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I want to make a Geogebra model where you can determine the length of any part ad where the end destination should be, but I seem to have stumbled upon a problem with my functions.

Can anyone review my formulas and help me finding the problem?

https://www.geogebra.org/calculator/cuhnenyr

Degree functions Pre determined variables

I later want to use this IK on an arduino robot arm that I have, and make it pick up stuff based on a live video of its surroundings.

My functions work but only when the robot-parts are at a specific lenght and Destination.

TazzenTazz
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1 Answers1

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there are basically 2 options to do this:

  1. using analytic solution

    this involves computing direct kinematics by multiplying 4x4 transform matrices representing each rotation and translation in their order analytically.

    And then doing inverse matrix of the result while all matrix elements are expressions not values !!! This usually leads to system of transcendental equations however your case have just few joints so it might be still manageable. If not numerical solutions are used to fit the input variables that solves the resulting equations.

  2. using iterative approach

    This involves direct kinematics (the same as in #1 but without the inverse) and then fitting the input variables to match desired position (minimizing error). There are many math optimization algorithms to do this however in robotics is usually used just:

    As this is iterative we can handle matrix elements as values so we can use standard linear algebra libs (or code the matrix multiplication on your own) so this is much much easier to implement and also this can easily handle changes of the kinematics on the run. However this solution tends to get stuck in local minima so you have to add detection of that and then randomize input and search again...

I strongly recommend to go for #2 as its much simpler.

Spektre
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