Matlab Functions used for the NASS Project

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

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