SLAM E 02
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| License | CC Attribution - NonCommercial - NoDerivatives 3.0 Germany: You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
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SLAM and path planning39 / 76
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00:00
INTEGRALPosition operatorDistribution (mathematics)Social classPresentation of a groupGleichverteilungRoboticsLocal ringRepresentation (politics)
00:18
Position operatorPrice indexTrailDistribution (mathematics)Local ringMobile WebComputer animation
00:25
Distribution (mathematics)
00:29
Distribution (mathematics)Local ringComputer animation
00:38
Order (biology)Price indexMobile WebSocial classFood energyDistribution (mathematics)RoboticsWorkstation <Musikinstrument>Source codePlanning
00:42
Distribution (mathematics)RoboticsComputer animation
00:47
ArmLocal ringComputer animation
00:53
RoboticsDifferent (Kate Ryan album)AlgorithmLocal ringPosition operatorArithmetic meanTrailSelf-organizationWorkstation <Musikinstrument>Computer animation
01:47
Self-organizationAxiom of choiceEndliche ModelltheorieGleichverteilung
01:53
Posterior probabilityEndliche ModelltheorieMeasurementVarianceState of matterGleichverteilungPhysical systemNormal distributionExpected value
02:39
Diagram
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Physical systemMeasurementComputer animationDiagram
Transcript: English(auto-generated)
00:00
And of course in general if I do not know anything about the position of my robot then a uniform distribution will be the proper representation and so my belief will be constant while the constant is chosen such that the integral over my entire arena will be one. Now let's introduce three important classes of localization problems.
00:22
The first and easiest one is position tracking and this is a problem we have worked on so far. So there's a known initial pose and typically a unimodal distribution for example a Gaussian distribution and then there's the problem of global localization and this means I don't have any indication of my initial pose and in general in order to solve that a unimodal
00:45
distribution is not useful. Now similar to that is a so-called kidnapped robot problem where a global localization problem is assumed plus there will be the possibility that someone kidnaps the robot and moves it to another place where the robot then has to recover and
01:04
determine its new global position. So now in reality robots are not kidnapped so often at least so far but the practical importance of this problem is that any global localization algorithm might eventually fail and if it does so it needs to recover from this failure
01:21
meaning it needs the ability to discover that the position that it might have tracked for a while is completely wrong and that therefore it needs to determine its global position again. So the practical importance is that the robot is able to recover from localization failures. So these are three different localization problems which are often mentioned in the standard robotics
01:46
literature. Now let's think about global localization again. So we just learned that if I don't know where I am then a uniform distribution would be the best possible choice. However if I'm interested in modeling this with a Gaussian another possibility would be to place a Gaussian
02:03
at the center with a very large variance. So in one day this would mean that this is my belief it is centered here but that doesn't matter because I will set the variance to be very large and so during filtering if I integrate this with my measurement my posterior belief will be almost
02:20
the same as the probability of my measurement and so even though I was unable to represent my initial belief exactly I had to replace the uniform distribution by this very flat Gaussian. I eventually end up after my first measurement in a good guess for my system state. Now what do you think would it be possible to model the belief by a very wide normal distribution and
02:43
subsequently rely on the measurements to determine our system state? Yes or no?