Well... Please read the posts more than once if needed!
I did not comment on whether it would work or not, I just pointed out that, contrary to your claims, there's not a single logic gate involved in your circuit.
But since you wanna discuss its functionality, here's a couple of hints to enhance your circuit:
1) Use white light. IR doesn't always work, as some material that look black to you may be white to IR and v.v. White light gives the response your eyes expect.
2) Using L293D with a 5V motor voltage is a really bad design choice, as the motors are limited to around 2.4V tops at 600mA (=1.44W), which limits your choice of motors (and the speed and torque of same) extremely much as well.
The design that I posted (for a reference to a circuit that is made with logic gates) is actually very easy to build, as I usually post PCB layouts for my circuits as well (the jumpers should have given you a clue towards that) and I don't see how a 40106 and a 4093 using power drlingtons should be more difficult to plug into a PCB - it's cheaper as well, but some of what you see as complex might be that I've included a ouple of current limited LED circuits.
The fact that you obviously don't know the difference between logic gates and your mash up of a driver chip, an op-amp and a voltage regulator, gives me the idea that you probably didn't design it yourself, but rather nicked it somewhere on the net?