Jacobian Matrix and Singularities | Robotics | Introduction | Part 1

Jacobian Matrix and Singularities | Robotics | Introduction | Part 1

In this video we will run through an introduction to using and finding the #Jacobian Matrix for #robotic systems. The Jacobian can be used to find:
1) Joint Velocities
2) Singularities
3) Torques and Forces on a robot's joint
--------------------------------------------------------------------------------------------------------------------
Intro music:
Happy Rock

----------------------------------------------------------------------------------------------------------------------
Subject material is obtained from:

John. J. Craig, Introduction to Robotics (Mechanics and Control). Pearson Education International.
-----------------------------------------------------------------------------------------------------------------------
Thumbs up and Subscribe Icons are made by

-----------------------------------------------------------------------------------------------------------------------
Hope this video helps.

If you have any questions, please leave a comment, and don't forget to like and subscribe.

Cheers everyone!

[ayavuyaklaas]

Please do more videos in Robotics, your explaining very good.

[MrLonglace]

this video really help me through my exam, thx a lot sir!

[enhaozheng]

Great videos!
The presentation method is also great! What type of device do you use?

[liliw]

Best video for Jacobian matrix!! Please keep making more video related robotics.

[PaulM]

This intro is much better, the previous was in higher volume than the rest of the video.

[AirAdventurer]

(I'm not 100% on this; I'm opening this interpretation up for comments)

I think the way you're doing Jacobian matrices, it's with a coordinate patch, mapping the generalized coordinates from the coordinate space into the configuration space (manifold) Q, and where the Jacobian (determinant of the Jacobian matrix) is zero, the vector field on the configuration space is zero, what is sometimes known as a critical point of a differential equation on the configuration space.

There is another way of thinking about critical points of differential equations (vector fields) on configuration spaces, as a section of the tangent bundle of the configuration space, \xi:Q -> TQ. Where there is a critical point of the differential equation, one can take the Jacobian of \xi (*not* the Jacobian of the coordinate patch), and this becomes the "A matrix" of the state-space representation of a plant function about the critical point. *This* Jacobian matrix will have eigenvalues, some of which may have positive real part and some of which may have negative real part (let's assume none have zero real part, so the Hartman-Grobman Theorem applies), so we can put an open-loop controller and a unital feedback loop on the system near the critical point, making all the eigenvalues of the closed-loop system have negative real part ("stable eigenvalues"). We can then put the real part of all but two of the eigenvalues out between, say, -5 and -10 (called the "non-dominant eigenvalue"), and then, for the remaining two eigenvalues, put their real part, say, between 0 and -2 (called the "dominant eigenvalues"), and meet the design specifications of the control engineering problem with proper placement of the dominant eigenvalues.

Let me know what you think about this interpretation of the underlying mathematics.

[wweworld]

if jacobian matrix is not square than how to calculate singularities.

[sciWithSaj]

Please suggest any good books for robotics

[shukhratdad]

Thanks for your video. It is easy understandable. If I have a quiz in future, can I connect by email? If yes, please give me yours