Solving for a matrix

C is a variable matrix, C=[w,x,y,x]

I have an equation T*Q*M=B; All the matrices are 4*4

B and Q are known constant matrices. But T and M are matrices which have elements as a function of variables in C.

For example: T=[0,cos(x).sin(y),0,

0,0,0,0,

1,1,1,1

0,0,0,0]

Similarly M.

Is it possible to solve for the matrix C(i.e for the variables in C).Help if possible

[Walter Roberson]

Do you need all of the possible solutions as formulas ? Do you need any one numeric solution? Do you need any one numeric solution subject to some bounds constraints on x?

[hrushikesh kyathari]

I need any one solution.

[Walter Roberson]

Make a function that calculates T*Q*M-B and fsolve() it.

[hrushikesh kyathari]

Tsb=[cos(c(1,1)),-sin(c(1,1)),0,c(2,1),
     sin(c(1,1)),cos(c(1,1)),0,c(3,1),
     0,0,1,0.0963,
     0,0,0,1];
 Tbo=[1,0,0,0.1662,
     0,1,0,0,
     0,0,1,0.0026
     0,0,0,1];
 M=[1,0,0,0.033,
     0,1,0,0,
     0,0,1,0.6546,
     0,0,0,1];
 Slist=[0,0,1,0,0.033,0,
        0,-1,0,-0.5076,0,0,
        0,-1,0,-0.3526,0,0,
        0,-1,0,-0.2176,0,0,
        0,0,1,0,0,0]';
   Toe=FKinBody(M,Slist,c((4:8),1));
fun=(Tsb*Tbo*Toe)-X;
 H = fsolve(fun,-500)

This is my code, When I try to run Fsolve it is showing error:FUN must be a function, a valid character vector expression, or an inline function object.

[Walter Roberson]

What is FKinBody ?

In

fun=(Tsb*Tbo*Toe)-X;

what is X ? And what happened to B ?

Answer 1

[Walter Roberson]

Tsb = @(c) [cos(c(1)), -sin(c(1)), 0, c(2);
     sin(c(1)), cos(c(1)), 0, c(3);
     0, 0, 1, 0.0963;
     0, 0, 0, 1];
 Tbo=[1, 0, 0, 0.1662;
     0, 1, 0, 0;
     0, 0, 1, 0.0026;
     0, 0, 0, 1];
 M=[1, 0, 0, 0.033;
     0, 1, 0, 0;
     0, 0, 1, 0.6546;
     0, 0, 0, 1];
 Slist=[0, 0, 1,        0, 0.033, 0;
        0, -1, 0, -0.5076, 0, 0;
        0, -1, 0, -0.3526, 0, 0;
        0, -1, 0, -0.2176, 0, 0;
        0, 0, 1,        0, 0, 0]';
   Toe = @(c) FKinBody(M, Slist, c(4:8));
   fun = @(c) (Tsb(c) * Tbo * Toe(c)) - B;
   c0 = randi([-1000 1000], 1, 4);
   H = fsolve(fun, c0)

Answer 2

[John D'Errico]

You have what? 2 unknowns? I've seen various versions of these equations that you have written. But you do not have 16 unknowns.

You want 16 equations to be solved. That 4x4 matrix equation is equivalent to 16 equations. So unless you have 16 unknowns, you need to accept the solution will not be exact.

So you will use a solver that will handle a nonlinear least squares. I might suggest something like lsqnonlin or lsqcurvefit. They are not just there for curve fitting.