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Rework matlab directory

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Thomas Dehaeze 2024-10-27 11:15:39 +01:00
parent 54369b591c
commit 94bfca04cf
119 changed files with 513724 additions and 60 deletions
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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:
% - kinematics.J [6x6] - The Jacobian Matrix
% - kinematics.K [6x6] - The Stiffness Matrix
% - kinematics.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.kinematics.J = J;
stewart.kinematics.K = K;
stewart.kinematics.C = C;

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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;

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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

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function [MTr] = computeSampleError(WTm, WTr)
% computeSampleError -
%
% Syntax: [MTr] = computeSampleError(WTm, WTr)
%
% Inputs:
% - WTm - Homoegeneous transformation that represent the
% wanted pose of the sample with respect to the granite
% - WTr - Homoegeneous transformation that represent the
% measured pose of the sample with respect to the granite
%
% Outputs:
% - MTr - Homoegeneous transformation that represent the
% wanted pose of the sample expressed in a frame
% attached to the top platform of the nano-hexapod
MTr = zeros(4,4);
MTr = [WTm(1:3,1:3)', -WTm(1:3,1:3)'*WTm(1:3,4) ; 0 0 0 1]*WTr;
end

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function [] = describeNassSetup()
% describeNassSetup -
%
% Syntax: [] = describeNassSetup()
%
% Inputs:
% - -
%
% Outputs:
% - -
load('./mat/conf_simscape.mat', 'conf_simscape');
fprintf('Simscape Configuration:\n');
if conf_simscape.type == 1
fprintf('- Gravity is included\n');
else
fprintf('- Gravity is not included\n');
end
fprintf('\n');
load('./mat/nass_disturbances.mat', 'args');
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.Fty_x && args.Fty_z
fprintf('- Vibrations of the Translation Stage\n');
end
if args.Frz_z
fprintf('- Vibrations of the Spindle\n');
end
end
fprintf('\n');
load('./mat/nass_references.mat', 'args');
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');
load('./mat/controller.mat', 'controller');
fprintf('Controller:\n');
fprintf('- %s\n', controller.name);
fprintf('\n');
load('./mat/stages.mat', 'ground', 'granite', 'ty', 'ry', 'rz', 'micro_hexapod', 'axisc');
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');
load('./mat/stages.mat', 'mirror');
fprintf('Reference Mirror:\n');
if mirror.type == 2;
fprintf('- flexible fixation\n');
fprintf('- w = %.0f [Hz]\n', mirror.freq(1));
else
fprintf('- rigidly attached to the nano-hexapod\n');
end
fprintf('- m = %.0f [kg]\n', mirror.mass);
fprintf('\n');
load('./mat/stages.mat', 'nano_hexapod');
fprintf('Nano Hexapod:\n');
if nano_hexapod.type == 0;
fprintf('- no included\n');
elseif nano_hexapod.type == 1 || nano_hexapod.type == 3;
fprintf('- rigid\n');
elseif nano_hexapod.type == 2;
fprintf('- flexible\n');
fprintf('- Ki = %.0g [N/m]\n', nano_hexapod.actuators.K(1));
end
fprintf('\n');
load('./mat/stages.mat', 'sample');
fprintf('Sample:\n');
if sample.type == 0;
fprintf('- no included\n');
elseif sample.type == 1 || sample.type == 3;
fprintf('- rigid\n');
fprintf('- mass = %.0f [kg]\n', sample.mass);
fprintf('- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n', sample.inertia(1), sample.inertia(2), sample.inertia(3));
elseif sample.type == 2;
fprintf('- flexible\n');
fprintf('- mass = %.0f [kg]\n', sample.mass);
fprintf('- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n', sample.inertia(1), sample.inertia(2), sample.inertia(3));
% fprintf('- Kt = %.0g, %.0g, %.0g [N/m]\n', sample.K(1), sample.K(2), sample.K(3));
% fprintf('- Kr = %.0g, %.0g, %.0g [Nm/rad]\n', sample.K(4), sample.K(5), sample.K(6));
fprintf('- wt(x,y,z) = %.0f, %.0f, %.0f [Hz]\n', 1/2/pi*sqrt(sample.K(1)/sample.mass), 1/2/pi*sqrt(sample.K(1)/sample.mass), 1/2/pi*sqrt(sample.K(1)/sample.mass));
fprintf('- wr(x,y,z) = %.0f, %.0f, %.0f [Hz]\n', 1/2/pi*sqrt(sample.K(4)/sample.inertia(1)), 1/2/pi*sqrt(sample.K(5)/sample.inertia(2)), 1/2/pi*sqrt(sample.K(6)/sample.inertia(3)));
end
fprintf('\n');

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function [] = describeStewartPlatform(stewart)
% describeStewartPlatform - Display some text describing the current defined Stewart Platform
%
% Syntax: [] = describeStewartPlatform(args)
%
% Inputs:
% - stewart
%
% Outputs:
arguments
stewart
end
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')
fprintf('ACTUATORS:\n')
if stewart.actuators.type == 1
fprintf('- The actuators are classical.\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))
elseif stewart.actuators.type == 2
fprintf('- The actuators are mechanicaly amplified.\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))
end
fprintf('\n')
fprintf('JOINTS:\n')
switch stewart.joints_F.type
case 1
fprintf('- The joints on the fixed based are universal joints\n')
case 2
fprintf('- The joints on the fixed based are spherical joints\n')
case 3
fprintf('- The joints on the fixed based are perfect universal joints\n')
case 4
fprintf('- The joints on the fixed based are perfect spherical joints\n')
end
switch stewart.joints_M.type
case 1
fprintf('- The joints on the mobile based are universal joints\n')
case 2
fprintf('- The joints on the mobile based are spherical joints\n')
case 3
fprintf('- The joints on the mobile based are perfect universal joints\n')
case 4
fprintf('- The joints on the mobile based are perfect spherical joints\n')
end
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)
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')
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

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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:
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
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;
if ~strcmp(args.views, 'all')
figure;
else
f = figure('visible', 'off');
end
hold on;
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;
d_unit_vector = H/4;
d_label = H/20;
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
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
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
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
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
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
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
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
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
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;
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

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function [int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes(filename)
% extractNodes -
%
% Syntax: [n_xyz, nodes] = extractNodes(filename)
%
% Inputs:
% - filename - relative or absolute path of the file that contains the Matrix
%
% Outputs:
% - n_xyz -
% - nodes - table containing the node numbers and corresponding dof of the interfaced DoFs
arguments
filename
end
fid = fopen(filename,'rt');
if fid == -1
error('Error opening the file');
end
n_xyz = []; % Contains nodes coordinates
n_i = []; % Contains nodes indices
n_num = []; % Contains node numbers
n_dof = {}; % Contains node directions
while 1
% Read a line
nextline = fgetl(fid);
% End of the file
if ~isstr(nextline), break, end
% Line just before the list of nodes coordinates
if contains(nextline, 'NODE') && ...
contains(nextline, 'X') && ...
contains(nextline, 'Y') && ...
contains(nextline, 'Z')
while 1
nextline = fgetl(fid);
if nextline < 0, break, end
c = sscanf(nextline, ' %f');
if isempty(c), break, end
n_xyz = [n_xyz; c(2:4)'];
n_i = [n_i; c(1)];
end
end
if nextline < 0, break, end
% Line just before the list of node DOF
if contains(nextline, 'NODE LABEL')
while 1
nextline = fgetl(fid);
if nextline < 0, break, end
c = sscanf(nextline, ' %d %s');
if isempty(c), break, end
n_num = [n_num; c(1)];
n_dof{length(n_dof)+1} = char(c(2:end)');
end
nodes = table(n_num, string(n_dof'), 'VariableNames', {'node_i', 'node_dof'});
end
if nextline < 0, break, end
end
fclose(fid);
int_i = unique(nodes.('node_i')); % indices of interface nodes
% Extract XYZ coordinates of only the interface nodes
if length(n_xyz) > 0 && length(n_i) > 0
int_xyz = n_xyz(logical(sum(n_i.*ones(1, length(int_i)) == int_i', 2)), :);
else
int_xyz = n_xyz;
end

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function [P, R] = forwardKinematicsApprox(stewart, args)
% forwardKinematicsApprox - Computed the approximate pose of {B} with respect to {A} from the length of each strut and using
% the Jacobian Matrix
%
% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)
%
% Inputs:
% - stewart - A structure with the following fields
% - kinematics.J [6x6] - The Jacobian Matrix
% - args - Can have the following fields:
% - dL [6x1] - Displacement of each strut [m]
%
% Outputs:
% - P [3x1] - The estimated position of {B} with respect to {A}
% - R [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}
arguments
stewart
args.dL (6,1) double {mustBeNumeric} = zeros(6,1)
end
assert(isfield(stewart.kinematics, 'J'), 'stewart.kinematics should have attribute J')
J = stewart.kinematics.J;
X = J\args.dL;
P = X(1:3);
theta = norm(X(4:6));
s = X(4:6)/theta;
R = [s(1)^2*(1-cos(theta)) + cos(theta) , s(1)*s(2)*(1-cos(theta)) - s(3)*sin(theta), s(1)*s(3)*(1-cos(theta)) + s(2)*sin(theta);
s(2)*s(1)*(1-cos(theta)) + s(3)*sin(theta), s(2)^2*(1-cos(theta)) + cos(theta), s(2)*s(3)*(1-cos(theta)) - s(1)*sin(theta);
s(3)*s(1)*(1-cos(theta)) - s(2)*sin(theta), s(3)*s(2)*(1-cos(theta)) + s(1)*sin(theta), s(3)^2*(1-cos(theta)) + cos(theta)];

