As long as the robot is not moving....
True. The faster the robot/person moves the less accurate will be the read position. However far the robot moves in 300ms will be the inaccuracy. Through trial and error the delay period can be decreased thereby increasing the accuracy. Again, without knowing the details of the intended application we cannot know whether this inaccuracy is acceptable.
No. The flash of light would reach the corners in a fraction of a microsecond, unless a corner is over 300m away.
I covered this in Reply #18 when I said "...very minor difference (we are talking about the speed of light over a few metres) in the time...".
At that point there would be a very small known delay for the sensors/brain to process an interrupt and ready for the ping.
Thats what I was referring to when I wrote "..the latency involved in the process of sending and receiving the infrared.." The operative word here being "process". It covers everything from executing the code to turn on the infrared through propagation of the light waves to the receiver, to processing of the received signal by the micro at the other end.
The ping sent by one source, the corners only need to know the relative time post-known-delay to be able to calculate position.
I'm not clear on what you mean here. Are you changing the paradigm to a scenario where the ping is sent from the robot/person and is received by the corner units?
I'd use relative time because speed of sound changes with temperature and to a lesser extent, humidity.
Fast air flow in the room could fuzz that a bit but fast would be percent relative to speed of sound.
I think over a distance of 10 metres in an indoor environment, this will not be an issue. I made an ultrasonic dam level control (using a Maxbotix sensor) for a farm that this year has had temperatures between 42° C to -9° C and on occassions, thick fog (i.e. 100 humidity). The water level range was 8 metres. An external data logger used to verify its operation indicated that it was within 2 cm of true reading despite the wide range of environmental conditions.
I think the OP needs to specify his desired level of accuracy. If he/she wants it down to 0.5mm then he/she can spend a few thousand dollars on an autotracking Total Station. Compact, easy to setup (easier than laying down a wire grid on the floor that would require kilometres or wire for the area in question) and highly accurate but as usual, the cost/benefit trade-off.