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I am using a 6 DOF UR5 robotic arm. I am successfully sending it commands in the [X,Y,Z,RX,RY,RZ] format. When I read back these coordinates, I find that the X, Y, Z values are the same but the RX, RY, and RZ values are not. When I type the read values into my pendant, the preview shows that the orientation actually is what I want but I can not figure out how these RX, RY, RZ values can possibly be equivalent to each other. How can [X, Y, Z, -2.871, 0.539, -0.714] be equivalent to [X, Y, Z, 3.128, -0.587, 0.778]?

This picture from the pendant shows the rotated axes are the same: (original image)

enter image description here

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They are written in the angle-axis representation. In the angle axis representation, the direction of the 3d vector gives the axis of rotation (rotates counter clockwise around it). These two rotations are equivalent because the axes are the same but one is flipped (if you notice, one vector is approx -1.08 times the other). And because the axis is flipped and the rotation is no longer counterclockwise with respect to the original axis, the equivalent rotation is $2\pi - \theta$ radians compared to the $\theta$ of the other. So if you flip the axis, and adjust the magnitude appropriately, you can get the same rotation.

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  • $\begingroup$ Thanks, I'm going to try to work out the math to fully understand what you mean. $\endgroup$
    – Bobby
    Apr 10, 2023 at 17:51

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