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io9: 10 Pseudo-Science Theories We'd Like to See Retired Forever


PF Chang

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Eating gluten free = eating healthier.  Complete fad and waste of your dollars. The only ones that qualify are those with Celiac disease and even that is over diagnosed.  

 

If you say so. I had stomach problems my whole life but I tested negative for Celiacs. I eliminated gluten 3 years ago anyways. Stomach problems and joint pain went away. And yes, I still eat a lot of crap.

 

Been gluten free for 3 years now.

 

I guess it's coincidental for me.

 

edie..besides, a lot us aren't claiming that gluten free is healthier for the masses. They are just healthier for some individuals.

 

I know I feel better now without gluten in my diet.

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No, I'm doing it in C as I'm using Inverse Kinematics to program a robot to move it's hands into a position in three-dimensional space. I've decided to try the Jacobian method, and as I have more joints to move (shoulder Roll/Pitch/Yaw and Elbow = 4 joints) than there are dimensions for the end-effector, I have to find the Psuedoinverse of the Jacobian matrix rather than having the true inverse one could get when the number of joints is equal to the number of dimensions.

I did some Forward Kinematics in Octave (the free open-source terminal-based version of matlab) if it makes you feel any better. :)

Doing this in C sounds a greater deal more difficult. Are you finding the Jacobian matrix inverse because you are getting the rotational matrix in order to switch coordinates or am I just way off?
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Doing this in C sounds a greater deal more difficult. Are you finding the Jacobian matrix inverse because you are getting the rotational matrix in order to switch coordinates or am I just way off?

The way the Jacobian method works is that it does not find the final angles to acheive the desired end-effector immediately, but rather cuts it up into steps, and for each step, it tries to find which direction to change each angle. The Jacobian Matrix is comprised of a bunch of partial derivatives:

[dX/dTheta1 dY/dTheta1 dZ/dTheta1; dX/dTheta2 dY/dTheta2 dZ/dTheta2; ... dX/dThetaN dY/dThetaN dZ/dThetaN]

Realistically, we're working with in discreet time rather than continuous, so you can replace those derivatives with deltas such that dX = X_next - X_current, while dTheta is based on the step size you assign it, so dTheta = theta_current + step_size. So this linearizes how changes in each of the angles affects the change in the end-effector's position based on the current condition of the system.

So finding the X,Y,Z position of the next step based on the step size of the thetas will be using foreward kinematics which, indeed, uses the rotational matrices to find out where that leaves you in XYZ space.

So if X is position-space and THETA is angle-space, we get dX = J(THETA)dTHETA. We can caldulate dX with the forward kinematics making that a known, and we need to know how to change THETA, so to isolate, we need to multiply both sides by the Jacobian Inverse to get the identity matrix on the right, but since it's not a square matrix, we multiply by the Jacobian Pseudoinverse giving us Jt(THETA)dX = Jt(THETA)J(THETA)dTHETA ~= dTHETA

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