRa(:,:,i));
MRb(:,:,i) = [cross([0;1;0], Bs(:,i)) , cross(Bs(:,i), cross([0;1;0], Bs(:,i))) , Bs(:,i)];
MRb(:,:,i) = MRb(:,:,i)./vecnorm(MRb(:,:,i));
end
stewart.geometry.Aa = Aa;
stewart.geometry.Ab = Ab;
stewart.geometry.Ba = Ba;
stewart.geometry.Bb = Bb;
stewart.geometry.As = As;
stewart.geometry.Bs = Bs;
stewart.geometry.l = l;
stewart.struts_F.l = l/2;
stewart.struts_M.l = l/2;
stewart.platform_F.FRa = FRa;
stewart.platform_M.MRb = MRb;
end
#+end_src
*** =initializeCylindricalPlatforms=: Initialize the geometry of the Fixed and Mobile Platforms
#+begin_src matlab :tangle matlab/src/initializeCylindricalPlatforms.m :comments none :mkdirp yes :eval no
function [stewart] = initializeCylindricalPlatforms(stewart, args)
% initializeCylindricalPlatforms - Initialize the geometry of the Fixed and Mobile Platforms
%
% Syntax: [stewart] = initializeCylindricalPlatforms(args)
%
% Inputs:
% - args - Structure with the following fields:
% - Fpm [1x1] - Fixed Platform Mass [kg]
% - Fph [1x1] - Fixed Platform Height [m]
% - Fpr [1x1] - Fixed Platform Radius [m]
% - Mpm [1x1] - Mobile Platform Mass [kg]
% - Mph [1x1] - Mobile Platform Height [m]
% - Mpr [1x1] - Mobile Platform Radius [m]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - platform_F [struct] - structure with the following fields:
% - type = 1
% - M [1x1] - Fixed Platform Mass [kg]
% - I [3x3] - Fixed Platform Inertia matrix [kg*m^2]
% - H [1x1] - Fixed Platform Height [m]
% - R [1x1] - Fixed Platform Radius [m]
% - platform_M [struct] - structure with the following fields:
% - M [1x1] - Mobile Platform Mass [kg]
% - I [3x3] - Mobile Platform Inertia matrix [kg*m^2]
% - H [1x1] - Mobile Platform Height [m]
% - R [1x1] - Mobile Platform Radius [m]
arguments
stewart
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 125e-3
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
end
I_F = diag([1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
1/2 *args.Fpm * args.Fpr^2]);
I_M = diag([1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
1/2 *args.Mpm * args.Mpr^2]);
stewart.platform_F.type = 1;
stewart.platform_F.I = I_F;
stewart.platform_F.M = args.Fpm;
stewart.platform_F.R = args.Fpr;
stewart.platform_F.H = args.Fph;
stewart.platform_M.type = 1;
stewart.platform_M.I = I_M;
stewart.platform_M.M = args.Mpm;
stewart.platform_M.R = args.Mpr;
stewart.platform_M.H = args.Mph;
end
#+end_src
*** =initializeCylindricalStruts=: Define the inertia of cylindrical struts
#+begin_src matlab :tangle matlab/src/initializeCylindricalStruts.m :comments none :mkdirp yes :eval no
function [stewart] = initializeCylindricalStruts(stewart, args)
% initializeCylindricalStruts - Define the mass and moment of inertia of cylindrical struts
%
% Syntax: [stewart] = initializeCylindricalStruts(args)
%
% Inputs:
% - args - Structure with the following fields:
% - Fsm [1x1] - Mass of the Fixed part of the struts [kg]
% - Fsh [1x1] - Height of cylinder for the Fixed part of the struts [m]
% - Fsr [1x1] - Radius of cylinder for the Fixed part of the struts [m]
% - Msm [1x1] - Mass of the Mobile part of the struts [kg]
% - Msh [1x1] - Height of cylinder for the Mobile part of the struts [m]
% - Msr [1x1] - Radius of cylinder for the Mobile part of the struts [m]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - struts_F [struct] - structure with the following fields:
% - M [6x1] - Mass of the Fixed part of the struts [kg]
% - I [3x3x6] - Moment of Inertia for the Fixed part of the struts [kg*m^2]
% - H [6x1] - Height of cylinder for the Fixed part of the struts [m]
% - R [6x1] - Radius of cylinder for the Fixed part of the struts [m]
% - struts_M [struct] - structure with the following fields:
% - M [6x1] - Mass of the Mobile part of the struts [kg]
% - I [3x3x6] - Moment of Inertia for the Mobile part of the struts [kg*m^2]
% - H [6x1] - Height of cylinder for the Mobile part of the struts [m]
% - R [6x1] - Radius of cylinder for the Mobile part of the struts [m]
arguments
stewart
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
end
stewart.struts_M.type = 1;
%% Compute the properties of the cylindrical struts
Fsm = args.Fsm;
Fsh = args.Fsh;
Fsr = args.Fsr;
Msm = args.Msm;
Msh = args.Msh;
Msr = args.Msr;
I_F = [1/12 * Fsm * (3*Fsr^2 + Fsh^2), ...
