Using 4 (all driven or 2WD) traction wheels in a non-square configuration will cause the robot to skip around while turning, due to the fact that either the front or the back wheels can’t slide on the carpet.
That is correct, using 4 tractions wheels in a narrow (28"x38") robot. The traction is to great for the robot to counter and thus the robot will skip as you turn it.
Using 2 traction wheels and 2 omniwheels (all driven or 2WD) in a non-square configuration will turn freely, as the omnis can swing.
If you have the omni wheels on the same side (like traction in front, omni in rear) the side with the omni wheels will freely turn. This allows the robot to turn easily, but also get pushed easily from the side.
Using 4 driven traction wheels in a square configuration will allow free turning?
This is making the robot chassis in a 38x28 format. It is the same as above, if you are using four traction wheels you will be skipping around the field, but less then the narrow setup. This allows you turn a little bit easier then the narrow 4wd traction setup.
Using 6 wheel drive somehow magically works?
Using 6 wheel drive with the center wheel lowered basically turns the robot into 4wd when turning. When turning the weight of the robot will make it pivot on the center wheel, which will raise up the other two wheels in the system. The distance between the wheels when turning goes from the full length of the frame to half, thus the reason for quick manuverable turns for 6wd robots.
**Using non-square traction tank treads somehow works **
Tank tracks provide a lot of traction, they are great for not beaing pushed from side to side. The big downfall is turning, some teams would add a bogey wheel in the middle of the track and lower it like a 6wd system. Other teams like my first year robot, we added a bogey 5th wheel that raised the front half of our tracks and let us turn easily in high gear.
Hope this helps.