Date: January 14, 2024

Topic: Total Probability

Recall

Notes

Terms

Prior: initial belief distribution

Posterior: updated belief distribution after taking into account new information

Mutually Exclusive: disjointed events (cannot occur at same time)

Collectively Exhaustive: collection of events filling the entire state space (union)

Partition: set of events that are both *mutually exclusive *****and collectively exhaustive

Localization: process of determining the location of an object with respect to its environment

Divide and Conquer: solve a problem by breaking it down and solving the sub-problems

When a robot manages to sense something in its environment, it generates a belief of where it can be.

Hence, the belief moves (and decreases) as the robot moves along its area.

When a door is sensed again, the robot generates the same posterior belief of its location, and then multiplies it with the prior belief to confirm that it is at the 2nd green door.

Overview of robot sensing (Bayes Theorem)

1. Uniform Maximum Confusion

• At beginning, unsure of location, so the probability of being at any location is uniform

2. Having a belief

• A measurement is taken indicating that a green door is seen
• Increase probability at green doors and decrease probabilities elsewhere after measurement (posterior)

3. Moving

• When the robot moves to the right, the beliefs are also moved to the right (but with decreased probability)
• This is because the robot knows it can be at 3 possible locations, but since movement is noisy, the peaks flatten

4. Sensing a door again

• If a door is sensed again during the prior, a multiplication (convolution) happens
• This gives a posterior of having a high probability at the 2nd green door
• Places far away from the door are then multiplied to give a low probability
• Hence, the robot has localized itself and knows where it is (2nd door)

When the robot senses something, it multiplies where it senses with the current probability distribution

<aside> 📌 SUMMARY: Robot motion relies on sensing objects in the environment for localization

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Date: January 14, 2024

Topic: Robot Motion

<aside> 📌 SUMMARY: Robot motion is often noisy, leading to lowered probabilities as the robot moves right.

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