1/12 * Fsm * (3*Fsr^2 + Fsh^2), ...
1/2 * Fsm * Fsr^2];
I_M = [1/12 * Msm * (3*Msr^2 + Msh^2), ...
1/12 * Msm * (3*Msr^2 + Msh^2), ...
1/2 * Msm * Msr^2];
stewart.struts_M.I = I_M;
stewart.struts_F.I = I_F;
stewart.struts_M.M = args.Msm;
stewart.struts_M.R = args.Msr;
stewart.struts_M.H = args.Msh;
stewart.struts_F.type = 1;
stewart.struts_F.M = args.Fsm;
stewart.struts_F.R = args.Fsr;
stewart.struts_F.H = args.Fsh;
end
#+end_src
*** =initializeStrutDynamics=: Add Stiffness and Damping properties of each strut
#+begin_src matlab :tangle matlab/src/initializeStrutDynamics.m :comments none :mkdirp yes :eval no
function [stewart] = initializeStrutDynamics(stewart, args)
% initializeStrutDynamics - Add Stiffness and Damping properties of each strut
%
% Syntax: [stewart] = initializeStrutDynamics(args)
%
% Inputs:
% - args - Structure with the following fields:
% - K [6x1] - Stiffness of each strut [N/m]
% - C [6x1] - Damping of each strut [N/(m/s)]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - actuators.type = 1
% - actuators.K [6x1] - Stiffness of each strut [N/m]
% - actuators.C [6x1] - Damping of each strut [N/(m/s)]
arguments
stewart
args.type char {mustBeMember(args.type,{'1dof', '2dof', 'flexible'})} = '1dof'
args.k (1,1) double {mustBeNumeric, mustBeNonnegative} = 20e6
args.kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.ke (1,1) double {mustBeNumeric, mustBeNonnegative} = 5e6
args.ka (1,1) double {mustBeNumeric, mustBeNonnegative} = 60e6
args.c (1,1) double {mustBeNumeric, mustBeNonnegative} = 2e1
args.cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.ce (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e6
args.ca (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
args.F_gain (1,1) double {mustBeNumeric} = 1
args.me (1,1) double {mustBeNumeric} = 0.01
args.ma (1,1) double {mustBeNumeric} = 0.01
end
if strcmp(args.type, '1dof')
stewart.actuators.type = 1;
elseif strcmp(args.type, '2dof')
stewart.actuators.type = 2;
elseif strcmp(args.type, 'flexible')
stewart.actuators.type = 3;
end
stewart.actuators.k = args.k;
stewart.actuators.c = args.c;
% Parallel stiffness
stewart.actuators.kp = args.kp;
stewart.actuators.cp = args.cp;
stewart.actuators.ka = args.ka;
stewart.actuators.ca = args.ca;
stewart.actuators.ke = args.ke;
stewart.actuators.ce = args.ce;
stewart.actuators.F_gain = args.F_gain;
stewart.actuators.ma = args.ma;
stewart.actuators.me = args.me;
end
#+end_src
*** =initializeJointDynamics=: Add Stiffness and Damping properties for spherical joints
#+begin_src matlab :tangle matlab/src/initializeJointDynamics.m :comments none :mkdirp yes :eval no
function [stewart] = initializeJointDynamics(stewart, args)
% initializeJointDynamics - Add Stiffness and Damping properties for the spherical joints
%
% Syntax: [stewart] = initializeJointDynamics(args)
%
% Inputs:
% - args - Structure with the following fields:
% - type_F - 'universal', 'spherical', 'universal_p', 'spherical_p'
% - type_M - 'universal', 'spherical', 'universal_p', 'spherical_p'
% - Kf_M [6x1] - Bending (Rx, Ry) Stiffness for each top joints [(N.m)/rad]
% - Kt_M [6x1] - Torsion (Rz) Stiffness for each top joints [(N.m)/rad]
% - Cf_M [6x1] - Bending (Rx, Ry) Damping of each top joint [(N.m)/(rad/s)]
% - Ct_M [6x1] - Torsion (Rz) Damping of each top joint [(N.m)/(rad/s)]
% - Kf_F [6x1] - Bending (Rx, Ry) Stiffness for each bottom joints [(N.m)/rad]
