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06-18 Implementing Constraints

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    What we do is we make a matrix and also a vector.
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    We label the matrix, which is quadratic, with all the poses and all the landmarks.
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    Here we assume the landmarks are distinguishable.
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    Every time we make an observation, say between two poses,
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    they become little additions, locally,
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    in the 4 elements in the matrix defined over those poses.
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    For example, if the robot moves from x0 to x1,
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    and we therefore believe x1 should be the same as x0, say, plus 5,
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    the way we enter this into the matrix is in two ways.
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    First, 1 x0 and -1 x1--add it together should be -5.
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    So we look at the equation here--x0 minus x1 equals -5.
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    These are added into the matrix that starts with 0 everywhere,
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    and it's a constraint that relates x0 and x1 by -5. It's that simple.
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    Secondly, we do the same with x1 as positive, so we add 1 over here.
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    For that, x1 minus x0 equals +5, so you put 5 over here and a -1 over here.
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    Put differently, the motion constraint that relates x0 to x1 by the motion of 5
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    has modified incrementally by adding values the matrix for L elements
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    that fall between x0 and x1.
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    We basically wrote that constraint twice.
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    In both cases, we made sure the diagonal element was positive,
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    and then we wrote the correspondant off-diagonal element as a negative value,
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    and we added the corresponding value on the right side.
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    Let me ask you a question.
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    Suppose we know we go from x1 to x2 and whereas the motion over here
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    was +5, say, now it's -4, so we're moving back in the opposite direction.
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    What would be the new values for the matrix over here?
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    I'll give you a hint.
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    They only affect values that occur in the region between x1 and x2 and over here.
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    Remember, these are additive.
Title:
06-18 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=PL3475310BFB1CBE34

To gain access to interactive quizzes, homework, programming assignments and a helpful community, join the class at http://www.udacity.com

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Video Language:
English
Team:
Udacity
Project:
CS373 - Artificial Intelligence
Duration:
02:01
Amara Bot added a translation

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