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MoveIt currently does not provide a method to request specific end-effector velocities.

We would welcome such an addition and it is clearly feasible. You can generate a valid time-parameterization for your cartesian trajectory using the moveit_core/trajectory_processing module. These methods generate velocities according to the maxima specified for each joint. If you want to attain a constant end-effector velocity you can rescale the timing relative to the slowest segment.