My team’s robot has this issue where when having more than 7 cubes in the tray, it just gives up and tilts completely backward. Although we have an anti-tip, because of it bending our bot is basically immobile. The wheels get lifted up and we are unable to do anything.
How do we keep a solid center of mass so that the bot is actually usable?
Having a steeper tray angle will help. Some other things you could do is put your cortex and battery towards the front of your robot
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You can also add counterweights to the front of your robot.
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The issue is that our bot will then proceed to tip forward.
We can’t have a steeper tray angle or we would be out of 18x18x18
Would it tip forward when placing the cubes?
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Maybe you can have a counterweight that moves?
We don’t have space to incorporate that in our bot
Are you using aluminum for your base?
You might want to make your base heavier bc then the center of mass would vary less.
Make your anti tips more rigid. and make sure that they contact the ground at all times.
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Lower your cubes to floor tiles first, then lean forward without intake motors in hold or break mode. At that point why would your robot tilt forward? Make sure your counter weights are behind front wheels…
Unless I am misunderstanding, counter weights should work well.
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You could have a stopper (for your tilter) that flips out when your robot deploys during the autonomous period. That way, you can keep in size before the match and still have a steeper tray angle. A simple c channel on a hinge will do the trick
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Try to move your brain and battery to the front of the bot too. Preferably under the tray
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Ok. You have two possible solutions. You can make you anti tips more rigid. And also make sure they touch the ground so you stay up right. And something that helps. Is to move all your weight to the front. Like the brain and battery. (Try to get it far up as possible.) 
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Make the anti tips out of steel