The video mentioned $12,000 in sunk costs and a projected parts cost in volume of $1400 per unit which is indeed substantial amounts of money, it was considered excessive when I spent $1000 on parts for my Thesis project so this steps it up another order of magnitude.
My thesis project (2D pong playing robot - linear bearing rail, paddle on a motorized timing belt, 87 fps uEye USB 2.0 camera above the table and computer vision algorithm running on the PC, sending commands to the NXP LPC23xx based PID motor controller) was also around $1000 and it was considered expensive, that's why I'm so shocked a student can afford to spend $12k. But I did my project in 2008 and it was in Poland, so quite different circumstances.
I worked 3 jobs to pay for the project (not all simultaneously, only 2 at a time), was also studying full time.
Chapeau bas!
This is serious commitment.
Motion control is great fun, did you ever make real world measurements of your system? I worked for most of a year on precision positioning for some scientific applications and when we actually measured the results the trapezoidal profile was as far as we needed to go, anything more complicated added no further accuracy or speed.
Not really, just messing around. Couple of years ago I bought CNC-3020T, wired STM32F4 to the original controller (LPT based) and wrote various bits of code, motion control, fancy C++ g-code parser. I've implemented this first:
http://staff.bath.ac.uk/ensmns/Publications/pc074.pdf (it has a downside - profile has to be symmetrical), then something inspired by TinyG code, but in the end I wanted the machine working, not just occupying desk space, so I dropped STM32 and my C++ experiments and wired Beagle Bone Black with LinuxCNC (MachineKit) and got the machine running in no time.
From my brief experience trapezoidal profiles seem to be perfectly fine for heavier, damped machines, based on leadscrews etc - such as my Chinese CNC. Maybe for 3D printers with very lightweight extruders and timing belts S-curves make much more sense as they limit the jerk. You have to admit that this TinyG demo video is quite impressive:
Another thing that bothers me in 3D printers and cheap CNCs is the lack of feedback loops. A while ago I bought AS5311 linear magnetic encoder and 300 mm magnetic adhesive strip from Austria Microsystems when I find some spare time I want to experiment with that.