Configuration, and Configuration Space (Topology and Representation) of a Robot

Configuration, and Configuration Space (Topology and Representation) of a Robot | Lesson 2

Рет қаралды 12,031

Mecharithm - Robotics and Mechatronics

Күн бұрын

🌟 Contents 🌟
💎(00:00) Introduction
💎(00:07) Summary of the Lesson
💎(00:28) Introduction to Dr. Madi Babaiasl
💎(03:09) Configuration of a Door
💎(03:29) Configuration of a Point on a Plane
💎(03:49) Configuration of a Robot
💎(04:17) Configuration of a two-DOF Robot
💎(05:40) The topology of the Configuration Space of a Two-DOF Robot
💎(06:13) The topology of a Configuration Space
💎(06:43) Important Notes on Topology
💎(08:15) 1D Spaces and Their Topologies
💎(08:53) 2D Spaces and Their Topologies
💎(09:57) Representation of the C-space of a Point on a Plane
💎(10:27) Representation of the C-space of the 2D Surface of a Sphere
💎(11:48) Representation of the C-space of the 2R Planar Robot
💎(12:36) Singularities in the C-space Representation of a 2R Planar Robot Arm
💎(13:27) Explicit vs. Implicit Representation of a C-space
💎(14:10) Explicit and Implicit Representation of the C-space of a Point on a Circle
💎(15:24) Explicit and Implicit Representation of the C-space of the 2D surface of a Sphere
This is the second lesson on Fundamentals of Robotics, and it will be your guide to know everything you have ever needed to know about the configuration and configuration space (its topology and representation) of a robot.
In this lesson, we will talk about the configuration of the robot. Then, the configuration space and topology of the configuration space will be discussed, and finally, we will talk about different ways to represent the configuration space.
You can read the whole lesson at the following link too:
🌐www.mecharithm.com/configurat...
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References:
📘 Textbooks:
Modern Robotics: Mechanics, Planning, and Control by Frank Park and Kevin Lynch
A Mathematical Introduction to Robotic Manipulation by Murray, Lee, and Sastry
📹Videos:
- Gluing a Torus by Bothmer Channel:
• Gluing a Torus
🌐Websites:
- Configuration Space Visualization of 2-D Robotic Manipulator:
www.cs.unc.edu/~jeffi/c-space...
💲 If you enjoyed this video, please consider contributing to help us with our mission of making Robotics and Mechatronics available for everyone. We sincerely thank you for your generous contribution (you can do this by the Thanks button under the video).
©️ Tutorials and learning material are proprietary to Mecharithm, but sampling is permitted with proper attribution to the main source.
#configuration #configurationspace #space #1dspace #2dspace #door #twodofrobot #planarrobot #robotarm #robot #robotics #mechatronics #learning #mechanicalengineering #computerscience #mecharithm #mechanicalengineering #explicitrepresentation #implicitrepresentation #representation #pointonaplane #sphere #torus #stem #stemeducation #robotconfigurationspace #configurationspacedefinition #applicationoftopologyinrobotics #cspace #cspacerobotics

Пікірлер: 39

@eboandjiani4769 9 ай бұрын

thanks a lot for the clear explanation and the vitisual representation. I have had read the book and watched the videos of the author in coursera, but honestly, I could not grasp the main idea before watching your video.

@mecharithm-robotics 9 ай бұрын

you are very welcome. These lessons are now followed by labs too: github.com/madibabaiasl/modern-robotics-I-course/wiki --> jump to lab 5 for this lesson. note that you can do all labs in simulation too. look at the initial labs for how to setup the simulation environment.

@hummingbird5964 7 ай бұрын

which course on coursera?

@alexfish7792 4 ай бұрын

5:28 After a year or more of study, I finally understand what this torus is about. Thank you for the visual example.

@xxxiu13 11 ай бұрын

Very intuitive explanation! Thanks!

@farshadaali 2 жыл бұрын

many thanks for your course on the configuration space. I have read Ch3. of the reference, but there were so many questions unanswered in my mind. Watching your video cleared up everything for me. Thanks again and keep up the good job!

@mecharithm-robotics 2 жыл бұрын

Thanks, Farshad for your feedback. Great to hear that.

@leandrogcosta 3 ай бұрын

Wow

@serdarserdar2270 3 жыл бұрын

Thank you.

@mecharithm-robotics 3 жыл бұрын

You are very welcome.

@amalhassam1026 2 жыл бұрын

Awesome

@ehsanmalekipour9988 3 жыл бұрын

I enjoyed the video, Thanks

@mecharithm-robotics 3 жыл бұрын

Thanks Ehsan

@user-zo9er5ie7m 11 ай бұрын

I am student of robotics and automation, i found ur explanation very useful to me. Kindly bring tutorial on how to integrate electronics and robotics

@eshginguluzade1209 3 жыл бұрын

I loved your way to the explain things, specifically by showing those plastic links. I started to read the first book you mentioned and searched the topics on KZfaq to learn more and found you. Unfortunately, I see that you give up creating videos. Anyway, thanks for taking your time to create this video.

@mecharithm-robotics 3 жыл бұрын

Eshgin, thanks for the comment and feedback. We are currently working on the videos. We invested in a better camera and microphone to increase the quality of the videos. Stay tuned!

@yousifmor3403 Жыл бұрын

thanks a lot !

