Inverse differential kinematics equation X_dot = J*q_dot

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Venkatesh Sripada
回答： Jyotsna Talluri 2019-8-5
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

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采纳的回答

Jyotsna Talluri
Jyotsna Talluri 2019-8-5
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.

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