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function [stewart] = generateCubicConfiguration(stewart, args)
% generateCubicConfiguration - Generate a Cubic Configuration
%
% Syntax: [stewart] = generateCubicConfiguration(stewart, args)
%
% Inputs:
% - stewart - A structure with the following fields
% - geometry.H [1x1] - Total height of the platform [m]
% - args - Can have the following fields:
% - Hc [1x1] - Height of the "useful" part of the cube [m]
% - FOc [1x1] - Height of the center of the cube with respect to {F} [m]
% - FHa [1x1] - Height of the plane joining the points ai with respect to the frame {F} [m]
% - MHb [1x1] - Height of the plane joining the points bi with respect to the frame {M} [m]
%
% 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.Hc (1,1) double {mustBeNumeric, mustBePositive} = 60e-3
args.FOc (1,1) double {mustBeNumeric} = 50e-3
args.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
args.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
end
assert(isfield(stewart.geometry, 'H'), 'stewart.geometry should have attribute H')
H = stewart.geometry.H;
sx = [ 2; -1; -1];
sy = [ 0; 1; -1];
sz = [ 1; 1; 1];
R = [sx, sy, sz]./vecnorm([sx, sy, sz]);
L = args.Hc*sqrt(3);
Cc = R'*[[0;0;L],[L;0;L],[L;0;0],[L;L;0],[0;L;0],[0;L;L]] - [0;0;1.5*args.Hc];
CCf = [Cc(:,1), Cc(:,3), Cc(:,3), Cc(:,5), Cc(:,5), Cc(:,1)]; % CCf(:,i) corresponds to the bottom cube's vertice corresponding to the i'th leg
CCm = [Cc(:,2), Cc(:,2), Cc(:,4), Cc(:,4), Cc(:,6), Cc(:,6)]; % CCm(:,i) corresponds to the top cube's vertice corresponding to the i'th leg
CSi = (CCm - CCf)./vecnorm(CCm - CCf);
Fa = CCf + [0; 0; args.FOc] + ((args.FHa-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
Mb = CCf + [0; 0; args.FOc-H] + ((H-args.MHb-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
stewart.platform_F.Fa = Fa;
stewart.platform_M.Mb = Mb;

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function [K] = generateDiagPidControl(G, fs)
%%
pid_opts = pidtuneOptions(...
'PhaseMargin', 50, ...
'DesignFocus', 'disturbance-rejection');
%%
K = tf(zeros(6));
for i = 1:6
input_name = G.InputName(i);
output_name = G.OutputName(i);
K(i, i) = tf(pidtune(minreal(G(output_name, input_name)), 'PIDF', 2*pi*fs, pid_opts));
end
K.InputName = G.OutputName;
K.OutputName = G.InputName;
end

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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;

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function [U_exc] = generateShapedNoise(args)
% generateShapedNoise - Generate a Shaped Noise excitation signal
%
% Syntax: [U_exc] = generateShapedNoise(args)
%
% Inputs:
% - args - Optinal arguments:
% - Ts - Sampling Time - [s]
% - V_mean - Mean value of the excitation voltage - [V]
% - V_exc - Excitation Amplitude, could be numeric or TF - [V rms]
% - t_start - Time at which the noise begins - [s]
% - exc_duration - Duration of the noise - [s]
% - smooth_ends - 'true' or 'false': smooth transition between 0 and V_mean - [-]
arguments
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-4
args.V_mean (1,1) double {mustBeNumeric} = 0
args.V_exc = 1
args.t_start (1,1) double {mustBeNumeric, mustBePositive} = 5
args.exc_duration (1,1) double {mustBeNumeric, mustBePositive} = 10
args.smooth_ends logical {mustBeNumericOrLogical} = true
end
t_noise = 0:args.Ts:args.exc_duration;
if isnumeric(args.V_exc)
V_noise = args.V_mean + args.V_exc*sqrt(1/args.Ts/2)*randn(length(t_noise), 1)';
elseif isct(args.V_exc)
V_noise = args.V_mean + lsim(args.V_exc, sqrt(1/args.Ts/2)*randn(length(t_noise), 1), t_noise)';
end
t_smooth_start = args.Ts:args.Ts:args.t_start;
V_smooth_start = zeros(size(t_smooth_start));
V_smooth_end = zeros(size(t_smooth_start));
if args.smooth_ends
Vd_max = args.V_mean/(0.7*args.t_start);
V_d = zeros(size(t_smooth_start));
V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
V_smooth_start = cumtrapz(V_d)*args.Ts;
V_smooth_end = args.V_mean - V_smooth_start;
end
V_exc = [V_smooth_start, V_noise, V_smooth_end];
t_exc = args.Ts*[0:1:length(V_exc)-1];
U_exc = [t_exc; V_exc];

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function [U_exc] = generateSinIncreasingAmpl(args)
% generateSinIncreasingAmpl - Generate Sinus with increasing amplitude
%
% Syntax: [U_exc] = generateSinIncreasingAmpl(args)
%
% Inputs:
% - args - Optinal arguments:
% - Ts - Sampling Time - [s]
% - V_mean - Mean value of the excitation voltage - [V]
% - sin_ampls - Excitation Amplitudes - [V]
% - sin_freq - Excitation Frequency - [Hz]
% - sin_num - Number of period for each amplitude - [-]
% - t_start - Time at which the excitation begins - [s]
% - smooth_ends - 'true' or 'false': smooth transition between 0 and V_mean - [-]
arguments
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-4
args.V_mean (1,1) double {mustBeNumeric} = 0
args.sin_ampls double {mustBeNumeric, mustBePositive} = [0.1, 0.2, 0.3]
args.sin_period (1,1) double {mustBeNumeric, mustBePositive} = 1
args.sin_num (1,1) double {mustBeNumeric, mustBePositive, mustBeInteger} = 3
args.t_start (1,1) double {mustBeNumeric, mustBePositive} = 5
args.smooth_ends logical {mustBeNumericOrLogical} = true
end
t_noise = 0:args.Ts:args.sin_period*args.sin_num;
sin_exc = [];
for sin_ampl = args.sin_ampls
sin_exc = [sin_exc, args.V_mean + sin_ampl*sin(2*pi/args.sin_period*t_noise)];
end
t_smooth_start = args.Ts:args.Ts:args.t_start;
V_smooth_start = zeros(size(t_smooth_start));
V_smooth_end = zeros(size(t_smooth_start));
if args.smooth_ends
Vd_max = args.V_mean/(0.7*args.t_start);
V_d = zeros(size(t_smooth_start));
V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
V_smooth_start = cumtrapz(V_d)*args.Ts;
V_smooth_end = args.V_mean - V_smooth_start;
end
V_exc = [V_smooth_start, sin_exc, V_smooth_end];
t_exc = args.Ts*[0:1:length(V_exc)-1];
U_exc = [t_exc; V_exc];

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function [ref] = generateSpiralAngleTrajectory(args)
% generateSpiralAngleTrajectory -
%
% Syntax: [ref] = generateSpiralAngleTrajectory(args)
%
% Inputs:
% - args
%
% Outputs:
% - ref - Reference Signal
arguments
args.R_tot (1,1) double {mustBeNumeric, mustBePositive} = 10e-6 % [rad]
args.n_turn (1,1) double {mustBeInteger, mustBePositive} = 5 % [-]
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [s]
args.t_turn (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
args.t_end (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
end
time_s = 0:args.Ts:args.n_turn*args.t_turn;
time_e = 0:args.Ts:args.t_end;
Rx = sin(2*pi*time_s/args.t_turn).*(args.R_tot*time_s/(args.n_turn*args.t_turn));
Ry = cos(2*pi*time_s/args.t_turn).*(args.R_tot*time_s/(args.n_turn*args.t_turn));
Rx = [Rx, 0*time_e];
Ry = [Ry, Ry(end) - Ry(end)*time_e/args.t_end];
t = 0:args.Ts:args.Ts*(length(Rx) - 1);
ref = zeros(length(Rx), 7);
ref(:, 1) = t;
ref(:, 5) = Rx;
ref(:, 6) = Ry;

