oo Robot Localization using SIR Sample x' from(x, y, 8) Iterate oI-n-model according to action af, to get proposal distribution mportance 3)Resample i epent
Robot Localization using SIR i I. Sample {x t} from (x, y, θ) II. Iterate: 1) Sample from motion model according to action a Prediction t, to get proposal distribution q(x) 2) Add importance weights 3) Resample Measurement
●。● Robot Localization using SIR Take sample set ( Xt11 Iterate For each sample x 1) Sample from p(X,1 Xt-1, a,-1 2) Attach importance weights p(x1)p(1|x1)p(x1|x+1,a12) WIx Z,x t x (x|x1=1,a1) ll. Resample from W(Xy
Robot Localization using SIR i I. Take sample set {x t-1} II. Iterate: i For each sample x t-1 1) Sample from p(xt-1| xit-1,at-1) 2) Attach importance weights = t x w it ) = x p it ) z p | x t ) x p t | xit −1, a ) = z p | xi ( t ) ( ( t i ( i t −1 ( ( ( i x q it ) x p t | xit −1, a ) t −1 II i I. Resample from w(x ) t
●。● Motion model as Proposal distribution o Importance sampling efficiency o difference between g(x and p(x) o Motion model and posterior are often close o Motion model is gaussian
Motion model as Proposal distribution | Importance sampling efficiency ∝ difference between q(x) and p(x) | Motion model and posterior are (often) close | Motion model is Gaussian
Motion model as proposal ●。● distribution o Motion model is gaussian about translation and rotation Start location 10 meters
Motion model as Proposal distribution | Motion model is Gaussian about translation and rotation
oo Sampling from Motion Model o a common motion model Decompose motion into rotation translation rotation Rotation 卩=△1,02e=a△d+Q2△ Translation:p=△d,o2△d=a3△d+a4△1+△2) Rotation: =△91022=a△d+a2△2 o Compute rotation translation rotation from odometry o For each particle, sample a new motion triplet by from gaussians described above o Use geometry to generate posterior particle position
Sampling from Motion Model | A common motion model: • Decompose motion into rotation, translation, rotation • Rotation: µ = ∆θ1, σ2 ∆θ1 = α1∆d+ α 2∆θ1 • Translation: µ = ∆d, σ 2 = α 3 ∆d+ α 4(∆θ1+ ∆θ 2) ∆d • Rotation: µ = ∆θ1,σ2 ∆θ 2 = α1∆d+ α 2∆θ2 | Compute rotation, translation, rotation from odometry | For each particle, sample a new motion triplet by from Gaussians described above | Use geometry to generate posterior particle position