126 lines
3.5 KiB
Matlab
126 lines
3.5 KiB
Matlab
function error_nass = convertErrorBasis(pos, setpoint, ty, ry, rz)
|
|
% convertErrorBasis -
|
|
%
|
|
% Syntax: convertErrorBasis(p_error, ty, ry, rz)
|
|
%
|
|
% Inputs:
|
|
% - p_error - Position error of the sample w.r.t. the granite [m, rad]
|
|
% - ty - Measured translation of the Ty stage [m]
|
|
% - ry - Measured rotation of the Ry stage [rad]
|
|
% - rz - Measured rotation of the Rz stage [rad]
|
|
%
|
|
% Outputs:
|
|
% - P_nass - Position error of the sample w.r.t. the NASS base [m]
|
|
% - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]
|
|
%
|
|
% Example:
|
|
%
|
|
|
|
%% If line vector => column vector
|
|
if size(pos, 2) == 6
|
|
pos = pos';
|
|
end
|
|
|
|
if size(setpoint, 2) == 6
|
|
setpoint = setpoint';
|
|
end
|
|
|
|
%% Position of the sample in the frame fixed to the Granite
|
|
P_granite = [pos(1:3); 1]; % Position [m]
|
|
R_granite = [setpoint(1:3); 1]; % Reference [m]
|
|
|
|
%% Transformation matrices of the stages
|
|
% T-y
|
|
TMty = [1 0 0 0 ;
|
|
0 1 0 ty ;
|
|
0 0 1 0 ;
|
|
0 0 0 1 ];
|
|
|
|
% R-y
|
|
TMry = [ cos(ry) 0 sin(ry) 0 ;
|
|
0 1 0 0 ;
|
|
-sin(ry) 0 cos(ry) 0 ;
|
|
0 0 0 1 ];
|
|
|
|
% R-z
|
|
TMrz = [cos(rz) -sin(rz) 0 0 ;
|
|
sin(rz) cos(rz) 0 0 ;
|
|
0 0 1 0 ;
|
|
0 0 0 1 ];
|
|
|
|
%% Compute Point coordinates in the new reference fixed to the NASS base
|
|
% P_nass = TMrz*TMry*TMty*P_granite;
|
|
P_nass = TMrz\TMry\TMty\P_granite;
|
|
R_nass = TMrz\TMry\TMty\R_granite;
|
|
|
|
dx = R_nass(1)-P_nass(1);
|
|
dy = R_nass(2)-P_nass(2);
|
|
dz = R_nass(3)-P_nass(3);
|
|
|
|
%% Compute new basis vectors linked to the NASS base
|
|
% ux_nass = TMrz*TMry*TMty*[1; 0; 0; 0];
|
|
% ux_nass = ux_nass(1:3);
|
|
% uy_nass = TMrz*TMry*TMty*[0; 1; 0; 0];
|
|
% uy_nass = uy_nass(1:3);
|
|
% uz_nass = TMrz*TMry*TMty*[0; 0; 1; 0];
|
|
% uz_nass = uz_nass(1:3);
|
|
|
|
ux_nass = TMrz\TMry\TMty\[1; 0; 0; 0];
|
|
ux_nass = ux_nass(1:3);
|
|
uy_nass = TMrz\TMry\TMty\[0; 1; 0; 0];
|
|
uy_nass = uy_nass(1:3);
|
|
uz_nass = TMrz\TMry\TMty\[0; 0; 1; 0];
|
|
uz_nass = uz_nass(1:3);
|
|
|
|
%% Rotations error w.r.t. granite Frame
|
|
% Rotations error w.r.t. granite Frame
|
|
rx_nass = pos(4);
|
|
ry_nass = pos(5);
|
|
rz_nass = pos(6);
|
|
|
|
% Rotation matrices of the Sample w.r.t. the Granite
|
|
Mrx_error = [1 0 0 ;
|
|
0 cos(-rx_nass) -sin(-rx_nass) ;
|
|
0 sin(-rx_nass) cos(-rx_nass)];
|
|
|
|
Mry_error = [ cos(-ry_nass) 0 sin(-ry_nass) ;
|
|
0 1 0 ;
|
|
-sin(-ry_nass) 0 cos(-ry_nass)];
|
|
|
|
Mrz_error = [cos(-rz_nass) -sin(-rz_nass) 0 ;
|
|
sin(-rz_nass) cos(-rz_nass) 0 ;
|
|
0 0 1];
|
|
|
|
% Rotation matrix of the Sample w.r.t. the Granite
|
|
Mr_error = Mrz_error*Mry_error*Mrx_error;
|
|
|
|
%% Use matrix to solve
|
|
R = Mr_error/[ux_nass, uy_nass, uz_nass]; % Rotation matrix from NASS base to Sample
|
|
|
|
[thetax, thetay, thetaz] = RM2angle(R);
|
|
|
|
error_nass = [dx; dy; dz; thetax; thetay; thetaz];
|
|
|
|
%% Custom Functions
|
|
function [thetax, thetay, thetaz] = RM2angle(R)
|
|
if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
|
|
thetay = -asin(R(3, 1));
|
|
% thetaybis = pi-thetay;
|
|
thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
|
|
% thetaxbis = atan2(R(3, 2)/cos(thetaybis), R(3, 3)/cos(thetaybis));
|
|
thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
|
|
% thetazbis = atan2(R(2, 1)/cos(thetaybis), R(1, 1)/cos(thetaybis));
|
|
else
|
|
thetaz = 0;
|
|
if abs(R(3, 1)+1) < 1e-6 % R31 = -1
|
|
thetay = pi/2;
|
|
thetax = thetaz + atan2(R(1, 2), R(1, 3));
|
|
else
|
|
thetay = -pi/2;
|
|
thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
|
|
end
|
|
end
|
|
end
|
|
|
|
end
|