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function [U_exc] = generateSweepExc(args)
% generateSweepExc - Generate a Sweep Sine excitation signal
%
% Syntax: [U_exc] = generateSweepExc(args)
%
% Inputs:
% - args - Optinal arguments:
% - Ts - Sampling Time - [s]
% - f_start - Start frequency of the sweep - [Hz]
% - f_end - End frequency of the sweep - [Hz]
% - V_mean - Mean value of the excitation voltage - [V]
% - V_exc - Excitation Amplitude for the Sweep, could be numeric or TF - [V]
% - t_start - Time at which the sweep begins - [s]
% - exc_duration - Duration of the sweep - [s]
% - sweep_type - 'logarithmic' or 'linear' - [-]
% - smooth_ends - 'true' or 'false': smooth transition between 0 and V_mean - [-]
arguments
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-4
args.f_start (1,1) double {mustBeNumeric, mustBePositive} = 1
args.f_end (1,1) double {mustBeNumeric, mustBePositive} = 1e3
args.V_mean (1,1) double {mustBeNumeric} = 0
args.V_exc = 1
args.t_start (1,1) double {mustBeNumeric, mustBeNonnegative} = 5
args.exc_duration (1,1) double {mustBeNumeric, mustBePositive} = 10
args.sweep_type char {mustBeMember(args.sweep_type,{'log', 'lin'})} = 'lin'
args.smooth_ends logical {mustBeNumericOrLogical} = true
end
t_sweep = 0:args.Ts:args.exc_duration;
if strcmp(args.sweep_type, 'log')
V_exc = sin(2*pi*args.f_start * args.exc_duration/log(args.f_end/args.f_start) * (exp(log(args.f_end/args.f_start)*t_sweep/args.exc_duration) - 1));
elseif strcmp(args.sweep_type, 'lin')
V_exc = sin(2*pi*(args.f_start + (args.f_end - args.f_start)/2/args.exc_duration*t_sweep).*t_sweep);
else
error('sweep_type should either be equal to "log" or to "lin"');
end
if isnumeric(args.V_exc)
V_sweep = args.V_mean + args.V_exc*V_exc;
elseif isct(args.V_exc)
if strcmp(args.sweep_type, 'log')
V_sweep = args.V_mean + abs(squeeze(freqresp(args.V_exc, args.f_start*(args.f_end/args.f_start).^(t_sweep/args.exc_duration), 'Hz')))'.*V_exc;
elseif strcmp(args.sweep_type, 'lin')
V_sweep = args.V_mean + abs(squeeze(freqresp(args.V_exc, args.f_start+(args.f_end-args.f_start)/args.exc_duration*t_sweep, 'Hz')))'.*V_exc;
end
end
if args.t_start > 0
t_smooth_start = args.Ts:args.Ts:args.t_start;
V_smooth_start = zeros(size(t_smooth_start));
V_smooth_end = zeros(size(t_smooth_start));
if args.smooth_ends
Vd_max = args.V_mean/(0.7*args.t_start);
V_d = zeros(size(t_smooth_start));
V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
V_smooth_start = cumtrapz(V_d)*args.Ts;
V_smooth_end = args.V_mean - V_smooth_start;
end
else
V_smooth_start = [];
V_smooth_end = [];
end
V_exc = [V_smooth_start, V_sweep, V_smooth_end];
t_exc = args.Ts*[0:1:length(V_exc)-1];
U_exc = [t_exc; V_exc];

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function [ref] = generateXYZTrajectory(args)
% generateXYZTrajectory -
%
% Syntax: [ref] = generateXYZTrajectory(args)
%
% Inputs:
% - args
%
% Outputs:
% - ref - Reference Signal
arguments
args.points double {mustBeNumeric} = zeros(2, 3) % [m]
args.ti (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % Time to go to first point and after last point [s]
args.tw (1,1) double {mustBeNumeric, mustBeNonnegative} = 0.5 % Time wait between each point [s]
args.tm (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % Motion time between points [s]
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % Sampling Time [s]
end
time_i = 0:args.Ts:args.ti;
time_w = 0:args.Ts:args.tw;
time_m = 0:args.Ts:args.tm;
% Go to initial position
xyz = (args.points(1,:))'*(time_i/args.ti);
% Wait
xyz = [xyz, xyz(:,end).*ones(size(time_w))];
% Scans
for i = 2:size(args.points, 1)
% Go to next point
xyz = [xyz, xyz(:,end) + (args.points(i,:)' - xyz(:,end))*(time_m/args.tm)];
% Wait a litle bit
xyz = [xyz, xyz(:,end).*ones(size(time_w))];
end
% End motion
xyz = [xyz, xyz(:,end) - xyz(:,end)*(time_i/args.ti)];
t = 0:args.Ts:args.Ts*(length(xyz) - 1);
ref = zeros(length(xyz), 7);
ref(:, 1) = t;
ref(:, 2:4) = xyz';

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function [ref] = generateYZScanTrajectory(args)
% generateYZScanTrajectory -
%
% Syntax: [ref] = generateYZScanTrajectory(args)
%
% Inputs:
% - args
%
% Outputs:
% - ref - Reference Signal
arguments
args.y_tot (1,1) double {mustBeNumeric, mustBePositive} = 10e-6 % [m]
args.z_tot (1,1) double {mustBeNumeric, mustBePositive} = 10e-6 % [m]
args.n (1,1) double {mustBeInteger, mustBePositive} = 10 % [-]
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-4 % [s]
args.ti (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
args.tw (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
args.ty (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
args.tz (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
end
time_i = 0:args.Ts:args.ti;
time_w = 0:args.Ts:args.tw;
time_y = 0:args.Ts:args.ty;
time_z = 0:args.Ts:args.tz;
% Go to initial position
y = (time_i/args.ti)*(args.y_tot/2);
% Wait
y = [y, y(end)*ones(size(time_w))];
% Scans
for i = 1:args.n
if mod(i,2) == 0
y = [y, -(args.y_tot/2) + (time_y/args.ty)*args.y_tot];
else
y = [y, (args.y_tot/2) - (time_y/args.ty)*args.y_tot];
end
if i < args.n
y = [y, y(end)*ones(size(time_z))];
end
end
% Wait a litle bit
y = [y, y(end)*ones(size(time_w))];
% End motion
y = [y, y(end) - y(end)*time_i/args.ti];
% Go to initial position
z = (time_i/args.ti)*(args.z_tot/2);
% Wait
z = [z, z(end)*ones(size(time_w))];
% Scans
for i = 1:args.n
z = [z, z(end)*ones(size(time_y))];
if i < args.n
z = [z, z(end) - (time_z/args.tz)*args.z_tot/(args.n-1)];
end
end
% Wait a litle bit
z = [z, z(end)*ones(size(time_w))];
% End motion
z = [z, z(end) - z(end)*time_i/args.ti];
t = 0:args.Ts:args.Ts*(length(y) - 1);
ref = zeros(length(y), 7);
ref(:, 1) = t;
ref(:, 3) = y;
ref(:, 4) = z;

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matlab/src/getJacobianNanoHexapod.m Normal file
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function [J] = getJacobianNanoHexapod(Hbm)
% getJacobianNanoHexapod -
%
% Syntax: [J] = getJacobianNanoHexapod(Hbm)
%
% Inputs:
% - Hbm - Height of {B} w.r.t. {M} [m]
%
% Outputs:
% - J - Jacobian Matrix
Fa = [[-86.05, -74.78, 22.49],
[ 86.05, -74.78, 22.49],
[ 107.79, -37.13, 22.49],
[ 21.74, 111.91, 22.49],
[-21.74, 111.91, 22.49],
[-107.79, -37.13, 22.49]]'*1e-3; % Ai w.r.t. {F} [m]
Mb = [[-28.47, -106.25, -22.50],
[ 28.47, -106.25, -22.50],
[ 106.25, 28.47, -22.50],
[ 77.78, 77.78, -22.50],
[-77.78, 77.78, -22.50],
[-106.25, 28.47, -22.50]]'*1e-3; % Bi w.r.t. {M} [m]
H = 95e-3; % Stewart platform height [m]
Fb = Mb + [0; 0; H]; % Bi w.r.t. {F} [m]
si = Fb - Fa;
si = si./vecnorm(si); % Normalize
Bb = Mb - [0; 0; Hbm];
J = [si', cross(Bb, si)'];

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matlab/src/getTransformationMatrixAcc.m Normal file
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function [M] = getTransformationMatrixAcc(Opm, Osm)
% getTransformationMatrixAcc -
%
% Syntax: [M] = getTransformationMatrixAcc(Opm, Osm)
%
% Inputs:
% - Opm - Nx3 (N = number of accelerometer measurements) X,Y,Z position of accelerometers
% - Opm - Nx3 (N = number of accelerometer measurements) Unit vectors representing the accelerometer orientation
%
% Outputs:
% - M - Transformation Matrix
M = zeros(length(Opm), 6);
for i = 1:length(Opm)
Ri = [0, Opm(3,i), -Opm(2,i);
-Opm(3,i), 0, Opm(1,i);
Opm(2,i), -Opm(1,i), 0];
M(i, 1:3) = Osm(:,i)';
M(i, 4:6) = Osm(:,i)'*Ri;
end
end

