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cs685-probabilistic-1

# cs685-probabilistic-1 - Probabilistic Robotics Overview of...

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11/16/09 1 Probabilistic Robotics Overview of probability, Representing uncertainty Propagation of uncertainty, Bayes Rule Localization and Mapping Slides from Autonomous Robots (Siegwart and Nourbaksh), Chapter 5 Probabilistic Robotics (S. Thurn et al. ) Probabilistic Robotics Key idea: Explicit representation of uncertainty using the calculus of probability theory Perception = state estimation Action = utility optimization

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11/16/09 2 Pr (A) denotes probability that proposition A is true. Axioms of Probability Theory A Closer Look at Axiom 3
11/16/09 3 Using the Axioms Discrete Random Variables X denotes a random variable . X can take on a countable number of values in {x 1 , x 2 , …, x n }. P(X=x i ) , or P(x i ) , is the probability that the random variable X takes on value x i . P( ) is called probability mass function . E.g. This is just shorthand for P(Room = office), P(Room = kitchen), P(Room = bedroom), P(Room = corridor)

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11/16/09 4 Continuous Random Variables X takes on values in the continuum. p(X=x) , or p(x) , is a probability density function . E.g. Joint and Conditional Probability P(X=x and Y=y) = P(x,y) If X and Y are independent then P(x,y) = P(x) P(y) P(x | y) is the probability of x given y P(x | y) = P(x,y) / P(y) P(x,y) = P(x | y) P(y) If X and Y are independent then P(x | y) = P(x ) (verify using definitions of conditional probability and independence)
11/16/09 5 Law of Total Probability, Marginals Map building Previously Motion planning – assumed that map is know Now how to build the map of the environment using sensors Sensor measurements have noise and various ambiguities, how does it propagate to the quality of the map If we move in time, need to combine the measurements to improve the the map (this depends on the type of map representation) If we move we need to keep track of our own position – localization Mapping and localization are closely related and are one of the key problems in robot navigation Later SLAM – simultaneous localization and mapping

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11/16/09 6 Localization and Map Building Noise and aliasing; odometric position estimation To localize or not to localize Probabilistic map-based localization Other examples of localization system Autonomous map building © R. Siegwart, I. Nourbakhsh Localization, Where am I? Perception © R. Siegwart, I. Nourbakhsh
11/16/09 7 Challenges of Localization Knowing the absolute position (e.g. GPS) is not sufficient (low accuracy in obstructed areas, not good in indoors environments) Localization in human-scale in relation with environment Planning in the Cognition step requires more than only position as input (it is better to know where you are locally in your environment) Perception and motion plays an important role Sensor noise Sensor aliasing Effector noise Odometric position estimation © R. Siegwart, I. Nourbakhsh Sensor Noise Sensor noise in mainly influenced by environment e.g. surface reflection properties, illumination …

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cs685-probabilistic-1 - Probabilistic Robotics Overview of...

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