Awesome

ai_for_robotics

Code and notes based on Udacity course AI for Robotics.

Also found these summary notes: https://storage.googleapis.com/supplemental_media/udacityu/cs373/Brief%20Course%20Summary.pdf

Localization:

localization : initial belief --> sense --> move --> sense --> move

i.e. : initial belief --> ( back & forth : sense <--> move )

move loses info

sense gains info

belief = probability
sense = multiplication followed by normalization
move = addition (convolution)

Bayes Rule, for Localization:

p(A|B) = p(A) * p(B|A) / p(B)

p(Xi|M) = p(Xi) * p(M|Xi) / p(M)

(let Xi = probability of being at a given position xi)
(let M = probability of getting a given measurement)

p(Xi|M) = prior * measurement probability / p(M)

p(M) = normalization constant

p(M) = sum over i of ( p(Xi) * p(M|Xi) )

So: p(Xi|M) = p(Xi) * p(M|Xi) / sum over i of ( p(Xi) * p(M|Xi) )

Theorem of Total Probabiltiy, for Motion:

p(A) = p(B) * p(A|B)

p(Xit) = sum over j of ( p(Xjt-1) * p(Xi|Xj) )

(let t = current time stamp)
(let t-1 = previous time stamp)

Comparing Filters:

Filters:	Histogram Filters	Kalman Filters	Particle Filters
State Space	discrete	continuous :)	continuous :)
Belief 'Bumps' Allowed	multimodal :)	unimodal	multimodal :)
Algorithm Efficiency	exponential (dims)	quadratic :)	? (keep =< 4 dimensions)
Robot Position Accuracy	approx. (discrete)	approx. (linear vs. non-linear)	approximate

Histogram Filter: Measurement Updates

Approximate / proportional

P(X|Z) <- P(Z|X) P(X)

P(X|Z) <-(resampling)- importance weights * particles

Kalman Filter: Motion Updates

Gaussians

P(X') = sum ( P(X'|X) P(X) )

P(X') = sum of each ( sample * particle )

But the key advantage of particle filters is: easy to program. :)

Google Car:

Histogram Methods + Particle Methods

Robot model: 2 stationary, 2 non-stationary wheels. "Bicycle model" because half of it stationary/non wheels.

Sensor data: map (not landmarks) <- match with snapshots.

Additional sensors: GPS, inertial, etc.

Particle Filter:

Per "guess" particle: (x,y,direction) --> particles --> approx. posterior probability representation of position

"Survival of the fittest 'guess' particles" (with min(real-guess) or max(importance wts) --> resample (cluster --> cluster) with higher-importance particles being more likely (not guaranteed) to be chosen and copied multiple times.