I have personally talked with Randall Monroe about this.
The question you ask is a bit hard to answer because you have to ask what "based off of" actually means.
Was XKCD the first to introduce to the world the concept of a robot? Obviously not.
Was XKCD the first to introduce to the world the concept of a robot in a ball? No
Was XKCD the first to introduce to the world the concept of a robot in a ball using omniwheels? I would argue yes. Randall has also told me yes.
Here are the facts:
- Disney's omniwheel patent was filed in 2010
- Randall's comic was released April 21, 2008
- Most importantly: Dirk Ruiken who is on the patent has on his personal website that he started working on a "Confidential: Disney Balancing Character" during the summer of 2008!
The summer of 2008 is when the patent holder first started working on BB8! This is only several months after Randall's comic was published. Do you think the comic may have had some part in the design?
When I asked Randall about his design he mentioned two key items to me
- He did come up the omni-wheel design on his own and he does not feel like doing anything about the Disney patent despite his comic being prior art because Disney is not making him take down his comic
- He mentioned that his design actually uses 3 omni-wheels instead of 4 because it is impossible for 3 points to wobble unlike 4 points. He said it was easier to draw 4 wheels which is why he did it.
As is the case with many inventions I believe everyone borrowed from each other. Although, the fact that the Disney's patent holder started work on BB8 after the comic was published, I am going to guess that BB8's engineers looked at the comic and it influenced the design.
I hope this best answers the question.