Regular singular point at infinity speakers
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What do robots have in common with black holes? They both have singularities! In this post, we find out what singularities are, why they can cause havoc for roboticists and how to overcome them.
If you are interested in science, the word "singularity" probably makes you think of a black hole. Black holes are pretty popular right now, since the LIGO lab in America proved the existence of gravitational waves. This means that the force of gravity gets so big, it goes to infinity.
Robotic singularities use exactly the same concept as black holes. But, wait! Let's back up for a second. What are robotic singularities? How can they possibly be anything like black holes? In this post we'll show why singularities can ruin your day, and how roboticists can overcome them.
Imagine this. You want to use your robot to paint a line using a spray painting gun. To paint a perfect line, the robot needs to move at a constant velocity. If the robot changes velocity, some parts of the line will have more paint than others. This won't look very good. If the robot slows down too much, we'll get an unsightly blob of paint. Obviously, it's important that the robot moves along the line at a constant velocity.
Robots are precise. Usually they can handle this without a problem. However, if there are any kinematic singularities in the line, the paint job could be ruined. Watch this short video which demonstrates robot singularities.
It shows various examples of the three types of singularity for a 6-axis robot, which we'll discuss in a moment. The second example of a "wrist singularity" shows the robot trying and failing to follow a straight line at a constant velocity. What's causing this failure?
A singularity right in the middle of the line. You could solve this problem in a couple of ways, but first it's important to understand what's happening. Remember I said that the gravity at the center of a black hole "goes to infinity? At the center of the black hole the gravitational force is theoretically infinite. This might not actually be true nobody knows , but it's basically a property of math.
Mathematics can easily handle the concept of infinity. The real world can't. Lots of mathematical equations tend to infinity. As this physicist explains , theoretically you should create a singularity in your bathtub every time you pull the plug. The basic equation for the spiraling water says that the closer you get to the center of the plughole, the faster the water spins. According to the equation, the water should be moving infinitely fast right at the center.
In reality that's not what happens. Physical systems cannot move infinitely fast as far as we know. Robot singularities happen because robots are controlled by math w hich is okay with infinity , but are made of real, physical moving parts which isn't.
Singularities are caused by the inverse kinematics of the robot. If you need an introduction to robot kinematics, check out our previous post. When placed at a singularity, there may be an infinite number of ways for the kinematics to achieve the same tip position of the robot.
If the optimal solution is not chosen, assuming there is one, the robot joints could be commanded to move in an impossible way. Infinite velocity is not the only type of singularity that causes problems and certain types of singularities can be more problematic than others.
Some robots can be put in such a bad position that they need to be turned off, moved and restarted manually. The Stewart Platform is a parallel robot which has several difficult singularities. This video shows one singularity which causes the robot to lose rigidity in two actuators and fall down completely. This happens because the mathematics requires that the linear actuator becomes infinitely stiff, which is obviously impossible. This follow-up video shows how the platform can't be moved back to the correct position, because the actuator controllers have an infinite gain at the singularity.
Thankfully, industrial robots are not as problematic as the Stewart Platform. However, these singularities can still cause havoc. Therefore, the three types of singularities are defined by which joint alignments cause the problem:.
This video shows a useful simulation of these robot singularities. In the video, the joints are colored red when they are commanded to an infinite velocity, which shows the whole idea pretty clearly. Manufacturers program their robots so that singularities don't break the robot. However, in the past this just meant that if one joint was commanded to move too fast, the robot stopped completely with an error message.
This was not a very elegant solution. These days, many robot manufacturers are improving their singularity avoidance. In the video I introduced above , the robot had been programmed with a maximum speed for each joint. When the wrist j oint was commanded "to infinity" , this caused the software to reduce the velocity of the tip. The robot slowed down when it reached the middle of the line.