% - Kt_F [6x1] - Torsion (Rz) Stiffness for each bottom joints [(N.m)/rad]
% - Cf_F [6x1] - Bending (Rx, Ry) Damping of each bottom joint [(N.m)/(rad/s)]
% - Cf_F [6x1] - Torsion (Rz) Damping of each bottom joint [(N.m)/(rad/s)]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - stewart.joints_F and stewart.joints_M:
% - type - 1 (universal), 2 (spherical), 3 (universal perfect), 4 (spherical perfect)
% - Kx, Ky, Kz [6x1] - Translation (Tx, Ty, Tz) Stiffness [N/m]
% - Kf [6x1] - Flexion (Rx, Ry) Stiffness [(N.m)/rad]
% - Kt [6x1] - Torsion (Rz) Stiffness [(N.m)/rad]
% - Cx, Cy, Cz [6x1] - Translation (Rx, Ry) Damping [N/(m/s)]
% - Cf [6x1] - Flexion (Rx, Ry) Damping [(N.m)/(rad/s)]
% - Cb [6x1] - Torsion (Rz) Damping [(N.m)/(rad/s)]
arguments
stewart
args.type_F char {mustBeMember(args.type_F,{'2dof', '3dof', '4dof', '6dof', 'flexible'})} = '2dof'
args.type_M char {mustBeMember(args.type_M,{'2dof', '3dof', '4dof', '6dof', 'flexible'})} = '3dof'
args.Kf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cf_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kt_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ct_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cf_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kt_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ct_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ka_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ca_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cr_F (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ka_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Ca_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Kr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.Cr_M (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
args.K_M double {mustBeNumeric} = zeros(6,6)
args.M_M double {mustBeNumeric} = zeros(6,6)
args.n_xyz_M double {mustBeNumeric} = zeros(2,3)
args.xi_M double {mustBeNumeric} = 0.1
args.step_file_M char {} = ''
args.K_F double {mustBeNumeric} = zeros(6,6)
args.M_F double {mustBeNumeric} = zeros(6,6)
args.n_xyz_F double {mustBeNumeric} = zeros(2,3)
args.xi_F double {mustBeNumeric} = 0.1
args.step_file_F char {} = ''
end
switch args.type_F
case '2dof'
stewart.joints_F.type = 1;
case '3dof'
stewart.joints_F.type = 2;
case '4dof'
stewart.joints_F.type = 3;
case '6dof'
stewart.joints_F.type = 4;
case 'flexible'
stewart.joints_F.type = 5;
otherwise
error("joints_F are not correctly defined")
end
switch args.type_M
case '2dof'
stewart.joints_M.type = 1;
case '3dof'
stewart.joints_M.type = 2;
case '4dof'
stewart.joints_M.type = 3;
case '6dof'
stewart.joints_M.type = 4;
case 'flexible'
stewart.joints_M.type = 5;
otherwise
error("joints_M are not correctly defined")
end
stewart.joints_M.Ka = args.Ka_M;
stewart.joints_M.Kr = args.Kr_M;
stewart.joints_F.Ka = args.Ka_F;
stewart.joints_F.Kr = args.Kr_F;
stewart.joints_M.Ca = args.Ca_M;
stewart.joints_M.Cr = args.Cr_M;
stewart.joints_F.Ca = args.Ca_F;
stewart.joints_F.Cr = args.Cr_F;
stewart.joints_M.Kf = args.Kf_M;
stewart.joints_M.Kt = args.Kt_M;
stewart.joints_F.Kf = args.Kf_F;
stewart.joints_F.Kt = args.Kt_F;
stewart.joints_M.Cf = args.Cf_M;
stewart.joints_M.Ct = args.Ct_M;
stewart.joints_F.Cf = args.Cf_F;
stewart.joints_F.Ct = args.Ct_F;
stewart.joints_F.M = args.M_F;
stewart.joints_F.K = args.K_F;
stewart.joints_F.n_xyz = args.n_xyz_F;
