Hypothetically, if you put a chair (of the plastic lawn chair variety probably) on a drivetrain, what would you need to do to keep it safe to ride on? This is entirely in theory, I have no intention of actually building it.
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Have it never move and bolt it to the ground
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No.
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A couple million in engineers, and a couple 10’s of millions in budget.
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Yes.
But putting a person in that chair? No.
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Sweet Jesus! Will someone actually sell a million dollar insurance policy to high school students for a scratch built robot to ride on?
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Entirely in theory? I’ve heard that one before.
When you go to college, find the Formula SAE or Baja SAE teams. You might fit right in.
As far as keeping a robot drivetrain safe to ride on–START with the previously-mentioned teams and their specification documents for driver securement. No plastic lawn chairs allowed, do it right the first time because if something goes wrong it’s on YOU. And include full vehicular PPE for the rider.
As a case in point, I do believe that Quals 89 - Los Angeles Regional sponsored by The Roddenberry Foundation 2014 - The Blue Alliance will be VERY informative. Specifically the video, look upper right.
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Hypothetically, make sure the chair is well secured, the robot is limited to a very low speed (preferably mechanically), and the person on the robot is the person driving the robot, and I think you could let a child ride it.
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You’d also probably want the chair to be lower than a regular chair. We’ve built trailers with stools to tow people into a pep rally. You definitely want it going a lot slower than robot speed.
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New kitbot? The swerve modules can bolt directly onto the feet of the chair
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While you’re essentially asking “How can I make a safe robotic wheelchair that won’t require me to need a wheelchair after riding it?”
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Don’t do this
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Research existing solutions. Yes electric wheelchairs exist but that’s not what OP is after. Really something more like this: FurniBOT Electric Smart Chair – ZiiROBOT Mobility
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From a safety perspective an FRC drivetrain is not a great thing to be positioned over top of. If you slipped off the chair you are likely to get caught in a KOP belt system really easily. Most FRC bots have exposed gears, sprockets, etc that you would get snagged on if there was a sudden stop needed.
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FRC robot safety is safety theater at worst, and not true OSHA/ANSI level safe at best. For robots that will carry a payload (not even a live payload mind you) speeds of an AGV (Autonomous Guided Vehicle) in an area with humans is limited to 1.2 m/s (way slower than FRC capable speeds) per ANSI. Riding on the robot is turning it into something more akin to a Tugger or Forkjack. These has safety switches and multiple estops on all sides of the vehicle. Either safety mats or a weight sensor on the chair/ground to make sure the operator is fully seated correctly. The vehicle would come to an Estop otherwise. An Estop is not just cutting motor power. This also means engaging a physical brake system like an Electro magnetic solenoid that when powered removes a metal rod from a slot the wheel hub to let the wheel move. When power is cut in any scenario the EM turns off and the rod slams back into place. You would also have safety distance sensors if it was operating autonomously with someone on it. If it is always under manual control then you need a safety shutoff if the controller gets disconnected. The FRC driver station will force a software estop to a roboRio. This is not good enough if you are on the robot yourself. You need a physically wired joystick with a way to ensure motor power will be cut if it is disconnected or not responsive.
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I recall a group of students doing this several years ago, and trying to talk me into sitting in the chair as soon as I arrived at the build site after work. During what was supposed to be a study period, where they should have been doing homework while waiting for mentors to get there, they had instead been using a smallish freshman as ballast to test the drivetrain, and wanted to step up to overload conditions. Fortunately, the head teacher showed up in time to put an end to the foolishness before someone got hurt.
/edit: back to the original question:
Theoretically safe? Heck no!
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Hypothetically, if you were to do something like this (not speaking from any personal experience here) you would definitely want to avoid using big flight sticks like many teams use for tank drives, because it would (hypothetically) be very hard to hold the sticks steady when the (hypothetical) robot accelerates and decelerates.
One may also want to include a footrest so the (imaginary) driver is able to rest their feet and use it to brace themselves.
you could (hypothetically) build a chair out of some scrap plywood, maybe even include a cup holder for maximum luxury.
It would hypothetically also be important to consider how securely the driver station laptop is mounted so it doesn’t get sent flying on fast turns (especially if using an arcade drive style control scheme)
All hypothetical though of course 
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Adding onto this, make sure the driver is the one holding the controller and not a second party. In fact, using an RC controller instead of an FRC driver station can in some ways be more convenient and safer than relying on a DS laptop at all. The slower the better, if someone were to make this, however ill-advised.
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Don’t ever do this lol.
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You will need a different chair, lawn chairs aren’t gonna cut it. You will need something sturdy and it needs to be well secured. There needs to be a seat-belt system in place. However, the best solution is to screw the drivers foot onto the drivetrain itself, such that regardless of speed, the driver cannot physically ever get off the robot. Even if they wanted to.
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The robot must be limited to a slow speed, the driver should be wearing a helmet, gloves, and IRL minecraft diamond armor (preferably enchanted), 3 golden apples, and a totem (for revive in case of death)
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(somehow) cover up the top of the drivetrain, there is a bunch of sensitive and dangerous stuff on the drivetrain such as belt systems. Putting a metal sheet over the top provides a floor for the drivers legs to rest safely. If possible, it is best for the driver to levitate above the robot, such that the drivers cannot even touch the robot.
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In case the driver ran out of minecraft totems, have a Fortnite reboot van nearby, so you can pick up their reboot card and revive them.
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Flame decal. (Self-explanatory)
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bajillion dollar life insurance policy and Saul Goodman as your lawyer.
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Plane ticket to Columbia to escape authorities if number 6. doesn’t work
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We did this nine years ago. The chair was a La-Z-Boy, the robot was fully enclosed in 3/4" plywood. We used mecanums with a very slow gear ratio and set to a low power percentage. The controller was in the hands of the rider. If I were to do it again today I would add wheel covers and bumpers.
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Obligatory Don’t Try This
I tried it when one of those hard plastic school chairs broke and the seat became separated from its metal frame. It was promptly zip-tied to a swerve drive base we had lying around. Was extremely jerky due to the standard robot acceleration/deceleration parameters still being used. Humans don’t like the g-forces as well as the robots do, so you had to have a very light touch on the sticks.
Things went pretty well until I got a little carried away with the donuts and the zip-ties snapped, causing the chair to tip backward and nearly crush the RoboRIO. Thankfully it didn’t.
Also note that we did at least try to be safe about it. Someone volunteered their belt, which I strapped around myself and the chair, to keep me from flying off the thing. Anyway this is the moment the zip-ties snapped and we put this idea to rest:
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The other half that I haven’t seen anyone ask yet, but since we’re talking safety… what defines this threshold “safe”?
Is it less that 1 injury per hour of operation? 1 injury per 1000 hours of operation? Are all injuries the same?
From there, think through failures. Uncontrolled motion, bolts shearing or falling out, battery fire, etc. etc. etc. - Judge their probability against the safety criteria.
The “is it safe” conversation boils down to “is the probability of dangerous failure higher than an acceptable threshold?”. IE - risk vs. reward tradeoff.
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Hypothetically, a good way to hold your driver station could be some 2x4s sticking out the back (forklift style) and use a bungee cord to hold your driver station on the forks so it doesn’t fly off like you said. (of course this is all hypothetical like you said, just spitting out ideas)
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