Holonomic vs. Nonholonomic Constraints for Robots | Fundamentals of Robotics

Holonomic vs. Nonholonomic Constraints for Robots | Fundamentals of Robotics | Lesson 4

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Mecharithm - Robotics and Mechatronics

Күн бұрын

🌟 Contents 🌟
💎 (00:00) Introduction
💎 (01:16) Holonomic (Configuration) Constraints for Robots
💎 (05:30) Velocity (Pfaffian) Constraints
💎 (06:22) Nonholonomic Constraints
💎 (07:07) Chassis of a Car Driving on a Plane
💎 (08:57) Steerable Needles
💎 (09:30) A Coin Rolling on a Plane without Slipping (A Classical Problem)
💎 (11:51) Summary of the Holonomic and Nonholonomic Constraints
In this video, you will learn that holonomic or configuration constraints reduce the degrees of freedom (dofs) of a robot, whereas nonholonomic constraints reduce the space of possible velocities.
This video also has a reading version that complements the video. Our suggestion is to watch the video and then read the reading for a deeper understanding. For the reading, refer to the link below:
www.mecharithm.com/holonomic-...
Be sure to also watch other lessons on Fundamentals of Robotics gathered together into a playlist for your convenience as some of the lessons are prerequisites for this lesson.
Thanks for watching! Ready to be a part of the Mecharithm family?👇
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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
💉 The steerable needle research is done by Fan Yang and Mahdieh Babaiasl under the supervision of Prof. John Swensen at M3 Robotics Lab.
💲 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.
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Пікірлер: 49

@kevinraetz3890 Жыл бұрын

At 8:20 you say that by inspection we can say that A(q)q_dot = 0 is not integratable, but why is that? Is it because we can't choose any phi that satisfied the equation without setting x_dot or y_dot to 0?

@mecharithm-robotics Жыл бұрын

Go back to 4:53 and 5:46, in order for the equation in 8:20 to be integrable, we need to find the function g_1(q) that satisfies the following equations: ∂g1/∂φ(q) = 0 ∂g1/∂x(q) = sinφ ∂g1/∂y(q) = -cosφ can you find such a function that satisfies these three equations?

@roboram7651 Жыл бұрын

@@mecharithm-robotics How to verify those functions satisfying the following equations (Only major doubt I have)? Also what I understand it, non- holonomic constraint is always needed for a mechanism to reach a point by reducing the velocity, not dof of c-space?

@syedanasnisar846 2 жыл бұрын

Thanks, ma'am for making robotics a piece of cake. Love from Pakistan.

@mecharithm-robotics 2 жыл бұрын

Thanks, Syed, for your feedback. Glad to hear that.

@ehsanmalekipour9988 3 жыл бұрын

Thanks for taking the time Like the previous two videos, it was very fluent and understandable

@mecharithm-robotics 3 жыл бұрын

Thank Ehsan for your feedback.

@andreaperna1402 9 ай бұрын

Thanks a lot, it was extremely helpful for the understanding of the first chapter of my Autonomous and Mobile Robotics's course. Subscribed!

@alibabayiasl2113 3 жыл бұрын

I'm proud of you😍😍😍

@mohammaditani4558 3 жыл бұрын

Great video! Thanks!

@mecharithm-robotics 3 жыл бұрын

Thanks for your feedback 🙏

@mistermind143 3 жыл бұрын

Super Amazing, I hope to have a PhD supervisor like you.

@mecharithm-robotics 3 жыл бұрын

🙏

@RBERAHMA 3 жыл бұрын

Thank you, I understood easily.

@mecharithm-robotics 3 жыл бұрын

Great to hear that. Thanks for your feedback.

@makesandmoocs8259 3 жыл бұрын

Thankyou very much !

@mecharithm-robotics 3 жыл бұрын

You are very welcome.

