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Analyze measurements with encoders fixed to plates

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Thomas Dehaeze 2021-06-30 22:45:20 +02:00
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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, mustBePositive} = 1 % Time to go to first point and after last point [s]
args.tw (1,1) double {mustBeNumeric, mustBePositive} = 0.5 % Time wait between each point [s]
args.tm (1,1) double {mustBeNumeric, mustBePositive} = 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} = 10e-6 % [m]
args.z_tot (1,1) double {mustBeNumeric} = 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, mustBePositive} = 1 % [s]
args.tw (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
args.ty (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
args.tz (1,1) double {mustBeNumeric, mustBePositive} = 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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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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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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