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matlab/src/initializeAmplifiedStrutDynamics.m Normal file
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function [stewart] = initializeAmplifiedStrutDynamics(stewart, args)
% initializeAmplifiedStrutDynamics - Add Stiffness and Damping properties of each strut
%
% Syntax: [stewart] = initializeAmplifiedStrutDynamics(args)
%
% Inputs:
% - args - Structure with the following fields:
% - Ka [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - Ca [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - Kr [6x1] - Vertical (residual) stiffness when the piezoelectric stack is removed [N/m]
% - Cr [6x1] - Vertical (residual) damping when the piezoelectric stack is removed [N/(m/s)]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - actuators.type = 2
% - actuators.K [6x1] - Total Stiffness of each strut [N/m]
% - actuators.C [6x1] - Total Damping of each strut [N/(m/s)]
% - actuators.Ka [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - actuators.Ca [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - actuators.Kr [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
% - actuators.Cr [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
arguments
stewart
args.Kr (6,1) double {mustBeNumeric, mustBeNonnegative} = 5e6*ones(6,1)
args.Cr (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ka (6,1) double {mustBeNumeric, mustBeNonnegative} = 15e6*ones(6,1)
args.Ca (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
end
K = args.Ka + args.Kr;
C = args.Ca + args.Cr;
stewart.actuators.type = 2;
stewart.actuators.Ka = args.Ka;
stewart.actuators.Ca = args.Ca;
stewart.actuators.Kr = args.Kr;
stewart.actuators.Cr = args.Cr;
stewart.actuators.K = K;
stewart.actuators.C = K;

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function [axisc] = initializeAxisc(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
end
axisc = struct();
switch args.type
case 'none'
axisc.type = 0;
case 'rigid'
axisc.type = 1;
case 'flexible'
axisc.type = 2;
end
% Structure
axisc.structure.density = 3400; % [kg/m3]
axisc.structure.STEP = './STEPS/axisc/axisc_structure.STEP';
% Wheel
axisc.wheel.density = 2700; % [kg/m3]
axisc.wheel.STEP = './STEPS/axisc/axisc_wheel.STEP';
% Mass
axisc.mass.density = 7800; % [kg/m3]
axisc.mass.STEP = './STEPS/axisc/axisc_mass.STEP';
% Gear
axisc.gear.density = 7800; % [kg/m3]
axisc.gear.STEP = './STEPS/axisc/axisc_gear.STEP';
save('./mat/stages.mat', 'axisc', '-append');

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function [cedrat] = initializeCedratPiezo()
%% Stewart Object
cedrat = struct();
cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m]
cedrat.ka = 10e7; % Linear Stiffness of the stack [N/m]
cedrat.c = 0.1*sqrt(1*cedrat.k); % [N/(m/s)]
cedrat.ca = 0.1*sqrt(1*cedrat.ka); % [N/(m/s)]
cedrat.L = 80; % Total Width of the Actuator[mm]
cedrat.H = 45; % Total Height of the Actuator [mm]
cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm]
cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg]
%% Save
save('./mat/stages.mat', 'cedrat', '-append');
end

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matlab/src/initializeController.m Normal file
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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
save('./mat/controller.mat', 'controller');

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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;

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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
Fsm = ones(6,1).*args.Fsm;
Fsh = ones(6,1).*args.Fsh;
Fsr = ones(6,1).*args.Fsr;
Msm = ones(6,1).*args.Msm;
Msh = ones(6,1).*args.Msh;
Msr = ones(6,1).*args.Msr;
I_F = zeros(3, 3, 6); % Inertia of the "fixed" part of the strut
I_M = zeros(3, 3, 6); % Inertia of the "mobile" part of the strut
for i = 1:6
I_F(:,:,i) = diag([1/12 * Fsm(i) * (3*Fsr(i)^2 + Fsh(i)^2), ...
1/12 * Fsm(i) * (3*Fsr(i)^2 + Fsh(i)^2), ...
1/2 * Fsm(i) * Fsr(i)^2]);
I_M(:,:,i) = diag([1/12 * Msm(i) * (3*Msr(i)^2 + Msh(i)^2), ...
1/12 * Msm(i) * (3*Msr(i)^2 + Msh(i)^2), ...
1/2 * Msm(i) * Msr(i)^2]);
end
stewart.struts_M.type = 1;
stewart.struts_M.I = I_M;
stewart.struts_M.M = Msm;
stewart.struts_M.R = Msr;
stewart.struts_M.H = Msh;
stewart.struts_F.type = 1;
stewart.struts_F.I = I_F;
stewart.struts_F.M = Fsm;
stewart.struts_F.R = Fsr;
stewart.struts_F.H = Fsh;

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function [] = initializeDisturbances(args)
% initializeDisturbances - Initialize the disturbances
%
% Syntax: [] = initializeDisturbances(args)
%
% Inputs:
% - args -
arguments
% Global parameter to enable or disable the disturbances
args.enable logical {mustBeNumericOrLogical} = true
% Ground Motion - X direction
args.Dwx logical {mustBeNumericOrLogical} = true
% Ground Motion - Y direction
args.Dwy logical {mustBeNumericOrLogical} = true
% Ground Motion - Z direction
args.Dwz logical {mustBeNumericOrLogical} = true
% Translation Stage - X direction
args.Fty_x logical {mustBeNumericOrLogical} = true
% Translation Stage - Z direction
args.Fty_z logical {mustBeNumericOrLogical} = true
% Spindle - Z direction
args.Frz_z logical {mustBeNumericOrLogical} = true
end
load('./mat/dist_psd.mat', 'dist_f');
dist_f.f = dist_f.f(2:end);
dist_f.psd_gm = dist_f.psd_gm(2:end);
dist_f.psd_ty = dist_f.psd_ty(2:end);
dist_f.psd_rz = dist_f.psd_rz(2:end);
Fs = 2*dist_f.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
N = 2*length(dist_f.f); % Number of Samples match the one of the wanted PSD
T0 = N/Fs; % Signal Duration [s]
df = 1/T0; % Frequency resolution of the DFT [Hz]
% Also equal to (dist_f.f(2)-dist_f.f(1))
t = linspace(0, T0, N+1)'; % Time Vector [s]
Ts = 1/Fs; % Sampling Time [s]
phi = dist_f.psd_gm;
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(phi(i)*df);
end
if args.Dwx && args.enable
rng(111);
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)))];;
Dwx = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m]
else
Dwx = zeros(length(t), 1);
end
if args.Dwy && args.enable
rng(112);
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)))];;
Dwy = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m]
else
Dwy = zeros(length(t), 1);
end
if args.Dwy && args.enable
rng(113);
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)))];;
Dwz = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m]
else
Dwz = zeros(length(t), 1);
end
if args.Fty_x && args.enable
phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(phi(i)*df);
end
rng(121);
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)))];;
u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty x [N]
Fty_x = u;
else
Fty_x = zeros(length(t), 1);
end
if args.Fty_z && args.enable
phi = dist_f.psd_ty;
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(phi(i)*df);
end
rng(122);
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)))];;
u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty z [N]
Fty_z = u;
else
Fty_z = zeros(length(t), 1);
end
if args.Frz_z && args.enable
phi = dist_f.psd_rz;
C = zeros(N/2,1);
for i = 1:N/2
C(i) = sqrt(phi(i)*df);
end
rng(131);
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)))];;
u = N/sqrt(2)*ifft(Cx); % Disturbance Force Rz z [N]
Frz_z = u;
else
Frz_z = zeros(length(t), 1);
end
u = zeros(length(t), 6);
Fd = u;
Dwx = Dwx - Dwx(1);
Dwy = Dwy - Dwy(1);
Dwz = Dwz - Dwz(1);
Fty_x = Fty_x - Fty_x(1);
Fty_z = Fty_z - Fty_z(1);
Frz_z = Frz_z - Frz_z(1);
save('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't', 'args');

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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;

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function [granite] = initializeGranite(args)
arguments
args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis', 'init'})} = 'flexible'
args.Foffset logical {mustBeNumericOrLogical} = false
args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3]
args.K (3,1) double {mustBeNumeric, mustBeNonnegative} = [4e9; 3e8; 8e8] % [N/m]
args.C (3,1) double {mustBeNumeric, mustBeNonnegative} = [4.0e5; 1.1e5; 9.0e5] % [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} = 0.8 % 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;
case 'modal-analysis'
granite.type = 3;
case 'init'
granite.type = 4;
end
granite.density = args.density; % [kg/m3]
granite.STEP = './STEPS/granite/granite.STEP';
granite.sample_pos = args.sample_pos; % [m]
granite.K = args.K; % [N/m]
granite.C = args.C; % [N/(m/s)]
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
load('mat/Foffset.mat', 'Fgm');
granite.Deq = -Fgm'./granite.K;
else
granite.Deq = zeros(6,1);
end
save('./mat/stages.mat', 'granite', '-append');