@alexandrevalente9994 2 жыл бұрын

Thanks a lot, this chapter was driving mad today. Thanks to your video now I understand almost everything in this chapter. Also thank you for these maths tips on the formulas, i was getting hard time while reading the book as I couldn’t understand the transformations since they were not explained. Nevertheless, I might need some more math tips (but not today, my brain is over).

@mecharithm-robotics 2 жыл бұрын

Thanks, Alexandre, glad that the video helped you! We are here to help and feel free to ask any questions that you have.

@alexandrevalente9994 2 жыл бұрын

@@mecharithm-robotics I am busy understanding the terms of the general equations... L1 x Cos Theta1 + L2 x Cos (Theta1 + Theta2)... If I understand, the First equation gives the horizontal position of the robot (because of the cosine) and the second equation gives the vertical position of the robot. If we consider, the 1st link (L1), the horizontal distance traveled by the upper tip (or joint) of L1, is the cosine (the projection) of the line formed by the projection of the upper tip (joint) to the ground and the fixed point of L1 on the ground (let's call it d). So L1 x Cos (Theta1) = d, now if we consider the vertical distance travelled by L1 at that angle is L1 x Sin (Theta1) and so on for the remaining links. Right ? So the 3 formulas are a system of equations that describe the movement of the 4-bar robot, and the 3rd one is a kind of constraint that tells the arms cannot exceed some displacement or movement. So the sum of the anlge at each time cannot exceed 2 x PI, otherwise we would have a robot that could rotate completely which is impossible for this one. Am i right ?

@alexandrevalente9994 2 жыл бұрын

Here is a figure of what I think: drive.google.com/file/d/1ErMbJ8F5j5bxm0RREqdKT6NK2Jk9YdKY/view?usp=sharing

@alexandrevalente9994 2 жыл бұрын

@@mecharithm-robotics In addition, those equations as they give the positions of the system (all the links) for a given angle, if we derive this with respect to the time, we get then a velocity... which is as stated in the book... the joint-velocity... in other words, the velocity at which the joints move from one angle to another, right ?

@alexandrevalente9994 2 жыл бұрын

So, all put together ... this permits to : a) control the robot so it never exceeds some maximum angle in order to keep the system in its operation limits. b) control the robot velocity in order to keep the joints in acceptable mechanical constraints.

@Maybe.019 2 жыл бұрын

thank you , that was pretty good

@mecharithm-robotics 2 жыл бұрын

You are very welcome. Great to hear that it was helpful.

@canadafaizan 2 жыл бұрын

Extremely helpful videos, thank you! Regarding the non holonomic constraints, when you say they are not integrable, could you please explain a bit more as to why you came to this reasoning?

@mecharithm-robotics 2 жыл бұрын

Faizan, thanks for your comment, and it is a great question. Suppose that we have a car that cannot move directly sideways without parallel parking. This is a velocity constraint (as we discussed in the lesson) because the car can reach any configuration on a plane (x,y,phi) despite this constraint. Therefore, we cannot integrate this velocity constraint to get the equivalent configuration constraint, and therefore it is a nonholonomic constraint. If it could have been integrated to get the configuration constraint then the car could not have reached all configurations on the plane (because it had configuration constraints that could reduce the dimension of the c-space). Hope this clarifies it.

@dungnguyenminh3308 Жыл бұрын

In the example of 4-link serial robot, you said that it satisfies 2 aforementioned conditions. But i do not understand the 4th link rotates relatively with respect to the origin, so how could its tip can coincident with the origin, and how could its orientation is horizontal? Thanks.

@mecharithm-robotics Жыл бұрын

It basically says that you can find the closed loop linkage’s equations by supposing a 4 link open chain subject to those two conditions since we want to simulate the closed loop robot right? They are assumptions that makes solving the closed loop linkage using the 4 link robot possible. 4 link robot’s kinematics is straight forward to derive.

@roboram7651 Жыл бұрын

Hi @Mecharithm - Robotics and Mechatronics. Excellent Presentations so far. But I confused with the non-holonomic representation of the coin as you explained in the last part of the video. Also, about the integration & matrix multiplications. Could you please refer any materials to workout?

