diff --git a/analyze_jacobian.m b/analyze_jacobian.m new file mode 100644 index 0000000..309f48e --- /dev/null +++ b/analyze_jacobian.m @@ -0,0 +1,46 @@ +figure; +plot(d_meas.Time, d.Data-d_meas.Data) + +%% +figure; +plot(error.Time, error.Data) +legend({'x', 'y', 'z', 'theta_x', 'theta_y', 'theta_z'}) + +%% +J = jacobian.Data(:, :, 1); + +% Norm of the jacobian with time +J_change = (jacobian.Data - J)./J; + +figure; +hold on; +plot(jacobian.Time, squeeze(J_change(1, 1, :))); +plot(jacobian.Time, squeeze(J_change(2, 2, :))); +plot(jacobian.Time, squeeze(J_change(3, 3, :))); +plot(jacobian.Time, squeeze(J_change(4, 4, :))); +plot(jacobian.Time, squeeze(J_change(5, 5, :))); +plot(jacobian.Time, squeeze(J_change(6, 6, :))); +legend({'Jxx', 'Jyy', 'Jzz', 'Jmx', 'Jmy', 'Jmz'}) +hold off; + +%% K change +K_init = J'*J; +K = zeros(size(jacobian.Data)); + +for i=1:length(jacobian.Time) + K(:, :, i) = jacobian.Data(:, :, i)'*jacobian.Data(:, :, i); +end + +K_change = (permute(K, [2, 1, 3]) - K_init)./K_init; + +figure; +hold on; +plot(jacobian.Time, squeeze(K_change(1, 1, :))); +plot(jacobian.Time, squeeze(K_change(2, 2, :))); +plot(jacobian.Time, squeeze(K_change(3, 3, :))); +plot(jacobian.Time, squeeze(K_change(4, 4, :))); +plot(jacobian.Time, squeeze(K_change(5, 5, :))); +plot(jacobian.Time, squeeze(K_change(6, 6, :))); +legend({'Kxx', 'Kyy', 'Kzz', 'Kmx', 'Kmy', 'Kmz'}) +hold off; + diff --git a/initializeParameters.m b/initializeParameters.m new file mode 100644 index 0000000..a5e6826 --- /dev/null +++ b/initializeParameters.m @@ -0,0 +1,80 @@ +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 diff --git a/params_micro_hexapod.m b/params_micro_hexapod.m new file mode 100644 index 0000000..cdf9121 --- /dev/null +++ b/params_micro_hexapod.m @@ -0,0 +1,93 @@ +%% +clear; close all; clc; + +%% Stewart Object +stewart = struct(); +stewart.h = 350; % Total height of the platform [mm] +stewart.jacobian = 0; % Point where the Jacobian is computed => Center of rotation [mm] + +%% Bottom Plate +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 +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]; + +%% Leg +Leg = struct(); + +Leg.stroke = 10e-3; % Maximum Stroke of each leg [m] +Leg.k.ax = 5e7; % Stiffness of each leg [N/m] +Leg.ksi.ax = 10; % Maximum amplification at resonance [] +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]; + +%% +stewart.BP = BP; +stewart.TP = TP; +stewart.Leg = Leg; +stewart.SP = SP; + +%% +stewart = initializeParameters(stewart); + +%% +clear BP TP Leg SP; + +%% +function element = updateDamping(element) + field = fieldnames(element.k); + for i = 1:length(field) + element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m); + end +end diff --git a/params_nano_hexapod.m b/params_nano_hexapod.m new file mode 100644 index 0000000..fe768bf --- /dev/null +++ b/params_nano_hexapod.m @@ -0,0 +1,93 @@ +%% +clear; close all; clc; + +%% Stewart Object +stewart = struct(); +stewart.h = 90; % Total height of the platform [mm] +stewart.jacobian = 174.5; % Point where the Jacobian is computed => Center of rotation [mm] + +%% Bottom Plate +BP = struct(); + +BP.rad.int = 0; % Internal Radius [mm] +BP.rad.ext = 150; % External Radius [mm] +BP.thickness = 10; % Thickness [mm] +BP.leg.rad = 100; % Radius where the legs articulations are positionned [mm] +BP.leg.ang = 5; % Angle Offset [deg] +BP.density = 8000; % Density of the material [kg/m^3] +BP.color = [0.7 0.7 0.7]; % Color [rgb] +BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness]; + +%% Top Plate +TP = struct(); + +TP.rad.int = 0; % Internal Radius [mm] +TP.rad.ext = 100; % Internal Radius [mm] +TP.thickness = 10; % Thickness [mm] +TP.leg.rad = 90; % Radius where the legs articulations are positionned [mm] +TP.leg.ang = 5; % Angle Offset [deg] +TP.density = 8000; % Density of the material [kg/m^3] +TP.color = [0.7 0.7 0.7]; % Color [rgb] +TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness]; + +%% Leg +Leg = struct(); + +Leg.stroke = 80e-6; % Maximum Stroke of each leg [m] +Leg.k.ax = 5e7; % Stiffness of each leg [N/m] +Leg.ksi.ax = 10; % Maximum amplification at resonance [] +Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm] +Leg.rad.top = 10; % 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 = 15; % [mm] +SP.height.top = 15; % [mm] +SP.density.bottom = 8000; % [kg/m^3] +SP.density.top = 8000; % [kg/m^3] +SP.color.bottom = [0.7 0.7 0.7]; % [rgb] +SP.color.top = [0.7 0.7 0.7]; % [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]; + +%% +stewart.BP = BP; +stewart.TP = TP; +stewart.Leg = Leg; +stewart.SP = SP; + +%% +stewart = initializeParameters(stewart); + +%% +clear BP TP Leg SP; + +%% +function element = updateDamping(element) + field = fieldnames(element.k); + for i = 1:length(field) + element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m); + end +end diff --git a/stewart_displacement.slx b/stewart_displacement.slx new file mode 100644 index 0000000..2b06f07 Binary files /dev/null and b/stewart_displacement.slx differ diff --git a/stewart_without_sensing.slx b/stewart_without_sensing.slx new file mode 100644 index 0000000..396c599 Binary files /dev/null and b/stewart_without_sensing.slx differ