Particle Filter Lab
Sep. 10, 2019
Particle Filters
• Particle filters are an implementation of recursive Bayesian filtering,where the posterior is represented by a set of weighted samples
• Nonparametric filter – can approximate complex probabilitydistributions without explicitly computing the closed form solutions
• Instead of a precise probability distribution, represent belief 𝑏𝑒𝑙 𝑥𝑡by a set of particles, where each particle tracks its own state estimate
• Random sampling used in generation of particles, which areperiodically re-sampled, with probability weighted by likelihood oflast generation of particles
Particle Filtering Algorithm // Monte Carlo LocalizationStep 1: Initialize particles uniformly distribute over space and assign initial weight
Step 2: Sample the motion model to propagate particles
Step 3: Read measurement model and assign (unnormalized) weight:
𝑤𝑡[𝑚]
= exp−𝑑2
2𝜎
Step 4: Calculate your position update estimate by adding the particle positions scaled by weight Note that weights must be normalized to sum to 1
Step 5: Choose which particles to resample in the next iteration by replacing less likely particles with more likely ones
Particle Filtering - Homework Demo
Particle Filtering - Homework
Step 1: Initialize particles uniformly distribute over space and assign initial weight
Particle Filtering - Homework
Step 2: Sample the motion model to propagate particles
Particle Filtering - Homework
Step 3: Read measurement model and assign (unnormalized) weight:
𝑤𝑡[𝑚]
= exp−𝑑2
2𝜎
Particle Filtering - Homework
Step 4: Calculate your position update estimate by adding the particle positions scaled by weight Note that weights must be normalized to sum to 1
Particle Filtering - Homework
Step 5: Choose which particles to resample in the next iteration by replacing less likely particles with more likely ones
Particle Filtering - Homework
Step 5: Choose which particles to resample in the next iteration by replacing less likely particles with more likely ones
Reference: https://www.youtube.com/watch?v=wNQVo6uOgYA
Particle Filtering - Lab Demo
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
Image Frame
World Frame
UR3 Base Frame
Maze Grid Frame
Turtle GUI Frame
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
Image Frame
yc
xc
(0, 0)
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
World Frame
xw
yw
zw
(0, 0)
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
UR3 Base Frame
(0, 0)
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
Maze Grid Frame
xM
yM
25 cm x 16 = 400 cm
(0, 0)
Particle Filtering - Lab Camera
UR3 Robot
“Mobile Robot”
Maze
Turtle GUI Frame
xT
yT
25 pixels x 16 = 400 pixels
(0, 0)
Questions?
Thank you !