As you know, There ALREADY is a hand cart that WILL FOLLOW THE GOLFER ALL OVER THE COURSE BY ITSELF. Don't remember the name of it, but I've seen a video of it following the golfer all over the course. It is designed to STOP when it gets inside a certain distance of the golfer, and the golfer CAN shut it off by the remote control, for around the greens or tee box.
I really doubt you can make your cart with a battery powerful enough to last 18 holes PLUS, and have the total cart weight only 20 pounds. You need a decent size electric motor to power it up and down hills. That alone will add enough weight to a regular 3 wheel hand cart to get it up to over 20 pounds. I just weighed my 3 wheel push cart and it weighs 19 pounds. It's made of light weight aluminum tubing. So unless you plan to make your cart out of some kind of plastic, I don't see you being able to make your cart weigh less than my cart. And then you have to add in the motor and battery. Not going to happen in my opinion.
The cart I mentioed also had the ability to navigate AROUND objects on the course, like other golfer or trees. Something you have not mentioned. Don't know the name of this cart, but I do know it was not a BAT cart I saw a video on.
PRICE? I don't know about any one else, but I would never think of paying $1000 for an electic golf cart. Not when I can buy a hand cart for less than $20 on sale. Or buy a better 3 whell push cart for under $100 just about anywhere I look.

NEW VENTURE? You state that your group was given an assignment to create a NEW venture. But what you are doing is nothing more than COPYING what has already been built and sold in the market place.

Stroke Counter? Are you serious? I don't know of ANY decent golfer that needs a stroke counter. And I don't know of any golfer that would be will to spend $1000 for a cart that would want or need a stroke counter. The only stroke counter a decent golfer NEEDS is a pencil, a score card, and the brains to count and write. Sorry, but this just isn't worth anything to a half way decent golfer.

Four wheel drive? Great idea. Would make the cart able to go up hills a two wheel drive cart couldn't. But for 4 wheel drive you NEED the ability to have the right wheels spin at a different rate than the left wheels. And yoo need the front or reat wheels to be able to rotate so as to STEER the cart right and left. All this will ADD more weight to your 20 pound cart.
Bottom line is I don't believe you can Build it. I don't know anyone that would Buy it for $1000, And it's ALREADY ON THE MARKET. Sorry, you just failed your assignment.