Is it legal to motorize the robot cart to avoid the long distance traveling at worlds?
Check out the event rules, section 6 on robot carts: https://www.firstinspires.org/sites/default/files/uploads/frc/EventRulesManual.pdf
When talking about a motorized cart, E601 is certainly a concern in the design and operation of the cart (it can be done, but you have to think through it!), and make sure the size is appropriate per E602.
I am by no means a rules expert here but:
Teams have done something at least similar in the past (I can’t remember the team name but I recall years ago seeing one with an Egyptian theme having a whole chariot robot cart that the driver actually rode on with the robot) However any motorized carts I have seen have not at any point exceeded walking speed.
I think you would get some grief or at least added hassle of additional inspection/review. I would suggest you strongly consider if this is something you want to spend time dealing with at worlds (or anywhere else you use such a cart)
You likely would encounter less issue if the cart is “assist only” in other words, someone must actively be pushing/pulling the cart to activate the motor and it only assists proportional to the human effort input (truthfully pretty easy to do with a strain gauge integrated into the handle)
You will still have to walk the distance, you most certainly cannot bring in a platform large enough for your whole drive team plus robot to ride from the pits to the field.
You would have to have batteries/chargers dedicated to your cart.
Robot carts often have to negotiate cable covers, door jambs, concrete joints, and other bumps that a motor may help with, or may make more difficult/dangerous as it tries to force its way over instead of carefully lifting over or whatever you may need to do otherwise.
Again, I am no rules expert, but I remember considering building something like this in the past and determining while cool, it would not be worth the added hassle.
All that said, it could be a fun engineering challenge and if you do it please do post it so we can oohhh and aahhh.
4564 Orange Chaos has a motorized cart that I believe is built on the base of a motorized wheel chair. Image stolen from their facebook page.
I would advise against it, at least as far as powered drive wheels. There are a number of teams (2767 included) that have motorized lifts on their carts to raise/lower the robot for any maintenance. Useful on occasion. That may be a better use of your time and invite less scrutiny.
Team 696 has a scissor lift motorized cart that I think is really cool. The only downside to the cart was you couldn’t push it unless you used the motors.