[JCharlton]

The 'Ultimate Encylopedia of Knots and Ropework' warns that Figure of Eight and Stevedore knots can both pull through a hole similar in diameter to that of the rope. With the large opening in the Davit, while they may be satisfactory for pulling your robot, may fail with smaller ropes. Figure Eight knots can also travel down a rope.

Suggested instead is the Ashley stopper knot, but if your rope is significantly smaller than the opening in the davit you may need a Monkey Fist to make a large enough ball.

If you're planning to use webbing or Velcro, well, that's a tricky one...

As for joining two similar sized ropes, it's difficult to define a 'best' knot as it depends on the rope material and use case. Many knots may snag or fail under particular or peculiar circumstances. For modern synthetic rope a Simple Simon Double would be worth a look, but I don't know if they'd be recommended for Dyneema or Vectran for example.