Inverse kinematics of 6-links manipulator

As promised in the previous article.

Let’s look at direct kinematics.
H = T_z(L_0) \cdot R_z(q_1) \cdot T_z(L_{11}) \cdot T_x(L_{12}) \cdot R_y(q_2) \cdot T_z(L_2) \cdot R_y(-q_3) \cdot T_z(L_{31}) \cdot R_x(-q_4) \cdot T_x(L_4) \cdot R_y(-q_5) \cdot T_x(L_5) \cdot R_x(-q_6)

Where T_a – translation matrix with respect to a axis, and R_a – rotational matrix with respect to a axis.
H – homogeneous transformation matrix, which contains the position and rotation of the endpoint in global coordinates. (L_{32} is already included in L_4 because there is no difference where J_4 is located on this link)

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Inverse kinematics of 2 and 3-links manipulator

With direct kinematics for an ordinary manipulator, everything is pretty simple. And what about the inverse? At a minimum, it’s worth to repeat that it is ambiguous. Let’s start with the two-links manipulator.

2-links manipulator
2-links manipulator
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Direct kinematics of 2-3-6-n-links manipulator

In the last article I have already described which question answers direct kinematics, and now we will look at examples of how to do this.

How to find the end position for 2-links manipulator? Geometry will tell! Obviously:

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Ubuntu 18.04, nvidia drivers and second monitor

I installed Ubuntu 18.04 from scratch (I decided to switch to ROS Melodic ). Understandable that ubuntu did not see nvidia drivers by default. But as it works – do not touch. But I decided to connect a second monitor … I checked hdmi cable … well, the second monitor is not exist anyway.

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Control Theory and System Identification

About a year ago I taught the course “System Identification and Simulation”, but at the very beginning with the professor we decided to check how the masters remember Control Theory. As a result, the half of the semester slid to “Recall All”.

Here I want to save some links that I used to prepare for classes and other useful things.
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Pupils, code readability and serious robotics

Once I was tinkering with an anthropomorphic robot. I got to the point where I rewrite almost all code from c++ to python. A colleague (more physicist than a programmer) after this trick very quickly (literally in a month) sketched and tested algorithms, and also wrote a graduate work on these algorithms. Readability is an important thing.
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