Skycam’s design allows for some intricate movements, and because the reels of cable from each tower can be controlled with stepper motors precision should be fairly possible. the system should be re-calibrated by pulling the unit tight between two towers (outside edge of the field), and then allowing one to loosen, while tightening a third, while pulling the slack into the adjacent edge. By measuring the amount of cable reeled in from the third tower you could calibrate each tower. this allows x and y movements. to travel downward on the z axis, simply remove tension from all units at the same amount.
As far as solving the push allowed for the planter and weeding tool, that force could be replaced by allowing gravity. if you meter our the cable by related amounts from each unit (not the same, but proportional based on the location in the field) quickly enough, then gravity’s force should allow you to get deep enough to plant or weed.
Below i have added a few links that might be helpful in this topic. The idea i have would be for farmbot that can work over a much larger area (such as an entire yard) and plant specific beds, while leaving other zones alone, such as common areas. This makes the unit much more usable, and allows the yields to be much higher. In addition, potentially looking at battery power, a water tank and on-board vacuum with a docking station to automatically refuel power and water could allow the simplification of wire management.
Skycam patent: https://patents.google.com/patent/US6873355
Mathematics of a gravity pile driver: https://books.google.com/books?id=x0J9BgAAQBAJ&pg=PA240&lpg=PA240&dq=gravity+driving+fence+posts&source=bl&ots=1HzHv697h5&sig=p04rxk1EPnSo0nVYYNUh8Bx0bbw&hl=en&sa=X&ved=2ahUKEwiavJeTtLPeAhUHzIMKHT09D3cQ6AEwF3oECAkQAQ#v=onepage&q=gravity%20driving%20fence%20posts&f=false
Explanation of trilateration (location within an xyz space using fixed points of reference): https://en.wikipedia.org/wiki/Trilateration
Example of the technique used to draw a picture in a smaller scale, This system includes software for the motor systems as well, and seems to be quite precise (albeit on a small scale): https://www.marginallyclever.com/product/robo-0048-zarplotter-table-top-drawing-robot/