stewart.joints_F.xi = args.xi_F;
stewart.joints_F.xi = args.xi_F;
stewart.joints_F.step_file = args.step_file_F;
stewart.joints_M.M = args.M_M;
stewart.joints_M.K = args.K_M;
stewart.joints_M.n_xyz = args.n_xyz_M;
stewart.joints_M.xi = args.xi_M;
stewart.joints_M.step_file = args.step_file_M;
end
#+end_src
*** =initializeStewartPose=: Determine the initial stroke in each leg to have the wanted pose
#+begin_src matlab :tangle matlab/src/initializeStewartPose.m :comments none :mkdirp yes :eval no
function [stewart] = initializeStewartPose(stewart, args)
% initializeStewartPose - Determine the initial stroke in each leg to have the wanted pose
% It uses the inverse kinematic
%
% Syntax: [stewart] = initializeStewartPose(stewart, args)
%
% Inputs:
% - stewart - A structure with the following fields
% - Aa [3x6] - The positions ai expressed in {A}
% - Bb [3x6] - The positions bi expressed in {B}
% - args - Can have the following fields:
% - AP [3x1] - The wanted position of {B} with respect to {A}
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - actuators.Leq [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
arguments
stewart
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
[Li, dLi] = inverseKinematics(stewart, 'AP', args.AP, 'ARB', args.ARB);
stewart.actuators.Leq = dLi;
end
#+end_src
*** =computeJacobian=: Compute the Jacobian Matrix
#+begin_src matlab :tangle matlab/src/computeJacobian.m :comments none :mkdirp yes :eval no
function [stewart] = computeJacobian(stewart)
% computeJacobian -
%
% Syntax: [stewart] = computeJacobian(stewart)
%
% Inputs:
% - stewart - With at least the following fields:
% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}
% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}
% - actuators.K [6x1] - Total stiffness of the actuators
%
% Outputs:
% - stewart - With the 3 added field:
% - geometry.J [6x6] - The Jacobian Matrix
% - geometry.K [6x6] - The Stiffness Matrix
% - geometry.C [6x6] - The Compliance Matrix
assert(isfield(stewart.geometry, 'As'), 'stewart.geometry should have attribute As')
As = stewart.geometry.As;
assert(isfield(stewart.geometry, 'Ab'), 'stewart.geometry should have attribute Ab')
Ab = stewart.geometry.Ab;
assert(isfield(stewart.actuators, 'k'), 'stewart.actuators should have attribute k')
Ki = stewart.actuators.k;
J = [As' , cross(Ab, As)'];
K = J'*diag(Ki)*J;
C = inv(K);
stewart.geometry.J = J;
stewart.geometry.K = K;
stewart.geometry.C = C;
end
#+end_src
*** =inverseKinematics=: Compute Inverse Kinematics
#+begin_src matlab :tangle matlab/src/inverseKinematics.m :comments none :mkdirp yes :eval no
function [Li, dLi] = inverseKinematics(stewart, args)
% inverseKinematics - Compute the needed length of each strut to have the wanted position and orientation of {B} with respect to {A}
%
% Syntax: [stewart] = inverseKinematics(stewart)
%
% Inputs:
% - stewart - A structure with the following fields
% - geometry.Aa [3x6] - The positions ai expressed in {A}
% - geometry.Bb [3x6] - The positions bi expressed in {B}
% - geometry.l [6x1] - Length of each strut
% - args - Can have the following fields:
% - AP [3x1] - The wanted position of {B} with respect to {A}
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
%
% Outputs:
% - Li [6x1] - The 6 needed length of the struts in [m] to have the wanted pose of {B} w.r.t. {A}
% - dLi [6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