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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;
save('./mat/stages.mat', 'ground', '-append');

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function [stewart] = initializeInertialSensor(stewart, args)
% initializeInertialSensor - Initialize the inertial sensor in each strut
%
% Syntax: [stewart] = initializeInertialSensor(args)
%
% Inputs:
% - args - Structure with the following fields:
% - type - 'geophone', 'accelerometer', 'none'
% - mass [1x1] - Weight of the inertial mass [kg]
% - freq [1x1] - Cutoff frequency [Hz]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - stewart.sensors.inertial
% - type - 1 (geophone), 2 (accelerometer), 3 (none)
% - K [1x1] - Stiffness [N/m]
% - C [1x1] - Damping [N/(m/s)]
% - M [1x1] - Inertial Mass [kg]
% - G [1x1] - Gain
arguments
stewart
args.type char {mustBeMember(args.type,{'geophone', 'accelerometer', 'none'})} = 'none'
args.mass (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e-2
args.freq (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e3
end
sensor = struct();
switch args.type
case 'geophone'
sensor.type = 1;
sensor.M = args.mass;
sensor.K = sensor.M * (2*pi*args.freq)^2;
sensor.C = 2*sqrt(sensor.M * sensor.K);
case 'accelerometer'
sensor.type = 2;
sensor.M = args.mass;
sensor.K = sensor.M * (2*pi*args.freq)^2;
sensor.C = 2*sqrt(sensor.M * sensor.K);
sensor.G = -sensor.K/sensor.M;
case 'none'
sensor.type = 3;
end
stewart.sensors.inertial = sensor;

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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,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'universal'
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'spherical'
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
args.Ka_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
args.Ca_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
args.Cr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ka_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
args.Ca_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
args.Cr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
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 'universal'
stewart.joints_F.type = 1;
case 'spherical'
stewart.joints_F.type = 2;
case 'universal_p'
stewart.joints_F.type = 3;
case 'spherical_p'
stewart.joints_F.type = 4;
case 'flexible'
stewart.joints_F.type = 5;
case 'universal_3dof'
stewart.joints_F.type = 6;
case 'spherical_3dof'
stewart.joints_F.type = 7;
end
switch args.type_M
case 'universal'
stewart.joints_M.type = 1;
case 'spherical'
stewart.joints_M.type = 2;
case 'universal_p'
stewart.joints_M.type = 3;
case 'spherical_p'
stewart.joints_M.type = 4;
case 'flexible'
stewart.joints_M.type = 5;
case 'universal_3dof'
stewart.joints_M.type = 6;
case 'spherical_3dof'
stewart.joints_M.type = 7;
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;

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function [] = initializeLoggingConfiguration(args)
arguments
args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none'
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
end
conf_log = struct();
switch args.log
case 'none'
conf_log.type = 0;
case 'all'
conf_log.type = 1;
case 'forces'
conf_log.type = 2;
end
conf_log.Ts = args.Ts;
save('./mat/conf_log.mat', 'conf_log');

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function [micro_hexapod] = initializeMicroHexapod(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init', 'compliance'})} = '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 (6,1) double {mustBeNumeric, mustBeNonnegative} = 2e7*ones(6,1)
args.Ci (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3*ones(6,1)
% 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)
% Force that stiffness of each joint should apply at t=0
args.Foffset logical {mustBeNumericOrLogical} = false
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', 'universal_p', ...
'type_M', 'spherical_p');
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');
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
load('mat/Foffset.mat', 'Fhm');
stewart.actuators.dLeq = -Fhm'./args.Ki;
else
stewart.actuators.dLeq = zeros(6,1);
end
switch args.type
case 'none'
stewart.type = 0;
case 'rigid'
stewart.type = 1;
case 'flexible'
stewart.type = 2;
case 'modal-analysis'
stewart.type = 3;
case 'init'
stewart.type = 4;
case 'compliance'
stewart.type = 5;
end
micro_hexapod = stewart;
save('./mat/stages.mat', 'micro_hexapod', '-append');

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function [micro_hexapod] = initializeMicroHexapod(args)
arguments
args.rigid logical {mustBeNumericOrLogical} = false
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
%% Stewart Object
micro_hexapod = struct();
micro_hexapod.h = 350; % Total height of the platform [mm]
micro_hexapod.jacobian = 270; % Distance from the top of the mobile platform to the Jacobian point [mm]
%% Bottom Plate - Mechanical Design
BP = struct();
BP.rad.int = 110; % Internal Radius [mm]
BP.rad.ext = 207.5; % External Radius [mm]
BP.thickness = 26; % Thickness [mm]
BP.leg.rad = 175.5; % Radius where the legs articulations are positionned [mm]
BP.leg.ang = 9.5; % Angle Offset [deg]
BP.density = 8000; % Density of the material [kg/m^3]
BP.color = [0.6 0.6 0.6]; % Color [rgb]
BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
%% Top Plate - Mechanical Design
TP = struct();
TP.rad.int = 82; % Internal Radius [mm]
TP.rad.ext = 150; % Internal Radius [mm]
TP.thickness = 26; % Thickness [mm]
TP.leg.rad = 118; % Radius where the legs articulations are positionned [mm]
TP.leg.ang = 12.1; % Angle Offset [deg]
TP.density = 8000; % Density of the material [kg/m^3]
TP.color = [0.6 0.6 0.6]; % Color [rgb]
TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
%% Struts
Leg = struct();
Leg.stroke = 10e-3; % Maximum Stroke of each leg [m]
if args.rigid
Leg.k.ax = 1e12; % Stiffness of each leg [N/m]
else
Leg.k.ax = 2e7; % Stiffness of each leg [N/m]
end
Leg.ksi.ax = 0.1; % Modal damping ksi = 1/2*c/sqrt(km) []
Leg.rad.bottom = 25; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 17; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb]
Leg.color.top = [0.5 0.5 0.5]; % Color [rgb]
Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
Leg.sphere.top = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
Leg.m = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
Leg = updateDamping(Leg);
%% Sphere
SP = struct();
SP.height.bottom = 27; % [mm]
SP.height.top = 27; % [mm]
SP.density.bottom = 8000; % [kg/m^3]
SP.density.top = 8000; % [kg/m^3]
SP.color.bottom = [0.6 0.6 0.6]; % [rgb]
SP.color.top = [0.6 0.6 0.6]; % [rgb]
SP.k.ax = 0; % [N*m/deg]
SP.ksi.ax = 10;
SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
SP.thickness.top = SP.height.top-Leg.sphere.top; % [mm]
SP.rad.bottom = Leg.sphere.bottom; % [mm]
SP.rad.top = Leg.sphere.top; % [mm]
SP.m = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
SP = updateDamping(SP);
%%
Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
Leg.support.top = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
%%
micro_hexapod.BP = BP;
micro_hexapod.TP = TP;
micro_hexapod.Leg = Leg;
micro_hexapod.SP = SP;
%%
micro_hexapod = initializeParameters(micro_hexapod);
%% Setup equilibrium position of each leg
micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, args.AP, args.ARB);
%% Save
save('./mat/stages.mat', 'micro_hexapod', '-append');
%%
function [element] = updateDamping(element)
field = fieldnames(element.k);
for i = 1:length(field)
element.c.(field{i}) = 2*element.ksi.(field{i})*sqrt(element.k.(field{i})*element.m);
end
end
%%
function [stewart] = initializeParameters(stewart)
%% Connection points on base and top plate w.r.t. World frame at the center of the base plate
stewart.pos_base = zeros(6, 3);
stewart.pos_top = zeros(6, 3);
alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases)
alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top
height = (stewart.h-stewart.BP.thickness-stewart.TP.thickness-stewart.Leg.sphere.bottom-stewart.Leg.sphere.top-stewart.SP.thickness.bottom-stewart.SP.thickness.top)*0.001; % TODO
radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base
radius_t = stewart.TP.leg.rad*0.001; % top radius in meters
for i = 1:3
% base points
angle_m_b = (2*pi/3)* (i-1) - alpha_b;
angle_p_b = (2*pi/3)* (i-1) + alpha_b;
stewart.pos_base(2*i-1,:) = [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0];
stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0];
% top points
% Top points are 60 degrees offset
angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6;
angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6;
stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height];
stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height];
end
% permute pos_top points so that legs are end points of base and top points
stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
%% leg vectors
legs = stewart.pos_top - stewart.pos_base;
leg_length = zeros(6, 1);
leg_vectors = zeros(6, 3);
for i = 1:6
leg_length(i) = norm(legs(i,:));
leg_vectors(i,:) = legs(i,:) / leg_length(i);
end
stewart.Leg.lenght = 1000*leg_length(1)/1.5;
stewart.Leg.shape.bot = [0 0; ...
stewart.Leg.rad.bottom 0; ...
stewart.Leg.rad.bottom stewart.Leg.lenght; ...
stewart.Leg.rad.top stewart.Leg.lenght; ...
stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
0 0.2*stewart.Leg.lenght];
%% Calculate revolute and cylindrical axes
rev1 = zeros(6, 3);
rev2 = zeros(6, 3);
cyl1 = zeros(6, 3);
for i = 1:6
rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
cyl1(i,:) = leg_vectors(i,:);
end
%% Coordinate systems
stewart.lower_leg = struct('rotation', eye(3));
stewart.upper_leg = struct('rotation', eye(3));
for i = 1:6
stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
end
%% Position Matrix
stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.thickness+stewart.Leg.sphere.top+stewart.SP.thickness.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)];
%% Compute Jacobian Matrix
aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
stewart.J = getJacobianMatrix(leg_vectors', aa');
end
%%
function J = getJacobianMatrix(RM, M_pos_base)
% RM: [3x6] unit vector of each leg in the fixed frame
% M_pos_base: [3x6] vector of the leg connection at the top platform location in the fixed frame
J = zeros(6);
J(:, 1:3) = RM';
J(:, 4:6) = cross(M_pos_base, RM)';
end
end

