The 1st attempt had a few problems.  It was noisy.  The motor stalled.  The string got stuck on the outside of the torturous path if it moved too fast.  A 24mm inner diameter spool was only big enough for 1m of string.  The string filled the center of the spool instead of spreading evenly.  The torturous path & the motor required a 55mm outer diameter gear.  The pinion gear eventually started slipping off the motor as the motor heated & melted the PLA.  If the string doesn't retract, the robot won't stop.  It has to retract if it's accidentally dropped.

Spool with torturous path.

Retractable leashes for pet animals have these problems solved, but they're too big to fit in the robot.

A conventional spool retracted the full 2 meters quite nicely.  2m is the longest it's going to be extended.  This motor is only a proof of concept.  A more robust brushless motor would come later. The mane problem is the string does tend to loosen & tangle when it's off.  Shorting the motor terminals doesn't provide much braking.  If it had a solenoid, it would be pretty complicated.

As the idea evolved, the smart leash could keep the robot behind the animal or beside the animal.  The difference is beside the animal, the joystick angle controls speed while the distance measurement controls steering.  It would be less accurate & there isn't enough room on the path, but it could be done.

Designs continued for the tangle proof spool & the joystick.  The tangle proof spool involved a torturous path for the string.  The joystick won't have a spring, but it'll freely follow the string.  It'll have a horn constraining horizontal movement but not vertical movement.  

An alternative design could have a 2 axis joystick.  The higher the vertical position, the slower it moves.  This could neglect the string length, but it must handle the case of the animal dropping the string.

Speed based on string length would drop to 0 if the animal dropped the string.  Speed based on string height would go to maximum.  It would be a dangerous situation.  The leading countermeasure is making an exception when the joystick is centered. In that case, stop moving.  

It's unclear if the vertical position could be sensed accurately enough.  The string isn't going to stay taught without the string retractor, so any kind of joystick needs the string retractor.