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 !