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function [] = initializeMirror(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'rigid'
args.shape char {mustBeMember(args.shape,{'spherical', 'conical'})} = 'spherical'
args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45 % [deg]
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 10 % [kg]
args.freq (6,1) double {mustBeNumeric, mustBeNonnegative} = 200*ones(6,1) % [Hz]
end
mirror = struct();
switch args.type
case 'none'
mirror.type = 0;
case 'rigid'
mirror.type = 1;
case 'flexible'
mirror.type = 2;
end
mirror.mass = args.mass;
mirror.freq = args.freq;
mirror.K = zeros(6,1);
mirror.K(1:3) = mirror.mass * (2*pi*mirror.freq(1:3)).^2;
mirror.C = zeros(6,1);
mirror.C(1:3) = 0.2 * sqrt(mirror.K(1:3).*mirror.mass);
mirror.Deq = zeros(6,1);
mirror.h = 0.05; % Height of the mirror [m]
mirror.thickness = 0.02; % Thickness of the plate supporting the sample [m]
mirror.hole_rad = 0.125; % radius of the hole in the mirror [m]
mirror.support_rad = 0.1; % radius of the support plate [m]
% point of interest offset in z (above the top surfave) [m]
switch args.type
case 'none'
mirror.jacobian = 0.205;
case 'rigid'
mirror.jacobian = 0.205 - mirror.h;
case 'flexible'
mirror.jacobian = 0.205 - mirror.h;
end
mirror.rad = 0.180; % radius of the mirror (at the bottom surface) [m]
mirror.cone_length = mirror.rad*tand(args.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
mirror.shape = [...
mirror.support_rad+5e-3 mirror.h-mirror.thickness
mirror.hole_rad mirror.h-mirror.thickness; ...
mirror.hole_rad 0; ...
mirror.rad 0 ...
];
if strcmp(args.shape, 'spherical')
mirror.sphere_radius = sqrt((mirror.jacobian+mirror.h)^2+mirror.rad^2); % Radius of the sphere [mm]
for z = linspace(0, mirror.h, 101)
mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius^2-(z-mirror.jacobian-mirror.h)^2) z];
end
elseif strcmp(args.shape, 'conical')
mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(args.angle) mirror.h];
else
error('Shape should be either conical or spherical');
end
mirror.shape = [mirror.shape; mirror.support_rad+5e-3 mirror.h];
save('./mat/stages.mat', 'mirror', '-append');

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function [nano_hexapod] = initializeNanoHexapod(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'init'})} = 'flexible'
% initializeFramesPositions
args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3
args.MO_B (1,1) double {mustBeNumeric} = 170e-3
% generateGeneralConfiguration
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 100e-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)
% initializeStrutDynamics
args.actuator char {mustBeMember(args.actuator,{'piezo', 'lorentz', 'amplified'})} = 'piezo'
args.k1 (1,1) double {mustBeNumeric} = 1e6
args.ke (1,1) double {mustBeNumeric} = 5e6
args.ka (1,1) double {mustBeNumeric} = 60e6
args.c1 (1,1) double {mustBeNumeric} = 10
args.F_gain (1,1) double {mustBeNumeric} = 1
args.k (1,1) double {mustBeNumeric} = -1
args.c (1,1) double {mustBeNumeric} = -1
% initializeJointDynamics
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'universal'
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'spherical'
args.Ka_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
args.Ca_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
args.Cr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
args.Ka_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
args.Ca_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
args.Cr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
% initializeCylindricalPlatforms
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-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} = 120e-3
% initializeCylindricalStruts
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
% inverseKinematics
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
% Equilibrium position of each leg
args.dLeq (6,1) double {mustBeNumeric} = zeros(6,1)
% Force that stiffness of each joint should apply at t=0
args.Foffset logical {mustBeNumericOrLogical} = false
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);
if args.k > 0 && args.c > 0
stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', args.k*ones(6,1), 'C', args.c*ones(6,1));
elseif args.k > 0
stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', args.k*ones(6,1), 'C', 1.5*sqrt(args.k)*ones(6,1));
elseif strcmp(args.actuator, 'piezo')
stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', 1e7*ones(6,1), 'C', 1e2*ones(6,1));
elseif strcmp(args.actuator, 'lorentz')
stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', 1e4*ones(6,1), 'C', 1e2*ones(6,1));
elseif strcmp(args.actuator, 'amplified')
stewart = initializeStrutDynamics(stewart, 'type', 'amplified', ...
'k1', args.k1*ones(6,1), ...
'c1', args.c1*ones(6,1), ...
'ka', args.ka*ones(6,1), ...
'ke', args.ke*ones(6,1), ...
'F_gain', args.F_gain*ones(6,1));
else
error('args.actuator should be piezo, lorentz or amplified');
end
stewart = initializeJointDynamics(stewart, ...
'type_F', args.type_F, ...
'type_M', args.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);
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer');
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
load('mat/Foffset.mat', 'Fnm');
stewart.actuators.dLeq = -Fnm'./stewart.Ki;
else
stewart.actuators.dLeq = args.dLeq;
end
switch args.type
case 'none'
stewart.type = 0;
case 'rigid'
stewart.type = 1;
case 'flexible'
stewart.type = 2;
case 'init'
stewart.type = 4;
end
nano_hexapod = stewart;
save('./mat/stages.mat', 'nano_hexapod', '-append');

