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Has the ROS community heard of cuspidal manipulators?

A few years ago I was struggling to make a 6DOF robot move along simple straight line paths. The robot couldn’t smoothly follow the path and had to make these ‘joint jumps’ which meant possible collisions, no matter how advanced the motion planning. It turns out we weren’t the only ones running into this, and the issue was with the kind of robot we got, not our motion planning. This kind of robot, the cuspidal manipulator, has the very cool ability to avoid singularities while moving from one posture (IK solution) to another, but also can’t make some motions.

As I tried understanding this better and asking around, I found that none of the people I talked to (roboticists, professors, robot designers) were familiar with the concept. I found an entire line of industrial robot arms that were canceled likely because of ‘weird behavior’ caused by being cuspidal, and a company going through the same struggles we were going through before. So I decided to dive in and explain this fairly unknown concept hopefully in a hopefully understandable way.

Very curious to hear if you’ve heard this before, if you might have run into this, or even if you know of more cuspidal robots in the wild!