Robotic singularity is a major headache for both manufacturers and users; encountering it can lead to serious consequences, including mechanical failure and loss of life. So what exactly is robotic singularity, how does it occur, and how can it be avoided? This article, written by Alex Owen-Hill of Robotiq, provides a comprehensive understanding of these troublesome issues.
If you're interested in science, the term "singularity" is likely to remind you of black holes. Since the LIGO laboratory in the US proved the existence of gravitational waves, black holes have been widely reported in the media and are well-known to the public. Physicists theorize that at the center of a black hole lies a "gravitational singularity," meaning that gravity there is extremely strong, even approaching infinity. The concept of a robotic singularity is exactly the same as that of a black hole.
What is a robotic singularity? How can they be like a black hole?
My robot is going crazy.
Imagine you want to draw a line with your robotic spray gun. For the line to be perfect, the robot needs to move at a constant speed. If the robot changes speed, the line might be uneven in thickness and won't look good. If the robot slows down too much, we might see unsightly spots on the line. Clearly, maintaining a constant speed is crucial when drawing the line. The robot is very precise. Under normal circumstances, the robot can handle this problem without any stress. However, if there's a singularity in the motion along the line, this task will be impossible.
Why do singularities exist? How can they be resolved? There are two ways to solve this problem, but first let's understand what happened.
The singularity tends to infinity
As I mentioned earlier, the gravity at the center of a black hole "tends to infinity." This means that the closer you get to the center, the stronger the gravity becomes. Theoretically, gravity is infinite at the center of a black hole. This may not be true (nobody knows), but it's a mathematical property. Mathematics can easily handle the concept of infinity, while the real world cannot.
Numerous mathematical equations tend towards infinity. As this physicist explains, theoretically, every time you pull the plug in the bathtub, you create a singularity. The basic principle is that the closer you get to the center of the hole, the faster the water flows. According to this theory, at the very center of the hole, the water speed tends towards infinity. In reality, however, this is not the case. As far as we know, the speed of physical systems cannot reach infinity.
The singularity in robots exists because they are controlled by mathematics (which can reach infinity), but move real physical components (which cannot reach infinity). If the controller commands a joint of the robot to "rotate 180 degrees at an infinite angular velocity," the robot joint will "say": I can't do it!
What is the singularity of robotics?
A singularity arises from the inverse kinematics of a robot. When encountering a singularity, there are potentially an infinite number of ways to reach the same position on the robot. Without choosing an optimal solution, assuming there is one, the robot's joints might be commanded to move in an impossible manner. Infinite speeds are not the only type of singularity that causes problems; other types can be even more problematic. If a robot encounters such a singularity, it needs to be shut down, the robotic arm moved, and then manually restarted.
Singularity of 3 types of robots
There are three types of singularities in six-axis industrial robots, but these singularities can still cause serious damage.
The U.S. National Standard for Industrial Robots and Robotic Systems defines a singularity as "unpredictable robot motion and velocity caused by the collinear alignment of two or more robot axes." Therefore, the three types of singularities are defined according to which joint collinearity causes the problem:
1. Wrist joint singularity - This typically occurs when the axes of the robot's two wrist joints (joints 4 and 6) are aligned in a straight line. This can cause these joints to attempt to rotate 180 degrees instantaneously.
2. Shoulder joint singularity - This occurs when the wrist joint at the center of the robot aligns with the axis of joint 1. It causes joints 1 and 4 to attempt to rotate 180 degrees instantaneously. There is another scenario where the robot's first and last joints (joints 1 and 6) align.
3. Elbow singularity - This occurs when the wrist joint at the center of the robot is in the same plane as joints 2 and 3. An elbow singularity looks like the robot "reaches too far," causing the elbow joint to lock in a certain position.
Video link: http://v.youku.com/v_show/id_XMTQ4OTgwOTE0NA==.html
The video above demonstrates a simulation of these robotic singularities. In the video, when they are commanded to move at infinite speeds, the joints are displayed in red, making it very clear.
How to avoid the singularity?
Manufacturers typically program robots to avoid singularities to prevent damage. However, in the past, this simply meant that if a joint was commanded to move at an excessively high speed, the robot would stop completely with an error message. This was not a perfect solution.
Over the years, many robot manufacturers have been improving their singularity avoidance technology. In the video above, each joint of the robot is programmed to have a maximum speed limit. When the wrist joint is commanded to move at "infinite" speed, the software reduces this speed. When it reaches the middle of the line, the robot's speed decreases. Once it passes the singularity, the robot continues to complete the remaining movement at the correct speed. The line-drawing work is still disrupted, but the robot remains functional and doesn't get stuck.
How programmers can avoid singularities
Avoiding singularities has been a hot topic for years. The industry has proposed various solutions, some of which have already been applied to industrial robots. For example, the ETS Control and Robotics Lab cited an excellent academic article that explains the mathematics behind robot singularities and provides examples of their application in industrial robots.
The more axes a robot has, the greater the likelihood of a singularity occurring, because more axes will align with other axes. Of course, additional axes can reach the same point by repositioning, thus mitigating the effects of singularities. This article provides a good introduction to the control of redundant robotic arms and discusses how to handle singularities through programming.
How technicians can avoid singularities
Over the years, roboticists have devised various innovative methods to avoid singularities. Singularities occur when robots are connected in straight lines and/or when joints approach 0 degrees. Therefore, engineers use tools to add a small angle to reduce the chance of the robot entering a singularity.
This technique remains a good way to avoid singularities. Installing the spray gun at a very small angle (5-15 degrees) usually ensures that the robot completely avoids singularities. This isn't always the case, but it's an inexpensive solution and easy to implement.
Finally, another good approach is to move the task to a region without singularities. While it doesn't always work, it's very effective.
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