Escape from the storage maze, part 2

Question

A former colleague and a friend of his have gotten themselves lost in a storage room in some abandoned building, so having nothing better to do you head out to try and rescue them. As you reach the storage room in question, you notice a small map scribbled on the wall, which looks like this:

Unfortunately, it seems the two of them didn't see the map, as they can only tell you that they're sitting at two different T-junctions

Your niece's boyfriend suggested throwing pumpkins at them to get their location, but you have a much saner plan: You will call out to the two lost ones and tell them to go down a specific path (either the right, left, or middle path from the junction), until they reach another intersection. Based on how long they walk, you will know how far each individual travels. You won't know whether or where they turn while they travel

You can only give one direction at a time, which both individuals will follow. You can't give directions while they are between intersections, and the directions can only state which of the three paths they should go down (i.e. no special conditions based on what they did previously). They will tell you if they end up at the same intersection or if either one is at a four-way intersection. You must get both of them to the exit at the bottom of the map

What instructions can you give to guarantee that both of the two lost in the maze can make it to the exit?

Answer 1

Employ the following pattern:

LLMMRMMRR
The reason is: It's the pattern to get from intersection #2 (at (10,4) on the map) facing north, to the exit. This pattern also turns people standing in other places to eventually hit place 2 facing north in the initial phase. So, each implementation would let a kid who ended up there facing a wall to directly get to the exit.
However, after 8 or so repeats a person could get stuck in the lower left loop, facing east. So use "MRMRR" to get them off and stop bothering. This seems to work regardless of whether ordering any of those dumbheads to go into a wall makes them turn towards that wall or not.

Answer 2

There are almost certainly quicker ways to get them both out, but the following is the simplest I could find.
This method doesn't care if the two meet up or encounter a four-way intersection, and ignores the distances except for a few special cases to avoid endless loops:

For reference, I've labelled the intersections in red, and the distances between them in blue:

Start by getting them to both repeatedly go Left, Left, Right.

This is always relative to their direction of approach and means take the leftmost or rightmost path. At a crossroads, left and right are 90-degree turns (we never use straight-on). At a T-junction there are always two exits that do not involve a U-turn; they are the left and right paths, even if one of them is physically straight on. This means directions can always be followed, at any intersection.

Note the distances, but don't do anything unless you hear one of the following patterns from either of them:

11, 11, 11 :

Someone has just gone round the loop from 16 three times. (The 11 distance here is not unique, but this is the only place you can hit three in a row on an L,L,R pattern.)

Immediately go Right, Left, Right and that person will be out of the maze.

Now go back to the L,L,R pattern and continue for the other person.

1, 15, 1 or 1, 15, 15, 1 :

Someone has just gone round the loop from 4 once or twice and then down to 6.

Immediately go Left, Left, Left, Left and that person will be out of the maze.

Now go back to the L,L,R pattern and continue for the other person.

How this works:

The L,L,R pattern takes us on one of several paths through the maze. Most of them eventually get to 21 with the correct turn to exit.
A few get stuck in endless loops through 4 or 16, and need the special cases above to escape the loop.

For each possible starting position and orientation, following the L,L,R pattern takes you through the following locations (just listing the location before the first L for brevity):
All of the following get to the exit:

21N - 14N - 12N - 2E - 5S - 3E - 7S - 1N - 3N - 5W - 9E - 12W - 14E - 13W - 19E - 16S - 9N - 5N - 2W - 1S - 7W - 13E - 14S - 21E - 20W - 17N - 18E - 8E - 4E - 6S - 10W - 18N - 17E - 11N - 21W - Out

16N - 19N - 13N - 7E - 3S - 1E - 2N - 12S - 9S - 16W - Out

15N - 11W - 17W - 20E - 10E - 6W - 15S - Out

The following hit an endless loop from 4 or 16 but can all be identified by a unique pattern of distances:

4N - 8S - 4N

4W - 8N - 18S - 10N - 20S - 21S - 11E - 15E - 6N - 4W

16E - 19W - 16E