arguments
stewart
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
assert(isfield(stewart.geometry, 'Aa'), 'stewart.geometry should have attribute Aa')
Aa = stewart.geometry.Aa;
assert(isfield(stewart.geometry, 'Bb'), 'stewart.geometry should have attribute Bb')
Bb = stewart.geometry.Bb;
assert(isfield(stewart.geometry, 'l'), 'stewart.geometry should have attribute l')
l = stewart.geometry.l;
Li = sqrt(args.AP'*args.AP + diag(Bb'*Bb) + diag(Aa'*Aa) - (2*args.AP'*Aa)' + (2*args.AP'* (args.ARB*Bb))' - diag(2* (args.ARB*Bb)'*Aa));
dLi = Li-l;
end
#+end_src
*** =displayArchitecture=: 3D plot of the Stewart platform architecture
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/displayArchitecture.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:displayArchitecture >>
This Matlab function is accessible [[file:../src/displayArchitecture.m ][here ]].
**** Function description
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
function [] = displayArchitecture(stewart, args)
% displayArchitecture - 3D plot of the Stewart platform architecture
%
% Syntax: [] = displayArchitecture(args)
%
% Inputs:
% - stewart
% - args - Structure with the following fields:
% - AP [3x1] - The wanted position of {B} with respect to {A}
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
% - F_color [color] - Color used for the Fixed elements
% - M_color [color] - Color used for the Mobile elements
% - L_color [color] - Color used for the Legs elements
% - frames [true/false] - Display the Frames
% - legs [true/false] - Display the Legs
% - joints [true/false] - Display the Joints
% - labels [true/false] - Display the Labels
% - platforms [true/false] - Display the Platforms
% - views ['all', 'xy', 'yz', 'xz', 'default'] -
%
% Outputs:
#+end_src
**** Optional Parameters
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
arguments
stewart
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
args.F_color = [0 0.4470 0.7410]
args.M_color = [0.8500 0.3250 0.0980]
args.L_color = [0 0 0]
args.frames logical {mustBeNumericOrLogical} = true
args.legs logical {mustBeNumericOrLogical} = true
args.joints logical {mustBeNumericOrLogical} = true
args.labels logical {mustBeNumericOrLogical} = true
args.platforms logical {mustBeNumericOrLogical} = true
args.views char {mustBeMember(args.views,{'all', 'xy', 'xz', 'yz', 'default'})} = 'default'
end
#+end_src
**** Check the =stewart= structure elements
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
FO_A = stewart.platform_F.FO_A;
assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
MO_B = stewart.platform_M.MO_B;
assert(isfield(stewart.geometry, 'H'), 'stewart.geometry should have attribute H')
H = stewart.geometry.H;
assert(isfield(stewart.platform_F, 'Fa'), 'stewart.platform_F should have attribute Fa')
Fa = stewart.platform_F.Fa;
assert(isfield(stewart.platform_M, 'Mb'), 'stewart.platform_M should have attribute Mb')
Mb = stewart.platform_M.Mb;
#+end_src
**** Figure Creation, Frames and Homogeneous transformations
:PROPERTIES:
:UNNUMBERED: t
:END:
The reference frame of the 3d plot corresponds to the frame $\{F\}$.
#+begin_src matlab
if ~strcmp(args.views, 'all')
figure;
else
f = figure('visible', 'off');
end
hold on;
#+end_src
We first compute homogeneous matrices that will be useful to position elements on the figure where the reference frame is $\{F\}$.
