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Which kind of trajectory would one use for a fine precision robot?

I know trapezoidal and cubic trajectories, but errors get very high when stopping at every configuration and when speeding up to the highest possible velocity.

How is this done in practise especially when not much deviation from a straight path is wanted?

In my case I try to get the end-effector to go a straight line with a three joint rotational robot.

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For very high-precision applications such as finishing, milling by CNC machines, jerk-bounded trajectories (that is, trajectories comprising polynomials of degree 3 of higher) are often used. If you search on Google Scholar using the term "jerk bounded", you can find loads of methods to plan such trajectories.

High-order polynomial trajectories (or splines) are not always necessary, however. For stiff articulated manipulators (such as position-controlled robots), they are usually stiff enough that using second-order (parabolic) polynomial trajectories is perfectly fine. The effect of (theoretically) unbounded-jerk is often negligible.


In your case, you mentioned that the errors got high when stopping and speeding up. I suspect that this might not come from the trajectory generation method you used.

If the robot you are using is custom-built, you might want to

  • Do kinematics calibration to make sure that the locations of joints and the tool are actually where you think they are; and

  • Check how well the motors can track your input commands.

Otherwise, you may check if this issue is related in any way to singularities.

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