Our team did a 4 wheel driven with “conventional” wheels (not omni, mechanum, or swerve) two years ago and… It didn’t work. We used the smooth ones from Lunar Lunacy on the front, and the event I drove (post season, I joined late) I ended up having to go backwards and swing the robot to the left (there was too much weight on the right side!) in increments to get it going the direction I wanted. It was not fun.
Now, if you can’t buy omni wheels (either the more expensive omni wheels or two pairs to mount interlaced), which are probably the best solution, I can understand. Our team is so poor we’re running out of nuts and bolts! In this case, I would highly suggest you switch to a two-wheel driven design, where the front is powered. The rear wheels should be slick, such as the Lunar Lunacy wheels; if you don’t have access to those, I’m sure a local team might have some for you to use, or you could try ripping the treads/rubber off of some other wheels (not sure how they’re bonded, though, might not work).
Another option is casters. I’ve heard them being trash talked on CD a bit, but if you trail them, the wiggle from direction change will be nonexistent and only show up when reversing (to remedy, use smaller wheels). This might not be as cheap as the slick wheels.
Of these options, our team is currently on the first alternative, using lunar lunacy wheels. They will be in the rear, with the front having this year’s treaded wheels being driven. We were also making sure to put most of our weight over them (this could also help while balancing three robots, we imagined). Based from my terrible experience with our past robot, this will work much better than having them in the front… We were eventually wanting to switch to casters, but we don’t have a way to make them.
If you wish to drive four wheels, and end up using the slick wheels on one side, I would highly trying to drive them at full tilt to break traction during a turn – I never got a chance to try this, but I think it would have worked on that one terrible robot we had (I just never had time to implement it, long story).