recursive bayes filters and related models for mobile robots

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Recursive Bayes Filters and related models for mobile robots

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Page 1: Recursive Bayes Filters and related models for mobile robots

Recursive Bayes Filters and

related modelsfor

mobile robots

Page 2: Recursive Bayes Filters and related models for mobile robots
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Recursive Bayes Filters

We will briefly review our derivation of Bayes filter from one of previous lectures first.

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Two steps of Bayes filter:

Prediction and Correction

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Two steps of Bayes filter: Prediction and Correction

• Use measurement to correct

controlFrom odometry and equations of motion

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• Both the prediction step and the correction step use the following:–Motion model–Sensor or observation model

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Formulas from previous slide

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Different Realizations of Bayes Filters

• Recursive filters

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Main Approaches to Bayes Filters

• Similar methods based on Bayesian probability, networks, and evolutionary algorithms also exist

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Probabilistic Motion Models

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Using only odometry in long run is definitely wrong

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Explain the meaning

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• In past we used velocity models for simple Braintenberg Vehicles• For MCECSBOT we will have to use perhaps the odometry-based

model

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Motion Model based on ODOMETRY

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Motion Model for a robot based on ODOMETRY

• This model will be more complicated for OMNI and MECCANO WHEELS

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Probability Distribution in Motion Model for a robot based on ODOMETRY

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Examples of Odometry-Based noise

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Velocity Based Motion Models

for a robot

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• It is easy to derive such model for a two-wheeled robot• We have done it as part of kinematics explanation in Fall quarter (for non-deterministic case).

Velocity Based Motion Models for a robot

Explain the meaning

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Motion Equation for Velocity Based Motion Models for a robot

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• We add an additional noise term now.

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• Here we fix the problem outlined in the previous slide

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Moving on circles

The dark clouds represent probability density

The dots represent samples of probability

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SensorModels

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Sensor model for Laser Scanners

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• You do not need to know too much if you are small and only want to move straight ahead

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Ray Cast Sensor Model

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Feature-based Model for Range-Bearing Sensors

error

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Summary• Bayes Filter is a framework for state estimation

• Motion model and sensor model are the central models in Bayes Filter

• These are all standard models for:– Robot motion– Laser-based range sensing– Similar sensors

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