@mecharithm-robotics Жыл бұрын

You're welcome!

@DheerajSinghal01 6 ай бұрын

Subscibed

@alexandrevalente9994 2 жыл бұрын

Thank you for these explanations. They are very clear. I couldn’t understand things at that level of details (especially the singularity problem) by reading the book, neither by watching the official course of Lynch on Coursera (too much synthesised). About the explanation of the singularity of Theta for the 2D circle by using explicit representation at the end of this video… You said that the values of Theta will lead to a singularity… is this for the 0° / 360 ° (or 2 PI) point ?

@mecharithm-robotics 2 жыл бұрын

Alexandre, thanks for your feedback. Focusing on singularities is not the focus of this video, and you are right about it. Think about singularity this way: You are given the desired configuration, and you are asked to find the angles that, if given to the robot's control system, it can get to that configuration. This inverse problem does not always have a unique solution. For instance, for a 2R planar robot, both angles (0 and 2pi) will give the same configuration. Think about this in terms of robot control. You are at a configuration, and because there are two solutions for the inverse problem to reach the desired configuration, the robot's control can send a 360 deg command to the actuators, and this angle can be beyond the joint limit for the robot that can cause catastrophic situations. Singularities generally mean that the inverse problem (which is having the desired configuration and finding a set of variables to reach that configuration is not always available, or multiple answers can give the same configuration). We'll talk about singularities over time. Try to watch the orientation videos (we talked about singularities for the 3-parameter representations for the orientation). There will be a lesson in the future that is solely dedicated to this with enough visualizations. At singular points, the robot will lose one or more of its dofs.

@markfarrens7733 Жыл бұрын

Very helpful thank you

@mecharithm-robotics Жыл бұрын

You are most welcome.

@anuragreghu827 3 жыл бұрын

Very good presentation.

@mecharithm-robotics 3 жыл бұрын

Thanks for your feedback 🙏

@sabzimatic 2 жыл бұрын

at 5:50, i believe it should not be donut but a 2 dimensional ring. Since both the links can only rotate in 2D space and not 3D space. If the 2nd link is perpendicularly joint to the first link then the rotation of 2nd link will form a donut. Please correct me if my understanding is inaccurate. Thank you

@mecharithm-robotics 2 жыл бұрын

Mandeep, thanks for your comment and feedback. that's exactly what is said in the video. "By simulating this we can see that the c-space of a 2 link robot arm has a torus or donut shape. In fact, the c-space is the 2-dimensional surface of a donut". It is the 2D surface of the donut.

@madhavpr Жыл бұрын

Great video. Thanks fot the course. Loved the visualizations. It was difficult to understand the concepts from the book. I have a stupid question- what's the definition of a singularity? Can you please define it intuitively and mathematically?

@mecharithm-robotics Жыл бұрын

Thank you for your feedback. singularity means that at a certain configuration, the robotic arm loses one or several of its degrees of freedom.

@mtzmechengr5781 2 жыл бұрын

Nice explanation! So is safe to say that the configuration space of a 2R robot is the annulus of the outer ring of two concentric circles and the topology of this cspace is a donut? Does the topology of any cspace always have a higher dimension of said cspace?

@mecharithm-robotics 2 жыл бұрын

Thanks for your comment Mtz, and for bringing up these awesome questions. The c-space of a 2R robot is the 2-d surface of a donut (you can get a plane by cutting it), and the topology is torus or donut-shaped (as you also mentioned). The topology of this c-space is two-dimensional (not higher-dimensional) as you can get a plane by cutting the torus. We can represent the configuration space with a minimum number of coordinates that match the C-space dimension with singularities or represent the C-space with the curved space embedded in Euclidean space of higher dimension subject to constraints for simplicity (example: we can represent a sphere with lat and longitude or (x,y,z) with one constraint). Hope this answer helps! If you have more questions do not hesitate to ask.

@mtzmechengr5781 2 жыл бұрын

@@mecharithm-robotics Yes this makes sense! I think you meant sphere instead of circle in this sentence:::: (example: we can represent a circle with lat and longitude or (x,y,z) with one constraint)

@mecharithm-robotics 2 жыл бұрын

@@mtzmechengr5781 yes you are right! typo! corrected!

@youtubethings1254 Жыл бұрын

Where are you from?

@mecharithm-robotics Жыл бұрын

Mecharithm is based in Austin, TX

@Gotenham 2 жыл бұрын

do we need the huge intro on your qualifications, we can see you know what you are talking abotu when you talk it well

@mecharithm-robotics 2 жыл бұрын

Gotenham, thanks for your feedback. You can start from (03:09) Configuration of a Door.

@fleurvanille7668 3 жыл бұрын

Please represent your carrier in another video with an appropriate title, time is precious. I just clicked on the video to know about the configuration space, but found my self wasting time seeing different stuff than configuration space's topic,

@mecharithm-robotics 3 жыл бұрын

Belle, Thanks for your feedback. We did not mean to waste your time but if you felt that way we deeply apologize. We put the timings underneath the video for you to skip any part that you do not want to watch, you could simply skip that part and get to the configuration space part. Life is too short for hatred and dislikes. Let's love and support each other and give constructive feedbacks whenever needed. We will try our best to fix the issue you mentioned from the next video. Happy Holidays and Peace out! ❤️