#+begin_src matlab
FTa = [eye(3), FO_A; ...
zeros(1,3), 1];
ATb = [args.ARB, args.AP; ...
zeros(1,3), 1];
BTm = [eye(3), -MO_B; ...
zeros(1,3), 1];
FTm = FTa*ATb*BTm;
#+end_src
Let's define a parameter that define the length of the unit vectors used to display the frames.
#+begin_src matlab
d_unit_vector = H/4;
#+end_src
Let's define a parameter used to position the labels with respect to the center of the element.
#+begin_src matlab
d_label = H/20;
#+end_src
**** Fixed Base elements
:PROPERTIES:
:UNNUMBERED: t
:END:
Let's first plot the frame $\{F\}$.
#+begin_src matlab
Ff = [0, 0, 0];
if args.frames
quiver3(Ff(1)*ones(1,3), Ff(2)*ones(1,3), Ff(3)*ones(1,3), ...
[d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
if args.labels
text(Ff(1) + d_label, ...
Ff(2) + d_label, ...
Ff(3) + d_label, '$\{F\}$', 'Color', args.F_color);
end
end
#+end_src
Now plot the frame $\{A\}$ fixed to the Base.
#+begin_src matlab
if args.frames
quiver3(FO_A(1)*ones(1,3), FO_A(2)*ones(1,3), FO_A(3)*ones(1,3), ...
[d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
if args.labels
text(FO_A(1) + d_label, ...
FO_A(2) + d_label, ...
FO_A(3) + d_label, '$\{A\}$', 'Color', args.F_color);
end
end
#+end_src
Let's then plot the circle corresponding to the shape of the Fixed base.
#+begin_src matlab
if args.platforms && stewart.platform_F.type == 1
theta = [0:0.01:2*pi+0.01]; % Angles [rad]
v = null([0; 0; 1]'); % Two vectors that are perpendicular to the circle normal
center = [0; 0; 0]; % Center of the circle
radius = stewart.platform_F.R; % Radius of the circle [m]
points = center*ones(1, length(theta)) + radius* (v(:,1)*cos(theta) + v(:,2)*sin(theta));
plot3(points(1,:), ...
points(2,:), ...
points(3,:), '-', 'Color', args.F_color);
end
#+end_src
Let's now plot the position and labels of the Fixed Joints
#+begin_src matlab
if args.joints
scatter3(Fa(1,:), ...
Fa(2,:), ...
Fa(3,:), 'MarkerEdgeColor', args.F_color);
if args.labels
for i = 1:size(Fa,2)
text(Fa(1,i) + d_label, ...
Fa(2,i), ...
Fa(3,i), sprintf('$a_{%i}$', i), 'Color', args.F_color);
end
end
end
#+end_src
**** Mobile Platform elements
:PROPERTIES:
:UNNUMBERED: t
:END:
Plot the frame $\{M\}$.
#+begin_src matlab
Fm = FTm*[0; 0; 0; 1]; % Get the position of frame {M} w.r.t. {F}
if args.frames
FM_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
quiver3(Fm(1)*ones(1,3), Fm(2)*ones(1,3), Fm(3)*ones(1,3), ...
FM_uv(1,1:3), FM_uv(2,1:3), FM_uv(3,1:3), '-', 'Color', args.M_color)
if args.labels
text(Fm(1) + d_label, ...
Fm(2) + d_label, ...
Fm(3) + d_label, '$\{M\}$', 'Color', args.M_color);
end
end
#+end_src
Plot the frame $\{B\}$.
#+begin_src matlab
FB = FO_A + args.AP;
if args.frames
FB_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
quiver3(FB(1)*ones(1,3), FB(2)*ones(1,3), FB(3)*ones(1,3), ...
FB_uv(1,1:3), FB_uv(2,1:3), FB_uv(3,1:3), '-', 'Color', args.M_color)
if args.labels
text(FB(1) - d_label, ...
FB(2) + d_label, ...
FB(3) + d_label, '$\{B\}$', 'Color', args.M_color);
end
end
#+end_src
Let's then plot the circle corresponding to the shape of the Mobile platform.
