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Forward Kinematics and Reverse Kinematics

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Ken
Ken 2016-9-25
评论： Walter Roberson 2016-9-25
In Robotics F.K. we have A*Si = B*phi where A, B are known matrices, Si is a vector with x, y and z as its elements, phi is the vector containing the angular velocity of each of the 2 wheels of the robot. MATLAB says that an eqn of the form Ax=B can be solved by A\B. I am not sure if this applies in my case i.e. A*Si = B*phi. This I know has been solved and I was told that A\B is the way to do it but does not work for me. Similarly I am stuck on the R.K. case. Please help

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John D'Errico
John D'Errico 2016-9-25
编辑：John D'Errico 2016-9-25
So A & B are known matrices. Si is a known vector.
OF COURSE IT APPLIES!
What A*Si? A known vector. Call it b.
So then you have a problem of the form
B*phi = v
Can you solve that using backslash? Yes. B is known. v is known.
Look at the equation. How do you solve it? Substitute variables.
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John D'Errico
John D'Errico 2016-9-25
编辑：John D'Errico 2016-9-25
It looks like you have an error in your equations. You give two different equations for R. I picked 0.5 for gamma. By the way, for your own good, please don't use gamma as the name of a variable. It will cause you a great deal of hell in the future, when you might need to use the function gamma. In general, don't use variable names that are the same as that of existing functions.
I picked a gamma of 0.5, then tried to test out your code.
J = @(gamma) [1,0,0; cos(gamma), sin(gamma), sin(gamma)];
C = @(gamma) [ 0, 1, 0; -sin(gamma), cos(gamma), cos(gamma)];
A = @(gamma) [J(gamma);C(gamma)];
A(.5)
ans =
1 0 0
0.87758 0.47943 0.47943
0 1 0
-0.47943 0.87758 0.87758
B = [0.3,0;0,0.3;0,0;0,0];
F = @(gamma) [.15, .15*cos(gamma) ; 0 , .15*cos(gamma);0 ,.3*sin(gamma)];
F(.5)
ans =
0.15 0.13164
0 0.13164
0 0.14383
R=B\A(.5)
R =
3.3333 0 0
2.9253 1.5981 1.5981
R = @(gamma) [10/3 ,0, 0; -(10/3)*cos(gamma), -(10/3)*sin(gamma) ,(5/3)*sin(gamma)];
R(.5)
ans =
3.3333 0 0
-2.9253 -1.5981 0.79904
So you see that the two formulas for R give different values for the second row of R. Check your equations carefully, as you have a mistake there.
Walter Roberson
Walter Roberson 2016-9-25
In your code you have
F = @(gamma) [[.15, .15*cos(gamma) ;
0 , .15*cos(gamma);
0 ,.3*sin(gamma)];
That starts with two '[' but ends in only one, so MATLAB thinks the array is still being formed.

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