[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.00,Default,,0000,0000,0000,,What we do is we make a matrix and also a vector.
Dialogue: 0,0:00:03.00,0:00:08.00,Default,,0000,0000,0000,,We label the matrix, which is quadratic, with all the poses and all the landmarks.
Dialogue: 0,0:00:08.00,0:00:12.00,Default,,0000,0000,0000,,Here we assume the landmarks are distinguishable.
Dialogue: 0,0:00:12.00,0:00:15.00,Default,,0000,0000,0000,,Every time we make an observation, say between two poses,
Dialogue: 0,0:00:15.00,0:00:18.00,Default,,0000,0000,0000,,they become little additions, locally,
Dialogue: 0,0:00:18.00,0:00:21.00,Default,,0000,0000,0000,,in the 4 elements in the matrix defined over those poses.
Dialogue: 0,0:00:21.00,0:00:25.00,Default,,0000,0000,0000,,For example, if the robot moves from x0 to x1,
Dialogue: 0,0:00:25.00,0:00:31.00,Default,,0000,0000,0000,,and we therefore believe x1 should be the same as x0, say, plus 5,
Dialogue: 0,0:00:31.00,0:00:33.00,Default,,0000,0000,0000,,the way we enter this into the matrix is in two ways.
Dialogue: 0,0:00:33.00,0:00:42.00,Default,,0000,0000,0000,,First, 1 x0 and -1 x1--add it together should be -5.
Dialogue: 0,0:00:42.00,0:00:48.00,Default,,0000,0000,0000,,So we look at the equation here--x0 minus x1 equals -5.
Dialogue: 0,0:00:48.00,0:00:51.00,Default,,0000,0000,0000,,These are added into the matrix that starts with 0 everywhere,
Dialogue: 0,0:00:51.00,0:00:58.00,Default,,0000,0000,0000,,and it's a constraint that relates x0 and x1 by -5. It's that simple.
Dialogue: 0,0:00:58.00,0:01:03.00,Default,,0000,0000,0000,,Secondly, we do the same with x1 as positive, so we add 1 over here.
Dialogue: 0,0:01:03.00,0:01:09.00,Default,,0000,0000,0000,,For that, x1 minus x0 equals +5, so you put 5 over here and a -1 over here.
Dialogue: 0,0:01:09.00,0:01:15.00,Default,,0000,0000,0000,,Put differently, the motion constraint that relates x0 to x1 by the motion of 5
Dialogue: 0,0:01:15.00,0:01:20.00,Default,,0000,0000,0000,,has modified incrementally by adding values the matrix for L elements
Dialogue: 0,0:01:20.00,0:01:22.00,Default,,0000,0000,0000,,that fall between x0 and x1.
Dialogue: 0,0:01:22.00,0:01:25.00,Default,,0000,0000,0000,,We basically wrote that constraint twice.
Dialogue: 0,0:01:25.00,0:01:29.00,Default,,0000,0000,0000,,In both cases, we made sure the diagonal element was positive,
Dialogue: 0,0:01:29.00,0:01:33.00,Default,,0000,0000,0000,,and then we wrote the correspondant off-diagonal element as a negative value,
Dialogue: 0,0:01:33.00,0:01:36.00,Default,,0000,0000,0000,,and we added the corresponding value on the right side.
Dialogue: 0,0:01:36.00,0:01:38.00,Default,,0000,0000,0000,,Let me ask you a question.
Dialogue: 0,0:01:38.00,0:01:41.00,Default,,0000,0000,0000,,Suppose we know we go from x1 to x2 and whereas the motion over here
Dialogue: 0,0:01:41.00,0:01:47.00,Default,,0000,0000,0000,,was +5, say, now it's -4, so we're moving back in the opposite direction.
Dialogue: 0,0:01:47.00,0:01:50.00,Default,,0000,0000,0000,,What would be the new values for the matrix over here?
Dialogue: 0,0:01:50.00,0:01:52.00,Default,,0000,0000,0000,,I'll give you a hint.
Dialogue: 0,0:01:52.00,0:01:58.00,Default,,0000,0000,0000,,They only affect values that occur in the region between x1 and x2 and over here.
Dialogue: 0,0:01:58.00,9:59:59.99,Default,,0000,0000,0000,,Remember, these are additive.