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function [nano_hexapod] = initializeNanoHexapodFinal(args)
arguments
%% Bottom Flexible Joints
args.flex_bot_type char {mustBeMember(args.flex_bot_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof'
args.flex_bot_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad]
args.flex_bot_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad]
args.flex_bot_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad]
args.flex_bot_kz (6,1) double {mustBeNumeric} = ones(6,1)*7e7 % Axial Stiffness [N/m]
args.flex_bot_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % X bending Damping [Nm/(rad/s)]
args.flex_bot_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Y bending Damping [Nm/(rad/s)]
args.flex_bot_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Torsionnal Damping [Nm/(rad/s)]
args.flex_bot_cz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Axial Damping [N/(m/s)]
%% Top Flexible Joints
args.flex_top_type char {mustBeMember(args.flex_top_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof'
args.flex_top_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad]
args.flex_top_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad]
args.flex_top_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad]
args.flex_top_kz (6,1) double {mustBeNumeric} = ones(6,1)*7e7 % Axial Stiffness [N/m]
args.flex_top_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % X bending Damping [Nm/(rad/s)]
args.flex_top_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Y bending Damping [Nm/(rad/s)]
args.flex_top_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Torsionnal Damping [Nm/(rad/s)]
args.flex_top_cz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Axial Damping [N/(m/s)]
%% Jacobian - Location of frame {A} and {B}
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
%% Relative Motion Sensor
args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts'
%% Top Plate
args.top_plate_type char {mustBeMember(args.top_plate_type,{'rigid', 'flexible'})} = 'rigid'
args.top_plate_xi (1,1) double {mustBeNumeric} = 0.01 % Damping Ratio
%% Actuators
args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible'
args.actuator_Ga (6,1) double {mustBeNumeric} = zeros(6,1) % Actuator gain [N/V]
args.actuator_Gs (6,1) double {mustBeNumeric} = zeros(6,1) % Sensor gain [V/m]
% For 2DoF
args.actuator_k (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*380000
args.actuator_ke (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*4952605
args.actuator_ka (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2476302
args.actuator_c (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*20
args.actuator_ce (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*200
args.actuator_ca (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*100
args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m]
% For Flexible Frame
args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m]
args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m]
% Misalignment
args.actuator_d_align (6,3) double {mustBeNumeric} = zeros(6,3) % [m]
args.actuator_xi (1,1) double {mustBeNumeric} = 0.01 % Damping Ratio
%% Controller
args.controller_type char {mustBeMember(args.controller_type,{'none', 'iff', 'dvf', 'hac-iff-struts'})} = 'none'
end
nano_hexapod = struct();
nano_hexapod.flex_bot = struct();
switch args.flex_bot_type
case '2dof'
nano_hexapod.flex_bot.type = 1;
case '3dof'
nano_hexapod.flex_bot.type = 2;
case '4dof'
nano_hexapod.flex_bot.type = 3;
case 'flexible'
nano_hexapod.flex_bot.type = 4;
end
nano_hexapod.flex_bot.kRx = args.flex_bot_kRx; % X bending stiffness [Nm/rad]
nano_hexapod.flex_bot.kRy = args.flex_bot_kRy; % Y bending stiffness [Nm/rad]
nano_hexapod.flex_bot.kRz = args.flex_bot_kRz; % Torsionnal stiffness [Nm/rad]
nano_hexapod.flex_bot.kz = args.flex_bot_kz; % Axial stiffness [N/m]
nano_hexapod.flex_bot.cRx = args.flex_bot_cRx; % [Nm/(rad/s)]
nano_hexapod.flex_bot.cRy = args.flex_bot_cRy; % [Nm/(rad/s)]
nano_hexapod.flex_bot.cRz = args.flex_bot_cRz; % [Nm/(rad/s)]
nano_hexapod.flex_bot.cz = args.flex_bot_cz; %[N/(m/s)]
nano_hexapod.flex_top = struct();
switch args.flex_top_type
case '2dof'
nano_hexapod.flex_top.type = 1;
case '3dof'
nano_hexapod.flex_top.type = 2;
case '4dof'
nano_hexapod.flex_top.type = 3;
case 'flexible'
nano_hexapod.flex_top.type = 4;
end
nano_hexapod.flex_top.kRx = args.flex_top_kRx; % X bending stiffness [Nm/rad]
nano_hexapod.flex_top.kRy = args.flex_top_kRy; % Y bending stiffness [Nm/rad]
nano_hexapod.flex_top.kRz = args.flex_top_kRz; % Torsionnal stiffness [Nm/rad]
nano_hexapod.flex_top.kz = args.flex_top_kz; % Axial stiffness [N/m]
nano_hexapod.flex_top.cRx = args.flex_top_cRx; % [Nm/(rad/s)]
nano_hexapod.flex_top.cRy = args.flex_top_cRy; % [Nm/(rad/s)]
nano_hexapod.flex_top.cRz = args.flex_top_cRz; % [Nm/(rad/s)]
nano_hexapod.flex_top.cz = args.flex_top_cz; %[N/(m/s)]
nano_hexapod.motion_sensor = struct();
switch args.motion_sensor_type
case 'struts'
nano_hexapod.motion_sensor.type = 1;
case 'plates'
nano_hexapod.motion_sensor.type = 2;
end
nano_hexapod.actuator = struct();
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.type = 1;
case 'flexible frame'
nano_hexapod.actuator.type = 2;
case 'flexible'
nano_hexapod.actuator.type = 3;
end
%% Actuator gain [N/V]
if all(args.actuator_Ga == 0)
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.Ga = ones(6,1)*(-2.5796);
case 'flexible frame'
nano_hexapod.actuator.Ga = ones(6,1); % TODO
case 'flexible'
nano_hexapod.actuator.Ga = ones(6,1)*23.2;
end
else
nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
end
%% Sensor gain [V/m]
if all(args.actuator_Gs == 0)
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.Gs = ones(6,1)*466664;
case 'flexible frame'
nano_hexapod.actuator.Gs = ones(6,1); % TODO
case 'flexible'
nano_hexapod.actuator.Gs = ones(6,1)*(-4898341);
end
else
nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
end
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.k = args.actuator_k; % [N/m]
nano_hexapod.actuator.ke = args.actuator_ke; % [N/m]
nano_hexapod.actuator.ka = args.actuator_ka; % [N/m]
nano_hexapod.actuator.c = args.actuator_c; % [N/(m/s)]
nano_hexapod.actuator.ce = args.actuator_ce; % [N/(m/s)]
nano_hexapod.actuator.ca = args.actuator_ca; % [N/(m/s)]
nano_hexapod.actuator.Leq = args.actuator_Leq; % [m]
case 'flexible frame'
nano_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
nano_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
nano_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
nano_hexapod.actuator.ks = args.actuator_ks; % Stiffness of one stack [N/m]
nano_hexapod.actuator.cs = args.actuator_cs; % Damping of one stack [N/m]
nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio
case 'flexible'
nano_hexapod.actuator.K = readmatrix('full_APA300ML_K.CSV'); % Stiffness Matrix
nano_hexapod.actuator.M = readmatrix('full_APA300ML_M.CSV'); % Mass Matrix
nano_hexapod.actuator.P = extractNodes('full_APA300ML_out_nodes_3D.txt'); % Node coordiantes [m]
nano_hexapod.actuator.d_align = args.actuator_d_align; % Misalignment
nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio
end
nano_hexapod.geometry = struct();
Fa = [[-86.05, -74.78, 22.49],
[ 86.05, -74.78, 22.49],
[ 107.79, -37.13, 22.49],
[ 21.74, 111.91, 22.49],
[-21.74, 111.91, 22.49],
[-107.79, -37.13, 22.49]]'*1e-3; % Ai w.r.t. {F} [m]
Mb = [[-28.47, -106.25, -22.50],
[ 28.47, -106.25, -22.50],
[ 106.25, 28.47, -22.50],
[ 77.78, 77.78, -22.50],
[-77.78, 77.78, -22.50],
[-106.25, 28.47, -22.50]]'*1e-3; % Bi w.r.t. {M} [m]
Fb = Mb + [0; 0; 95e-3]; % Bi w.r.t. {F} [m]
si = Fb - Fa;
si = si./vecnorm(si); % Normalize
Fc = [[-29.362, -105.765, 52.605]
[ 29.362, -105.765, 52.605]
[ 106.276, 27.454, 52.605]
[ 76.914, 78.31, 52.605]
[-76.914, 78.31, 52.605]
[-106.276, 27.454, 52.605]]'*1e-3; % Meas pos w.r.t. {F}
Mc = Fc - [0; 0; 95e-3]; % Meas pos w.r.t. {M}
nano_hexapod.geometry.Fa = Fa;
nano_hexapod.geometry.Fb = Fb;
nano_hexapod.geometry.Fc = Fc;
nano_hexapod.geometry.Mb = Mb;
nano_hexapod.geometry.Mc = Mc;
nano_hexapod.geometry.si = si;
nano_hexapod.geometry.MO_B = args.MO_B;
Bb = Mb - [0; 0; args.MO_B];
nano_hexapod.geometry.J = [nano_hexapod.geometry.si', cross(Bb, nano_hexapod.geometry.si)'];
switch args.motion_sensor_type
case 'struts'
nano_hexapod.geometry.Js = nano_hexapod.geometry.J;
case 'plates'
Bc = Mc - [0; 0; args.MO_B];
nano_hexapod.geometry.Js = [nano_hexapod.geometry.si', cross(Bc, nano_hexapod.geometry.si)'];
end
nano_hexapod.top_plate = struct();
switch args.top_plate_type
case 'rigid'
nano_hexapod.top_plate.type = 1;
case 'flexible'
nano_hexapod.top_plate.type = 2;
nano_hexapod.top_plate.R_flex = ...
{[ 0.53191886726305 0.4795690716524 0.69790817745892
-0.29070157897799 0.8775041341865 -0.38141720787774
-0.79533320729697 0 0.60617249143351 ],
[ 0.53191886726305 -0.4795690716524 -0.69790817745892
0.29070157897799 0.8775041341865 -0.38141720787774
0.79533320729697 0 0.60617249143351 ],
[-0.01420448131633 -0.9997254079576 -0.01863709726680
0.60600604129104 -0.0234330681729 0.79511481512719
-0.79533320729697 0 0.60617249143351 ],
[-0.51771438594672 -0.5201563363051 0.67927108019212
0.31530446231304 -0.8540710660135 -0.41369760724945
0.79533320729697 0 0.60617249143351 ],
[-0.51771438594671 0.5201563363052 -0.67927108019211
-0.31530446231304 -0.8540710660135 -0.41369760724945
-0.79533320729697 0 0.60617249143351 ],
[-0.01420448131632 0.9997254079576 0.01863709726679
-0.60600604129104 -0.0234330681729 0.79511481512719
0.79533320729697 0 0.60617249143351 ] };
nano_hexapod.top_plate.R_enc = ...
{ [-0.877504134186525 -0.479569071652412 0
0.479569071652412 -0.877504134186525 0
0 0 1 ],
[ 0.877504134186525 -0.479569071652413 0
0.479569071652413 0.877504134186525 0
0 0 1 ],
[ 0.023433068172945 0.999725407957606 0
-0.999725407957606 0.023433068172945 0
0 0 1 ],
[-0.854071066013566 -0.520156336305202 0
0.520156336305202 -0.854071066013566 0
0 0 1 ],
[ 0.854071066013574 -0.520156336305191 0
0.520156336305191 0.854071066013574 0
0 0 1 ],
[-0.023433068172958 0.999725407957606 0
-0.999725407957606 -0.023433068172958 0
0 0 1 ] };
nano_hexapod.top_plate.K = readmatrix('top_plate_K_6.CSV'); % Stiffness Matrix
nano_hexapod.top_plate.M = readmatrix('top_plate_M_6.CSV'); % Mass Matrix
nano_hexapod.top_plate.P = extractNodes('top_plate_out_nodes_3D_qua.txt'); % Node coordiantes [m]
nano_hexapod.top_plate.xi = args.top_plate_xi; % Damping ratio
end
switch args.controller_type
case 'none'
nano_hexapod.controller.type = 1;
case 'iff'
nano_hexapod.controller.type = 2;
case 'dvf'
nano_hexapod.controller.type = 3;
case 'hac-iff-struts'
nano_hexapod.controller.type = 4;
end
if nargout == 0
save('./mat/stages.mat', 'nano_hexapod', '-append');
end

