# Reference request: Path accuracy algorithm in the joint angle space

I am currently reviewing a path accuracy algorithm. The measured data are points in the 7 dimensional joint space (the robot under test is a 7 axes Robot, but this is not of importance for the question). As far as I know path accuracy is measured and assessed in configuration (3 D) space. Therefore I am wondering if a path accuracy definition in joint angle space has any practical value. Sure, if one looks at the joint angle space as a 7 dimensional vector space in the example (with Euclidean distance measure) one can do formally the math. But this seems very odd to me. For instance, an angle discrepancy between measured and expected for the lowest axis is of much more significance than a discrepancy for the axis near the actuator end effector.

So here is my Question: Can anyone point me to references where path accuracy in joint space and/or algorithms for its calculation is discussed ?

(I am not quite sure what tags to use. Sorry if I misused some.)

• I'm sorry, but I'm voting to close this question because, "Life Questions are off-topic. Questions about choosing how to spend your time (what book to read, which class to take, what robotics project to construct, what career to pursue, etc.) may be about difficult decisions, and they are often important, but they are too specific to your own situation and are unlikely to help future visitors to the site. They would be better off asked in Robotics Chat."
– Chuck
Feb 4, 2016 at 20:16
• I think this is an interesting question, and should perhaps be reworded to something like: "how do you measure path following accuracy on a 7 DOF robot arm".
– Ben
Feb 4, 2016 at 21:27
• @Johannes It can be useful to look at paths in joint space (where motor saturation and joint limits are easy to visualize). It might be useful to use some aggregate of actuator (ie joint space) error to change control algorithms in real time at the motor controllers which often have processing constraints. Feb 4, 2016 at 22:22
• @Johannes Don't forget that if you accept a poorly argued and written paper you are just condemning the rest of us to waste time looking at it. It's always good to help people with language and terminology if that's the only issue. Otherwise, if it does not make sense, just reject it. Feb 4, 2016 at 22:30
• @Chuck As the Header says, this is a reference request. Feb 5, 2016 at 12:40

The forward kinematics of the manipulator will correctly identify the larger displacements of the end effector for small rotations of the proximal joints, as opposed to the smaller displacements of the end effector for small rotations of the distal joints. When these motions are due to errors - all real mechanical systems have them - the established process for relating joint errors to task-space errors involves analytical perturbation analysis, and/or physical calibration of the system.

A good starting point would be Siciliano and Khatib, Handbook of Robotics. Check out the end of Chapter 14 (they only hit upon the topic but the references will certainly help). You can also look at the papers which describe 3D sensors for robot calibration. Those papers frequently derive the perturbation analysis, then show how the new sensor allowed the end effector errors to be reduced after calibration. I recommend many of the editions of Lenarcic's Advances in Robot Kinematics. The 2000 edition with Stanisic has a paper by Khalil et al regarding calibration techniques. Or a web search will find many such papers, e.g.,

http://www.columbia.edu/~yly1/PDFs2/wu%20recursive.pdf