Inverse differential kinematics equation X_dot = J*q_dot

Hello,

I am trying to solve a differential equation of the form X_dot = J*q_dot (X_dot and J are known).

where X_dot = [x_dot; y_dot; phi_dot], a column vector with position (x,y) and angle phi

J = Jacobian matrix, a 3x6 matrix

q_dot = [theta1_dot; theta2_dot;...theta6_dot], colunm vector with six angles theta1 to theta6.

I want to find q_dot from this equation. Is there any way I can do this?

---------My method-----------

I am currently using symbolic computation and have tried

x = [x; y; phi];
x_dot = diff(x,t);

q = [theta1; theta2; theta3; theta4; theta5; theta6];
q_dot = diff(q,t);

solvex = solve([pinv(J)*x_dot] == q_dot,[q])

I also have a long 3x6 Jacobian (J) with a lot of theta1's in 1st column, theta2's in 2nd column.....upto theta6's in 6th column. (Not to be confused, my J has a lot of terms in it and not just thetas. The other terms are constants that are predefined)

The issue is that I am getting a blank 0 x1 value for theta.

Is theta being both in the Jacobian and the output matrix confusing matlab?

Please let me know how to go about with this.

Thanks,

Venkatesh.

% Output from command line if it helps
solvex = 

  struct with fields:

    theta1: [0×1 sym]
    theta2: [0×1 sym]
    theta3: [0×1 sym]
    theta4: [0×1 sym]
    theta5: [0×1 sym]
    theta6: [0×1 sym]
    
    vpa(solvex.theta1)
 
ans =
 
Empty sym: 0-by-1

[Jyotsna Talluri]

Can you provide the dataset i.e.,the matrices x ,J,and q

Answer 1

[Jyotsna Talluri]

Hi,

If the matrix X is a function of t ,then X_dot = J*q_dot reduces to 7 equations with 5 unknowns (t,theta1 ,theta2,theta3 ,theta4,theta5,theta6).which cannot be solved. That is the reason you are getting empty results. When the system of equations don’t have a solution, we get empty results.