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lecture2-2010 - CS 547 Sensing and Planning in Robotics...

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CS 547: Sensing and Planning in Robotics Gaurav S. Sukhatme Computer Science Robotic Embedded Systems Laboratory University of Southern California [email protected] http://robotics.usc.edu/~gaurav
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Probabilistic Robotics Key idea: Explicit representation of uncertainty using the calculus of probability theory Perception = state estimation Action = utility optimization
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Advantages and Pitfalls Can accommodate inaccurate models Can accommodate imperfect sensors Robust in real-world applications Best known approach to many hard robotics problems Computationally demanding False assumptions Approximate
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Pr (A) denotes probability that proposition A is true. Axioms of Probability Theory 1 ) Pr( 0 A 1 ) Pr( = True ) Pr( ) Pr( ) Pr( ) Pr( B A B A B A - + = 0 ) Pr( = False
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A Closer Look at Axiom 3 B B A A B True ) Pr( ) Pr( ) Pr( ) Pr( B A B A B A - + =
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Using the Axioms ) Pr( 1 ) Pr( 0 ) Pr( ) Pr( 1 ) Pr( ) Pr( ) Pr( ) Pr( ) Pr( ) Pr( ) Pr( ) Pr( A A A A False A A True A A A A A A - = ¬ - ¬ + = - ¬ + = ¬ - ¬ + = ¬
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Discrete Random Variables X denotes a random variable . X can take on a finite number of values in {x 1 , x 2 , …, x n }.
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