1End Game• Nano-quiz make-up night Wed May 7 from5:30PM - 10PM in 32-123. Closed book, notes.• Email [email protected] by 5PM on Tuesday (today) ifyou 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 - 7:30PMPick up and turn in exams in 34-501• We will be watching for collaboration2Model-based Analysismodel ofsystemmodel ofworldbehavioralpropertiesModel-based Implementationinferencemethodmodel ofworldbehavior3Model-based Implementationinferencemethodmodel ofworldbehaviorModel-based Implementationinferencemethodmodel ofworldbehavior4Model-Based Inference ProblemsState estimation: What can I conclude about thecurrent state of the world given my history ofactions and observations?Action selection: What action should I take givenmy current beliefs about the state of the world?stateestimationobservationbelief actionselectionactionMarkov 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 allinformation relevant to predicting next state andobservation5State EstimationGiven a sequence of actions and observations,what state is the system in?Answer is a “belief state”: probability distributionover statesCopy Machine Problem6Time PassesOne Perfect Copy7Another Day in ParadiseA Blot on our Escutcheon8Robot LocalizationStates: robot posesActions: robot motionsObservations: sonar readingsDiscrete Grid• Discretize x, y• Discretize angleinto same granularity• Markov?• Big!!• But there’s structure9Transitionsodometry since last belief updateTransitionsodometry10TransitionsodometryTransitionsodometry11TransitionsodometryDiscretization introduces error; should add odometry error as wellObservations• 8 sonar readings• model readingsas independentgiven statenominal reading12Gaussian Distributionmean = 1, sigma 0.3 mean = 1, sigma 0.1probd dSonar Modeling“Nominal readings” assume• scattering (good readingfor any angle)• no beam width• robot at center of grid(x, y, th) cellOur robots• have different max readings (5.0, 2.465)• usually generate a max reading after 1.5 meters13Sonar Modelingdef 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 probtrueDist = 1obsDistprobP(O | S)highlowavg14State EstimationBelief incorporates history of observations and actionsPlanning• Assume most likelystate• Use 4 headings in staterepresentation(decreases spinning)• Update belief aftereach macro action•
View Full Document
Unlocking...