Totally doable (of course, since there are $10k systems out there). Think in the terms of an Unmaned Aerial (Or Ground) Vehicle:
$200 bucks off the rack (Atmega2560), 6 axis monitoring of your sprayer tank, $40 bucks for the (2) Ultrasonic sensors for the booms, the only question is the current requirements for the solenoids (for the motor cotrollers). High current electronic speed controllers?
Anyhow, a study on the PIDs for the Arduino will keep the sprayer from being the next mechanical bull attraction. You might have a couple weeks without dirty hands putting this together 