End Game Nano quiz make up night Wed May 7 from 5 30PM 10PM in 32 123 Closed book notes Email lpk mit edu by 5PM on Tuesday today if you have an excused extra NQ to take Software lab write up due this week Thu Fri Design lab check off required no write up Please do survey on the tutor Please do HKN review Practice final available on web review sessions TBA Ex Camera Final Wed 21 May 1 30PM 7 30PM Pick up and turn in exams in 34 501 We will be watching for collaboration 1 Model based Analysis model of system behavioral properties model of world Model based Implementation inference method behavior model of world 2 Model based Implementation inference method behavior model of world Model based Implementation inference method behavior model of world 3 Model Based Inference Problems observation state estimation belief action selection action State estimation What can I conclude about the current state of the world given my history of actions and observations Action selection What action should I take given my current beliefs about the state of the world Markov Model States Actions Observations P S 0 P S t S t 1 A t 1 P O t S t A model is Markov if the state contains all information relevant to predicting next state and observation 4 State Estimation Given a sequence of actions and observations what state is the system in Answer is a belief state probability distribution over states Copy Machine Problem 5 Time Passes One Perfect Copy 6 Another Day in Paradise A Blot on our Escutcheon 7 Robot Localization States robot poses Actions robot motions Observations sonar readings Discrete Grid Discretize x y Discretize angle into same granularity Markov Big But there s structure 8 Transitions odometry since last belief update Transitions odometry 9 Transitions odometry Transitions odometry 10 Transitions odometry Discretization introduces error should add odometry error as well Observations 8 sonar readings model readings as independent given state nominal reading 11 Gaussian Distribution prob d d mean 1 sigma 0 3 mean 1 sigma 0 1 Sonar Modeling Nominal readings assume scattering good reading for any angle no beam width robot at center of grid x y th cell Our robots have different max readings 5 0 2 465 usually generate a max reading after 1 5 meters 12 Sonar Modeling def obsProb obsDist trueDist if trueDist maxGoodReading expected trueDist else expected maxReading predProb gaussian obsDist expected sigma uniformError 1 maxReading prob 0 9 predProb 0 1 uniformError return prob trueDist 1 prob obsDist P O S high avg low 13 State Estimation Belief incorporates history of observations and actions Planning Assume most likely state Use 4 headings in state representation decreases spinning Update belief after each macro action Replan 14
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