Institut de Robòtica i Informàtica Industrial

Absolute2RelativeJacobian

PURPOSE ^

Jacobian of the relative displacement between two poses.

SYNOPSIS ^

function [H1 H2]=Absolute2RelativeJacobian(P1,P2)

DESCRIPTION ^

 Jacobian of the relative displacement between two poses.

 Returns the Jacobians of the Absolute2Relative function with respect its
 parameteres evaluated at P1 and P2.
 This is used in the linear filters to linearize Absolute2Relative and is
 denoted by H in our papers.

 See also Absolute2Relative.

CROSS-REFERENCE INFORMATION ^

This function calls:
This function is called by:

SOURCE CODE ^

0001 function [H1 H2]=Absolute2RelativeJacobian(P1,P2)
0002 % Jacobian of the relative displacement between two poses.
0003 %
0004 % Returns the Jacobians of the Absolute2Relative function with respect its
0005 % parameteres evaluated at P1 and P2.
0006 % This is used in the linear filters to linearize Absolute2Relative and is
0007 % denoted by H in our papers.
0008 %
0009 % See also Absolute2Relative.
0010 
0011   x1=P1.data(1);  y1=P1.data(2);  o1=P1.data(3);
0012     x2=P2.data(1);  y2=P2.data(2);% o2=P2.data(3);
0013   
0014     dx=(x2-x1);
0015     dy=(y2-y1);
0016 
0017     c1=cos(o1);
0018     s1=sin(o1);
0019 
0020     H1=[[-c1 -s1 -s1*dx+c1*dy ];
0021           [ s1 -c1 -c1*dx-s1*dy ];
0022           [  0   0    -1        ]];
0023         
0024     H2=[[ c1  s1 0];
0025           [-s1  c1 0];
0026           [  0   0 1]];
0027


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