I don't know anything about this industry but honestly the plan itself sounds inherently very sellable to your boss. You've already articulated it in a way that sounds like it's a totally logical choice.
The thing that I think could make this stronger is to make it more concrete.
Two thing I can think of here. One, do the research yourself of what exactly training you would need, how long it would take, what places you could get this from (ie what University classes etc), what outside help you would need, etc. That's the big part of your plan that sounds really fuzzy. "Software school or equivalent for programming" - software is a huge field, most "coding schools" or "boot camps" or whatever are focused on making you a web developer, not robotics. So maybe you could figure out the path that would make the most sense for robotics specifically.
Then two, (I think this part is maybe actually more important) do what you can do on your own with minimal investment: join a local robotics club, start reading up on robotics theory and practice with library books or a few cheaper choices from Amazon, learn everything you can currently from the current robotics guy, etc.
These actions will show you are talking the initiative and give the sense that you can be trusted to be interested in this new area before he has to invest a bunch of money into your training or doing a new hire or whatever. Be prepared to discuss all of that in concrete terms when you pitch it to your boss.
That doesn't mean you have to wait to bring it up, you can mention it to your boss, tell him the actions you intend to take (research necessary training to see if it would make sense, try to gain basic knowledge etc,). Then you report back every time you have progressed farther on your path: "hey boss, just sending you this email to let you know after talking with Current Robotics Guy and doing my own research I think I'd need classes in these areas BLAH BLAH BLAH. I can get that training from the following 3 sources Blah blah blah"
"Hey I talked with Robotics professor at Local College and found out blah blah blah"
"Hey, I wrote a basic program in whatever language the industry uses for robotics programming, see, it turns the light on whenever the sensor is obscured. This isn't so hard for a highly trained and intelligent engineer like me"
Stuff like that. As you follow through with your promise, it will hopefully give the impression that your proposal is basically inevitable and that your boss doesn't have to do any thinking whatsoever to make it happen. Besides, if your plan fails and your boss doesn't go for it, or starts going for it then disappoints you by cutting you out and hiring someone new with more experience, you will have still learned some valuable skills and increased your human capital. You can't lose!