#+begin_src matlab
if args.platforms && stewart.platform_M.type == 1
theta = [0:0.01:2*pi+0.01]; % Angles [rad]
v = null((FTm(1:3,1:3)*[0;0;1])'); % Two vectors that are perpendicular to the circle normal
center = Fm(1:3); % Center of the circle
radius = stewart.platform_M.R; % Radius of the circle [m]
points = center*ones(1, length(theta)) + radius* (v(:,1)*cos(theta) + v(:,2)*sin(theta));
plot3(points(1,:), ...
points(2,:), ...
points(3,:), '-', 'Color', args.M_color);
end
#+end_src
Plot the position and labels of the rotation joints fixed to the mobile platform.
#+begin_src matlab
if args.joints
Fb = FTm*[Mb;ones(1,6)];
scatter3(Fb(1,:), ...
Fb(2,:), ...
Fb(3,:), 'MarkerEdgeColor', args.M_color);
if args.labels
for i = 1:size(Fb,2)
text(Fb(1,i) + d_label, ...
Fb(2,i), ...
Fb(3,i), sprintf('$b_{%i}$', i), 'Color', args.M_color);
end
end
end
#+end_src
**** Legs
:PROPERTIES:
:UNNUMBERED: t
:END:
Plot the legs connecting the joints of the fixed base to the joints of the mobile platform.
#+begin_src matlab
if args.legs
for i = 1:6
plot3([Fa(1,i), Fb(1,i)], ...
[Fa(2,i), Fb(2,i)], ...
[Fa(3,i), Fb(3,i)], '-', 'Color', args.L_color);
if args.labels
text((Fa(1,i)+Fb(1,i))/2 + d_label, ...
(Fa(2,i)+Fb(2,i))/2, ...
(Fa(3,i)+Fb(3,i))/2, sprintf('$%i$', i), 'Color', args.L_color);
end
end
end
#+end_src
**** Figure parameters
#+begin_src matlab
switch args.views
case 'default'
view([1 -0.6 0.4]);
case 'xy'
view([0 0 1]);
case 'xz'
view([0 -1 0]);
case 'yz'
view([1 0 0]);
end
axis equal;
axis off;
#+end_src
**** Subplots
#+begin_src matlab
if strcmp(args.views, 'all')
hAx = findobj('type', 'axes');
figure;
s1 = subplot(2,2,1);
copyobj(get(hAx(1), 'Children'), s1);
view([0 0 1]);
axis equal;
axis off;
title('Top')
s2 = subplot(2,2,2);
copyobj(get(hAx(1), 'Children'), s2);
view([1 -0.6 0.4]);
axis equal;
axis off;
s3 = subplot(2,2,3);
copyobj(get(hAx(1), 'Children'), s3);
view([1 0 0]);
axis equal;
axis off;
title('Front')
s4 = subplot(2,2,4);
copyobj(get(hAx(1), 'Children'), s4);
view([0 -1 0]);
axis equal;
axis off;
title('Side')
close(f);
end
#+end_src
*** =describeStewartPlatform=: Display some text describing the current defined Stewart Platform
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/describeStewartPlatform.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:describeStewartPlatform >>
This Matlab function is accessible [[file:../src/describeStewartPlatform.m ][here ]].
