# PS2

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## Reading

In *Probabilistic Robotics*, read the remainder of Chapter 2
(Sections 2.3 through 2.7).

## Online Instruction

Work through lectures and embedded quizzes 11.1 through 11.17, “HMMs and Filters,” from the online Stanford AI class, starting here: https://www.ai-class.com/course/video/videolecture/138.

## Problems

1. In the Bayes Rule formula, instead of dividing by the denominator, the expression is often developed as a product with the factor η.

- What is the English phonetic spelling / pronunciation of this Greek character?
- What is its role in Bayes Rule calculations?

2. Figure 2.2 on page 25 of PR shows a dynamic Bayes network with three variables: x, u, and z.

- What is represented by each of these three variables? Hint: the answer is in the caption; you just have to match up the variables to

what they represent.

- What is the significance that u and z are shaded, while x is not?

3. In Exercise 2 on page 36 of PR:

- Solve (a).
- Write code for the simulator as suggested in (b), generating a simulated Markov process. You may use any language you like, but Python or C++ is suggested as those are the languages we will be using with ROS.
- Based on running your code, answer (c).
- Solve (f).

4. Follow along with the belief update calculations in section 2.4.2.

Based on this algorithm, write a program that can perform the act- predict-measure-update loop iteratively.

Program the robot to alternately take do_nothing and push actions.

How many time steps will it take for the robot to believe with 0.9999 (or higher) probability that the door is open? Turn in your code and explain how you got your answer.