Engineering domain: Robotics

##Task Description
The question: Find a set of joint variables that would produce a given tool pose for a 6-DOF robot

Frame 0 is fixed to the base. Frame 1 is fixed to the tool. Set the frame 0 as the reference, for frame 1, the homogeneous transformation matrix M_1in0 is:

M = [ 0.0000  0.0000  1.0000  -8.0000;
          1.0000  0.0000  0.0000   2.0000;
          0.0000  1.0000  0.0000   0.0000;
          0.0000  0.0000  0.0000   1.0000]];


The matrix of spatial screw axes is:

S = [ 0.0000  1.0000  0.0000  0.0000 -1.0000  0.0000;
        0.0000  0.0000  0.0000  1.0000  0.0000  1.0000;
        0.0000  0.0000 -1.0000  0.0000  0.0000  0.0000;
        0.0000  0.0000  2.0000  0.0000  0.0000  0.0000;
        1.0000  0.0000 -4.0000  0.0000  0.0000  0.0000;
        0.0000  0.0000  0.0000 -6.0000  0.0000 -8.0000 ];


The goal pose T_1in0 is:

T_1in0 = [ -0.5429   0.5940   0.5937  -9.3919;
                  0.6499  -0.1506   0.7449  -1.8656;
                  0.5319   0.7903  -0.3043   0.6739;
                  0            0            0            1.0000 ];

## Output Format
Find a set of joint variables θ that is:

theta=[theta_1; theta_2; theta_3; theta_4; theta_5; theta_6]

that would result in the given pose T_1in0.