**** Function description
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
function [] = describeStewartPlatform(stewart)
% describeStewartPlatform - Display some text describing the current defined Stewart Platform
%
% Syntax: [] = describeStewartPlatform(args)
%
% Inputs:
% - stewart
%
% Outputs:
#+end_src
**** Optional Parameters
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
arguments
stewart
end
#+end_src
**** Geometry
#+begin_src matlab
fprintf('GEOMETRY:\n')
fprintf('- The height between the fixed based and the top platform is %.3g [mm].\n', 1e3*stewart.geometry.H)
if stewart.platform_M.MO_B(3) > 0
fprintf('- Frame {A} is located %.3g [mm] above the top platform.\n', 1e3*stewart.platform_M.MO_B(3))
else
fprintf('- Frame {A} is located %.3g [mm] below the top platform.\n', - 1e3*stewart.platform_M.MO_B(3))
end
fprintf('- The initial length of the struts are:\n')
fprintf('\t %.3g, %.3g, %.3g, %.3g, %.3g, %.3g [mm]\n', 1e3*stewart.geometry.l)
fprintf('\n')
#+end_src
**** Actuators
#+begin_src matlab
fprintf('ACTUATORS:\n')
if stewart.actuators.type == 1
fprintf('- The actuators are modelled as 1DoF.\n')
fprintf('- The Stiffness and Damping of each actuators is:\n')
fprintf('\t k = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.k(1), stewart.actuators.c(1))
if stewart.actuators.kp > 0
fprintf('\t Added parallel stiffness: kp = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.kp(1))
end
elseif stewart.actuators.type == 2
fprintf('- The actuators are modelled as 2DoF (APA).\n')
fprintf('- The vertical stiffness and damping contribution of the piezoelectric stack is:\n')
fprintf('\t ka = %.0e [N/m] \t ca = %.0e [N/(m/s)]\n', stewart.actuators.ka(1), stewart.actuators.ca(1))
fprintf('- Vertical stiffness when the piezoelectric stack is removed is:\n')
fprintf('\t kr = %.0e [N/m] \t cr = %.0e [N/(m/s)]\n', stewart.actuators.kr(1), stewart.actuators.cr(1))
elseif stewart.actuators.type == 3
fprintf('- The actuators are modelled with a flexible element (FEM).\n')
end
fprintf('\n')
#+end_src
**** Joints
#+begin_src matlab
fprintf('JOINTS:\n')
#+end_src
Type of the joints on the fixed base.
#+begin_src matlab
switch stewart.joints_F.type
case 1
fprintf('- The joints on the fixed based are universal joints (2DoF)\n')
case 2
fprintf('- The joints on the fixed based are spherical joints (3DoF)\n')
end
#+end_src
Type of the joints on the mobile platform.
#+begin_src matlab
switch stewart.joints_M.type
case 1
fprintf('- The joints on the mobile based are universal joints (2DoF)\n')
case 2
fprintf('- The joints on the mobile based are spherical joints (3DoF)\n')
end
#+end_src
Position of the fixed joints
#+begin_src matlab
fprintf('- The position of the joints on the fixed based with respect to {F} are (in [mm]):\n')
fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_F.Fa)
#+end_src
Position of the mobile joints
#+begin_src matlab
fprintf('- The position of the joints on the mobile based with respect to {M} are (in [mm]):\n')
fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_M.Mb)
fprintf('\n')
#+end_src
**** Kinematics
#+begin_src matlab
fprintf('KINEMATICS:\n')
if isfield(stewart.kinematics, 'K')
fprintf('- The Stiffness matrix K is (in [N/m]):\n')
fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.K)
end
if isfield(stewart.kinematics, 'C')
fprintf('- The Damping matrix C is (in [m/N]):\n')
fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.C)
end
#+end_src
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* Helping Functions :noexport:
** Initialize Path
#+NAME : m-init-path
#+BEGIN_SRC matlab
addpath('./matlab/ '); % Path for scripts
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%% Path for functions, data and scripts
addpath('./matlab/mat/ '); % Path for Computed FRF
addpath('./matlab/src/ '); % Path for functions
addpath('./matlab/STEPS/ '); % Path for STEPS
addpath('./matlab/subsystems/ '); % Path for Subsystems Simulink files
%% Data directory
data_dir = './matlab/mat/ '
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#+END_SRC
#+NAME : m-init-path-tangle
#+BEGIN_SRC matlab
%% Path for functions, data and scripts
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addpath('./mat/ '); % Path for Data
addpath('./src/ '); % Path for functions
addpath('./STEPS/ '); % Path for STEPS
addpath('./subsystems/ '); % Path for Subsystems Simulink files
%% Data directory
data_dir = './mat/ ';
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#+END_SRC
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** Initialize Simscape Model
#+NAME : m-init-simscape
#+begin_src matlab
% Simulink Model name
mdl = 'nass_model';
#+end_src
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** Initialize other elements
#+NAME : m-init-other
#+BEGIN_SRC matlab
%% Colors for the figures
colors = colororder;
#+END_SRC
