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Is necessary openCR for a three omni-wheel robot
No
I want to ask if it's worth it to program the robot without openCR for things like odometry, movement, imu, etc?
This depends on how you define "worth it".
I'm assuming, you mean this with openCR. There are many robots out there that don't use this module. Thus, my answers above.
If you have more specific questions or concerns, please elaborate.