Ether,
It sounds like you're running a setup very similar to ours. I can't say we've "mastered" fine motor control with our mecanum wheels, but I'm happy to answer any questions you have. Here's a video of our practice robot, showing what we can/can't do:
http://www.youtube.com/watch?v=apcy5naz5TE
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Are you using 8" AndyMark mecanums?
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Yes.
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Are the wheels direct-driven, or chain-driven? If chain, what are the sprocket teeth counts?
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They are chain-driven. 19 tooth on the ToughBox output shaft, kit supplied 22 tooth on the Mecanum wheel hubs.
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Are you using the KoP AndyMark 12.75:1 toughbox? If not, what is your gear ratio?
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Yes we are using the KoP AndyMark ToughBoxes, unmodified.
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Are you using Victor or Jag motor controllers?
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We are using Jaguar motor controllers, using PWM control.
Our setup also uses the US Digital optical encoders, and the WPILib PIDController object. We are using closed loop I-only motor control, and we cube our joystick inputs before sending them to our control loop.
We also implemented a "slow-down" button, which scales both our translational and angular velocities to about 1/3 of max when held down. You can see it used in the video just prior to when our robot meets the ball - the robot seems to abruptly slow down.