Robot Singularity (Not the Type You’re Thinking of)

Robotic singularity that's specified in ANSI RIA R15.06

Thanks to often-sensationalized discussions inspired at least science fiction, the idea of a robotic singularity is typically associated with the technological singularity. Basically, this concept predicts that, due to accelerated technological progress and advancements in artificial intelligence, a (in the words of Vernor Vinge) “greater-than-human intelligence” will imminently be created. At this point, knowledge will reach a runaway effect, infinitely surpassing the capabilities of human comprehension.

The term singularity derives from physics, in which it describes a conceptual phenomenon with black holes. In the center of a black hole, there exists a gravitational singularity, a one-dimensional point containing a huge mass within an infinitely small space. In the singularity, density and gravity become infinite and space-time curves infinitely. Essentially, the laws of physics cease to operate.

When this term is adapted to describe the transcendental progression of knowledge, it typically becomes associated with killer robots bent on overthrowing their humans overlords. With industrial robots, however, the type of robots that dominates 90 percent of the market, a singularity is defined by ANSI/RIA R15.06-2012: Industrial Robots And Robot Systems – Safety Requirements as an “occurrence whenever the rank of the Jacobian matrix becomes less than full rank.”

Interchangeably called robot, robotic, or kinematic singularities or degeneracies, this process, like black holes, deals with a point that goes to infinity. Since robots exist to complete precise, repetitive purposes, when a singularity occurs, the laborious machines appear to go crazy.

The following video demonstrates several types of singularities:

In simple terms, the basis for this phenomenon is that the movement of robots is mapped out in Cartesian space (along x, y, and z axes) but carried out in joint space. Therefore, it is crucial to fully understand the mapping from joint space to Cartesian space (and vice-versa). If you specify the Cartesian velocities of the robot, you can find the joint parameter velocities with the inverse Jacobian (please refer to this resource by Columbia University on kinematic singularities for equations). Whenever the determinant of the Jacobian is 0, meaning that it cannot be inverted, a singularity occurs. This is because the joint velocity in joint space becomes infinite.

In a black hole, where the laws of physics do not apply, infinity really isn’t that much of a problem. However, for a machine operating in a factory, infinity almost certainly is an issue, as it isn’t attainable. When placed at a singularity, there can be an infinite number of ways for the kinematics of a robot to accomplish the same tip position. If the correct solution isn’t chosen, the robot could be commanded to move in an impossible way and may be forced to be turned off, moved, or manually restarted.

ANSI/RIA R15.06-2012 approaches singularity protection from the perspective of adequately guiding the robot. Since these high-axis speeds can be unexpected to an operator, the American National Standard calls for the robot control, in manual reduced-speed mode or hand guiding, to stop robot motion and provide a warning prior to the robot passing through or correcting for a singularity during coordinated motion and to generate an audible or visible warning signal while at a set velocity. The standard also notes that, in the case that the singularity can be controlled without creating hazardous motion, there is no need for additional protection.

If you’d like to learn more about industrial robots and their safety specifications, please refer to our post on industrial robots. You can also get ANSI/RIA R15.06-2012: Industrial Robots And Robot Systems – Safety Requirements from the ANSI Webstore.

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