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function [] = initializePosError(args)
% initializePosError - Initialize the position errors
%
% Syntax: [] = initializePosError(args)
%
% Inputs:
% - args -
arguments
args.error logical {mustBeNumericOrLogical} = false
args.Dy (1,1) double {mustBeNumeric} = 0 % [m]
args.Ry (1,1) double {mustBeNumeric} = 0 % [m]
args.Rz (1,1) double {mustBeNumeric} = 0 % [m]
end
pos_error = struct();
if args.error
pos_error.type = 1;
else
pos_error.type = 0;
end
pos_error.Dy = args.Dy;
pos_error.Ry = args.Ry;
pos_error.Rz = args.Rz;
save('./mat/pos_error.mat', 'pos_error');

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function [ref] = initializeReferences(args)
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
%% 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);
%% 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);
%% 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);
%% 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);
%% 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('mat/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));
%% Axis Compensation - Rm
t = [0, Ts];
Rm = [args.Rm_pos, args.Rm_pos];
Rm = struct('time', t, 'signals', struct('values', Rm));
%% Nano-Hexapod
t = [0, Ts];
Dn = zeros(length(t), 6);
switch args.Dn_type
case 'constant'
Dn = [args.Dn_pos, args.Dn_pos];
load('mat/stages.mat', 'nano_hexapod');
AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)];
tx = args.Dn_pos(4);
ty = args.Dn_pos(5);
tz = args.Dn_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)];
[~, Dnl] = inverseKinematics(nano_hexapod, 'AP', AP, 'ARB', ARB);
Dnl = [Dnl, Dnl];
otherwise
warning('Dn_type is not set correctly');
end
Dn = struct('time', t, 'signals', struct('values', Dn));
Dnl = struct('time', t, 'signals', struct('values', Dnl));
%% Save
save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Dnl', 'args', 'Ts');
end

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matlab/src/initializeRy.m Normal file
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function [ry] = initializeRy(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
args.Foffset logical {mustBeNumericOrLogical} = false
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;
case 'modal-analysis'
ry.type = 3;
case 'init'
ry.type = 4;
end
% Ry - Guide for the tilt stage
ry.guide.density = 7800; % [kg/m3]
ry.guide.STEP = './STEPS/ry/Tilt_Guide.STEP';
% Ry - Rotor of the motor
ry.rotor.density = 2400; % [kg/m3]
ry.rotor.STEP = './STEPS/ry/Tilt_Motor_Axis.STEP';
% Ry - Motor
ry.motor.density = 3200; % [kg/m3]
ry.motor.STEP = './STEPS/ry/Tilt_Motor.STEP';
% Ry - Plateau Tilt
ry.stage.density = 7800; % [kg/m3]
ry.stage.STEP = './STEPS/ry/Tilt_Stage.STEP';
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 args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
load('mat/Foffset.mat', 'Fym');
ry.Deq = -Fym'./ry.K;
else
ry.Deq = zeros(6,1);
end
save('./mat/stages.mat', 'ry', '-append');

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matlab/src/initializeRz.m Normal file
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function [rz] = initializeRz(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
args.Foffset logical {mustBeNumericOrLogical} = false
end
rz = struct();
switch args.type
case 'none'
rz.type = 0;
case 'rigid'
rz.type = 1;
case 'flexible'
rz.type = 2;
case 'modal-analysis'
rz.type = 3;
case 'init'
rz.type = 4;
end
% Spindle - Slip Ring
rz.slipring.density = 7800; % [kg/m3]
rz.slipring.STEP = './STEPS/rz/Spindle_Slip_Ring.STEP';
% Spindle - Rotor
rz.rotor.density = 7800; % [kg/m3]
rz.rotor.STEP = './STEPS/rz/Spindle_Rotor.STEP';
% Spindle - Stator
rz.stator.density = 7800; % [kg/m3]
rz.stator.STEP = './STEPS/rz/Spindle_Stator.STEP';
rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7];
rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4];
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
load('mat/Foffset.mat', 'Fzm');
rz.Deq = -Fzm'./rz.K;
else
rz.Deq = zeros(6,1);
end
save('./mat/stages.mat', 'rz', '-append');

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matlab/src/initializeSample.m Normal file
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function [sample] = initializeSample(args)
arguments
args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'init'})} = 'flexible'
args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m]
args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m]
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg]
args.freq (6,1) double {mustBeNumeric, mustBePositive} = 100*ones(6,1) % [Hz]
args.offset (1,1) double {mustBeNumeric} = 0 % [m]
args.Foffset logical {mustBeNumericOrLogical} = false
end
sample = struct();
switch args.type
case 'none'
sample.type = 0;
case 'rigid'
sample.type = 1;
case 'flexible'
sample.type = 2;
case 'init'
sample.type = 3;
end
sample.radius = args.radius; % [m]
sample.height = args.height; % [m]
sample.mass = args.mass; % [kg]
sample.offset = args.offset; % [m]
sample.inertia = [1/12 * sample.mass * (3*sample.radius^2 + sample.height^2); ...
1/12 * sample.mass * (3*sample.radius^2 + sample.height^2); ...
1/2 * sample.mass * sample.radius^2];
sample.K = zeros(6, 1);
sample.C = zeros(6, 1);
sample.K(1:3) = sample.mass .* (2*pi * args.freq(1:3)).^2; % [N/m]
sample.C(1:3) = 0.1 * sqrt(sample.K(1:3)*sample.mass); % [N/(m/s)]
sample.K(4:6) = sample.inertia .* (2*pi * args.freq(4:6)).^2; % [N/m]
sample.C(4:6) = 0.1 * sqrt(sample.K(4:6).*sample.inertia); % [N/(m/s)]
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
load('mat/Foffset.mat', 'Fsm');
sample.Deq = -Fsm'./sample.K;
else
sample.Deq = zeros(6,1);
end
save('./mat/stages.mat', 'sample', '-append');

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matlab/src/initializeSimscapeConfiguration.m Normal file
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function [] = initializeSimscapeConfiguration(args)
arguments
args.gravity logical {mustBeNumericOrLogical} = true
end
conf_simscape = struct();
if args.gravity
conf_simscape.type = 1;
else
conf_simscape.type = 2;
end
save('./mat/conf_simscape.mat', 'conf_simscape');

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matlab/src/initializeStewartPlatform.m Normal file
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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();

27
matlab/src/initializeStewartPose.m Normal file
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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;

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matlab/src/initializeStrutDynamics.m Normal file
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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,{'classical', 'amplified'})} = 'classical'
args.K (6,1) double {mustBeNumeric, mustBeNonnegative} = 20e6*ones(6,1)
args.C (6,1) double {mustBeNumeric, mustBeNonnegative} = 2e1*ones(6,1)
args.k1 (6,1) double {mustBeNumeric} = 1e6*ones(6,1)
args.ke (6,1) double {mustBeNumeric} = 5e6*ones(6,1)
args.ka (6,1) double {mustBeNumeric} = 60e6*ones(6,1)
args.c1 (6,1) double {mustBeNumeric} = 10*ones(6,1)
args.F_gain (6,1) double {mustBeNumeric} = 1*ones(6,1)
args.me (6,1) double {mustBeNumeric} = 0.01*ones(6,1)
args.ma (6,1) double {mustBeNumeric} = 0.01*ones(6,1)
end
if strcmp(args.type, 'classical')
stewart.actuators.type = 1;
elseif strcmp(args.type, 'amplified')
stewart.actuators.type = 2;
end
stewart.actuators.K = args.K;
stewart.actuators.C = args.C;
stewart.actuators.k1 = args.k1;
stewart.actuators.c1 = args.c1;
stewart.actuators.ka = args.ka;
stewart.actuators.ke = args.ke;
stewart.actuators.F_gain = args.F_gain;
stewart.actuators.ma = args.ma;
stewart.actuators.me = args.me;

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