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Why Hasn’t Anyone Heard of Cuspidal Robots?

Our very own Achille Verheye recently authored a two-part article on the topic of cuspidal robots. “What are cuspidal robots,” you ask? We’re glad you asked...


A few years ago, I was using the light-weight Kinova MICO robot arm to clean bathrooms. The robot was programmed to follow a circular path to clean a sink but would suddenly start spinning around itself or leave the path and collide.

We began to spend more and more resources creating advanced motion planning capabilities to deal with these odd motions but eventually had to give up and switched to a different robot arm. Only later did I realize that I was likely dealing with a cuspidal manipulator.

The Kinova Mico had trouble executing simple motions without leaving the intended path, which could cause collisions. These movements are different from instabilities arising from passing through a singularity when using the Jacobian transpose.

The Class of Robots You Haven’t Heard Of

All robot arms have a number of singularities which are a set of joint angles at which the robot loses the ability to move in a certain direction. These singularities are avoided because they can cause dangerous instabilities and unexpected motions, which can for example ruin a sanding or deburring operation. The hand of a robot arm can also reach the same point in space (x, y, z) with different sets of joint angles, which we call postures or inverse kinematics (IK) solutions. Press your hand against a flat surface and you can still move your elbow around (different postures) while keeping your hand in the same position. (Note: your arm has at least 7 degrees of freedom (axes) and thus can have infinite IK solutions).

When the robot above switches from one IK solution to another (often called the elbow down and elbow up solutions), it must pass through a state in which it’s fully stretched out or folded in. In and around that state, it loses the ability to move in one direction, essentially losing a degree of freedom.

It’s widely believed by robot designers and engineers that a robot must always pass through such a singularity when moving from one IK solution to another. It turns out that’s not true for all robots: the so-called cuspidal robots allow avoiding such singular posture-changing moves.

This isn’t something they teach you in school — most of the people in academia I spoke with including professors were surprised to hear of this. As a result, several cuspidal robots exist and their designers don’t even know.

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