The ball-catching example is interesting, as it's another control problem, and has been studied as such. The fielder must get to where the ball will land. The predictive method would be to look at the ball, estimate its trajectory, then go to where you predict it will come down. This will not be very effective, because you cannot estimate the trajectory well enough. Instead, one method that will work is to move so as to maintain the direction from yourself to the ball constant in both azimuth and elevation. This is a control task, akin to the cursor-tracking task I discussed in the posting. You just have to move faster or slower and vary your direction, in whatever way will keep the direction constant. (The reason this works is that if the direction is constant, the ball is moving directly towards you in the frame of reference that moves with you. Or directly away, but in that case you won't be able to run fast enough to catch it.)

Devise such a control model, put in some parameters, add the physics of flying balls, solve the differential equations, and compare the results to the performance of actual fielders, and you have explained it in terms of physics.

How would Jeffreyssai analyse a PID loop?