0618 Implementing Constraints

0:00  0:03What we do is we make a matrix and also a vector.

0:03  0:08We label the matrix, which is quadratic, with all the poses and all the landmarks.

0:08  0:12Here we assume the landmarks are distinguishable.

0:12  0:15Every time we make an observation, say between two poses,

0:15  0:18they become little additions, locally,

0:18  0:21in the 4 elements in the matrix defined over those poses.

0:21  0:25For example, if the robot moves from x0 to x1,

0:25  0:31and we therefore believe x1 should be the same as x0, say, plus 5,

0:31  0:33the way we enter this into the matrix is in two ways.

0:33  0:42First, 1 x0 and 1 x1add it together should be 5.

0:42  0:48So we look at the equation herex0 minus x1 equals 5.

0:48  0:51These are added into the matrix that starts with 0 everywhere,

0:51  0:58and it's a constraint that relates x0 and x1 by 5. It's that simple.

0:58  1:03Secondly, we do the same with x1 as positive, so we add 1 over here.

1:03  1:09For that, x1 minus x0 equals +5, so you put 5 over here and a 1 over here.

1:09  1:15Put differently, the motion constraint that relates x0 to x1 by the motion of 5

1:15  1:20has modified incrementally by adding values the matrix for L elements

1:20  1:22that fall between x0 and x1.

1:22  1:25We basically wrote that constraint twice.

1:25  1:29In both cases, we made sure the diagonal element was positive,

1:29  1:33and then we wrote the correspondant offdiagonal element as a negative value,

1:33  1:36and we added the corresponding value on the right side.

1:36  1:38Let me ask you a question.

1:38  1:41Suppose we know we go from x1 to x2 and whereas the motion over here

1:41  1:47was +5, say, now it's 4, so we're moving back in the opposite direction.

1:47  1:50What would be the new values for the matrix over here?

1:50  1:52I'll give you a hint.

1:52  1:58They only affect values that occur in the region between x1 and x2 and over here.

1:58 Remember, these are additive.
 Title:
 0618 Implementing Constraints
 Description:

Other units in this course below:
Unit 1: http://www.youtube.com/playlist?list=PL1EF620FCB11312A6
Unit 2: http://www.youtube.com/playlist?list=PL107FD47786234011
Unit 3: http://www.youtube.com/playlist?list=PL5493E5D24A081719
Unit 4: http://www.youtube.com/playlist?list=PLAADAB4F235FE8D65
Unit 5: http://www.youtube.com/playlist?list=PL1B9983ACF22B1920
Unit 6: http://www.youtube.com/playlist?list=PLC9ED5AC39694C141
QA: http://www.youtube.com/playlist?list=PL3475310BFB1CBE34To gain access to interactive quizzes, homework, programming assignments and a helpful community, join the class at http://www.udacity.com
 Video Language:
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 Team:
 Udacity
 Project:
 CS373  Artificial Intelligence
 Duration:
 02:01
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