@mecharithm-robotics Жыл бұрын

Thanks for your comment. The two nonholonomic constraints are changed into a matrix multiplication equation. If you do the matrix multiplication, you will get the two nonholonomic constraints that we wrote. Integration and matrix multiplication are covered in calculus and linear algebra courses in college, and you can refer to, for instance, Thomas' calculus for integration in detail and any linear algebra book, like Linear Algebra by Hoffman, covers matrices and their operations.

@roboram7651 Жыл бұрын

@@mecharithm-robotics Will do the same. Thanks for your support, Keep grooming us😃

@roboram7651 Жыл бұрын

Hello, you mentioned that a four-link mechanism has three loop constraints and a 1-dof c-space defined by four joint angles. If this is true, are there four equations for the loop constraints for a mechanism with six joint angles if it has two degrees of freedom? Also what I understand from the 3 loop closure equation is that, 1st equation is about X position, 2nd one is Y position and 3rd equation is for orientation?

@roboram7651 Жыл бұрын

Also how do you rewrite that x(dot)sin(pi) - y(dot)cos(pi)=0 in the form of plaffian constraint?

@sch0453 Жыл бұрын

why we calculate the chassis velocity not the wheels velocity first?

@ryanmckenna2047 5 ай бұрын

What is space of possible velocities called, velocity configuration space?

@alibabayiasl2113 3 жыл бұрын

😍😍😍😍

@alexandrevalente9994 2 жыл бұрын

Hi Mahdi, Since I am busy reviewing linear algebra and especially vector and matrices math. I am busy now with using Tensorflow to do matrices maths on a computer. Can you tell me if TF is used in robotics ? It is a fantastic tool, I use it indirectly with Keras for Deep learning in computer vision stuff. Thanks

@mecharithm-robotics 2 жыл бұрын

TF as you mentioned is used in machine learning and machine learning has numerous applications in robotics like ML-based robot control etc.

@mistermind143 3 жыл бұрын

I understood almost everything but still have confusion with Non-holonomic constraints.

@mecharithm-robotics 3 жыл бұрын

Thank you for your comment. Would you please be specific? In general, Nonholonomic constraints are velocity constraints, and they will reduce the possible velocities. For example, traditional cars (some autonomous vehicles have this option nowadays) cannot slide sideways (reducing the possible velocities of the vehicle). However, you can get the sideways motions with parallel parking (the car still has that degree of freedom).

@mistermind143 3 жыл бұрын

@@mecharithm-robotics Thank you mam for this prompt response. So far I understand your answer but I think I am not understanding C-space properly. I watched all of your videos but still do not understand the C-space properly which it comes to a bit complex problem in C-space.

@mecharithm-robotics 3 жыл бұрын

@@mistermind143 That's a great question and thanks for bringing that up. C-space is the space of configurations. The simplest example is finding the configuration of a point on a circle. We can define the position of every point on a circle with an angle from horizontal, right? So, the c-space has a dimension of one, and the topology of the c-space is a 1D circle or S^1. However, representation is different. We usually opt to represent the c-space embedded in a higher-dimensional Euclidean space because we understand Euclidean space better. For our example, you can represent the c-space by embedding the 1D space into a 2D Euclidean space (x-y) subject to one constraint that x^2+y^2 = 1 (2-1 = 1-dimensional space that we have).

@s864008 3 жыл бұрын

I think you are not clear on nonholonomic including all your examples. You shift away quickly from the concept.

@s864008 3 жыл бұрын

and why this lecture is a copy of northern university?

@mecharithm-robotics 3 жыл бұрын

Thanks for your comment, and sorry that it did not meet your expectations. What lecture are you referring to? We've never copy anything from anywhere. Most of the examples are classical problems and other people may have used them in their lectures. References used are in the caption if you are interested at all. We are sorry that we cannot cater to everybody's expectations.