When it passed the singularity, it was able to continue doing the rest of the line at the correct velocity. The paint job still would have been ruined, but the robot nevertheless functions correctly and doesn't get stuck. Singularity avoidance has been a developing topic for many years. Various solutions have been proposed and some are starting to make their way into industrial robots. For an introduction to the basics, the ETS Control and Robotics Lab cites a good academic paper which explains the mathematics behind robot singularities and gives examples using an industrial robot.
The more axes that a robot has, the more possibilities for singularities. This is because there are more axes which can line up with each other. However, as we discussed in a previous post , extra axes can also reduce the effect of singularities by allowing alternative positions to reach the same point. This paper gives a good introduction on the control of redundant robot arm manipulation , with discussions of how to deal with singularities through programming.
Robot technicians have come up with many ingenious ways to avoid singularities over the years. As a result, technicians started to add small angles to the tooling to reduce the chance that the robot moves into a singularity.
This technique is still a good way to avoid singularities. Mounting a spray painting gun at a very slight angle degrees can sometimes ensure that a robot avoids singularities completely. Not always, but it's a cheap solution and easy to try. Finally, another good technique is to move the task into a part of the workspace where there are no singularities. This is not always possible, but can be very effective.
Of course, you first need to understand what singularities are, but now you do! Have you had problems with robot singularities? What tricks do you use to lessen their effect? Have you seen any ingenious singularity avoidance techniques? Tell us in the comments below or join the discussion on LinkedIn , Twitter or Facebook. What's the best way to automate a sanding task? Material removal is vital for many manufacturing processes, but it take a lot Catherine Elie showcases Robotiq's new Sanding Kit as we get ready to delve into the world of sanding, polishing, deburring Search this site on Google Search Google.
Subscribe now. Select Topics. Latest Blog Post. Leave a comment. Written by Alex Owen-Hill. Alex Owen-Hill is a freelance writer and public speaker who blogs about a large range of topics, including science, presentation skills at CreateClarifyArticulate. As a recovering academic, he maintains a firm foot in the robotics world by blogging about industrial robotics. Connect with the writer:. Related posts.
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A Review of the “Third” integral
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Differential and Difference Equations with Applications
Who we've been given this differential equation right here. So I'm giving you uh step by step solution to this. Uh All the points are very clear, so I hope you understand this, wow. So of course we're just gonna do differential of that, which is this and then the differential of uh the same thing. That's a double to friendship.
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The conference will be held on ZOOM platform. The links to the virtual rooms will be sent, every day, within one hour from the start, to the emails which have been used to register. In view of the very uncertain situation related to the pandemic of Covid, we have decided to hold our conference entirely online on 6thth of September of If you have any questions please send us an email to: altecosmo20 gmail. Mariusz P. This is the fifth event in the series of fundamental cosmology conferences organized by the University of Szczecin previous were Cosmofun' , Grasscosmofun'09 , Multicosmofun'12 , Varcosmofun' This time the task of the conference is to bring together specialists dealing with the problems of alternative gravities who want to exchange the current ideas in this topic.
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The coupling of dimension reducation with other effects, such as fracture, debonding or delamination, micromagnetism, homogenization, pattern formation, and optimal design, will be addressed. In this talk, I propose to go to higher scalings of the elastic energy as a function of the thickness of the structure. I will also discuss what I view as potential modeling issues that seem inherent to the adopted approach. YouTube link , PM ET : Marta Lewicka , University of Pittsburgh Title: Geometry and morphogenesis: problems and prospects Zoom Meeting ID: , Passcode: Abstract: The shape of a leaf or flower in the garden, or its laboratory analogs built using swelling gels, raise several questions at the interface of biology, physics and mathematics: how might they be described, how can their shapes be predicted, and how can they eventually be controlled for function?
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We could try and make them move by changing their vertices and re-configuring their buffers each frame, but that's cumbersome and costs quite some processing power. There are much better ways to transform an object and that's by using multiple matrix objects. This doesn't mean we're going to talk about Kung Fu and a large digital artificial world. Matrices are very powerful mathematical constructs that seem scary at first, but once you'll grow accustomed to them they'll prove extremely useful.
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