3 – 04 Implementing Constraints Quiz V1

What we do is we make a matrix and also a vector. And we label the matrix, which is quadratic with all the poses and all the landmarks. Here we assume the landmarks are distinguishable and every time we make an observation, say between two poses, they become little additions locally in the four elements in the matrix defined over those poses. For example, if the robot moves from x_0 to x_1. We therefore believe x_1 should be the same as x_0 say plus five. The way we enter this into the matrix is in two ways. First, 1 x_0, minus 1 x_1, add it together should be minus five. We look on the equation here x_0 minus x_1 equals minus 5. These are added into the matrix that starts with zero everywhere and it’s a constraint that relates x_0, x_1 by minus 5, it’s that simple. Secondly, we do the same with x_1 as positive, so we add one over here and for that, x_1 minus x_0 equals five. You put five here and a minus one over here. Put differently the motion constraint that relates x_0 to x_1 by the motion of five, has modified incrementally by adding values, the matrix for all elements that fall between x_0 and x_1. We basically wrote that constraint twice in both cases, we make sure that the diagonal element was positive and the viewer the correspondents off-diagonal element as a negative value. We added the corresponding value on the right side. Let me ask you a question, suppose we know we go from x_1 to x_2 and whereas the motion over here was plus five. Now, it’s minus 4, so we moving back in the opposite direction. What will be the new value as for the matrix over here? I’ll give you a hint. They only affect values that occur in the region between x_1, x_2 and over here, and remember these are additive

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