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    Uncertainty

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    Gia Bang Nguyen
    The document discusses uncertainty and probability in artificial intelligence and robotics. It covers topics like Bayesian filtering and particle filtering which are approaches used to estimate the state of a robot using probabilistic methods under conditions of uncertainty.

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    Uncertainty

    Uploaded by

    Gia Bang Nguyen
    4 views28 pages
    The document discusses uncertainty and probability in artificial intelligence and robotics. It covers topics like Bayesian filtering and particle filtering which are approaches used to estimate the state of a robot using probabilistic methods under conditions of uncertainty.

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    Uncertainty (1)

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    The document discusses uncertainty and probability in artificial intelligence and robotics. It covers topics like Bayesian filtering and particle filtering which are approaches used to estimate the state of a robot using probabilistic methods under conditions of uncertainty.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    4 views28 pages

    Uncertainty

    Uploaded by

    Gia Bang Nguyen
    The document discusses uncertainty and probability in artificial intelligence and robotics. It covers topics like Bayesian filtering and particle filtering which are approaches used to estimate the state of a robot using probabilistic methods under conditions of uncertainty.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    You are on page 1of 28

    Artificial Intelligence

    Uncertainty

    Pham Viet Cuong


    Dept. Control Engineering & Automation, FEEE
    Ho Chi Minh City University of Technology
    Content
    ✓ Probability: Brief review
    ✓ Robot localization problem
    ✓ Baysian filter
    ✓ Particle filter

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 2
    Probability
    ✓ Probability that a random variable X has value x

    ✓ Example:

    ✓ Abbreviation:

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 3
    Probability
    ✓ Probability density function
    ❖ Univariate normal distribution

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 4
    Probability
    ✓ Probability density function mean vector covariance matrix
    ❖ Multivariate normal distributions

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 5
    Probability
    ✓ Probability density function
    ❖ Probability of the random variable falling within a particular range of
    values

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 6
    Probability
    ✓ Joint distribution of 2 random variables
    ✓ Conditional probability

    ✓ Bayes rule

    p(y) doesn’t depent on x

    ✓ Conditional independence

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 7
    Localization Problem
    ✓ Indoor

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 8
    Localization Problem
    ✓ Outdoor

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 9
    Why localization problem?
    ✓ Fundamental problem in robotics
    ✓ Control noise

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 10
    Localization Problem
    ✓ 1D localization ✓ 2D localization

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 11
    Robot & Environment
    ✓ State

    ✓ Control actions

    ✓ Sensor measurements

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 12
    Robot & Environment
    ✓ State evolution: state transition probability

    Markov process: a process for which


    predictions can be made regarding future
    outcomes based solely on its present state (as
    good as the ones that could be made knowing
    the process's full history)

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 13
    Robot & Environment
    ✓ Measurement model:

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 14
    Robot & Environment
    ✓ Measurement model:

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 15
    Robot & Environment
    ✓ Hidden Markov chain:

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 16
    Belief
    ✓ Belief

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 17
    Bayesian filter

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 18
    Bayes filter
    ✓ Example

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 19
    Bayes filter
    ✓ Example

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 20
    Bayes filter
    ✓ No closed form solution in general
    ✓ Two approachs:
    ❖ Gaussian filters
    ❖ Nonparametric filters

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 21
    Particle filter
    ✓ Represent the posterior bel(xt) by a set of random state samples

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 22
    Particle filter
    ✓ Approximate the belief bel(Xt) by the set of particles Xt

    ✓ Particles: samples of a posterior distribution

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 23
    Particle filter

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 24
    Particle filter

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 25
    Particle filter

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 26
    Probability

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 27
    Probability

    Pham Viet Cuong - Dept. Control Eng. & Automation, FEEE, HCMUT 28

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