6.01SC | Spring 2011 | Undergraduate

Introduction to Electrical Engineering and Computer Science I

Unit 4: Probability and Planning

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After a brief introduction to probability theory and computational search strategies, this unit focuses on modeling uncertainty and making robust plans. Robotic applications include mapping an unknown space, determining one’s location in a known space, and plotting a route through a maze.

 Two images representing how the robot navigates through a maze.

Topics Bayes’ theorem, search strategies
Lab Exercises

Mapping: drive robot around unknown space and make map

Localization: give robot map and ask it to find where it is

Planning: plot a route to a goal in a maze
Theme robust design in the face of uncertainty

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

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Session Overview

Conditional probability of events A and B. 

We’ve been talking about how to analyze and design systems, but we haven’t talked about how to make systems robust under uncertainty. In fact, we haven’t even talked about how to model uncertainty.

In this unit, we’ll address the problem that systems we design may have to operate under uncertainty, and that we may want those systems to be able to search the world for possible solutions to problems. We’ll introduce the basics of probability and search in this session, and apply those concepts to our design challenges.

The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources.

Session Content

Readings

Read sections 7.1-7.4 of the course notes.

Lecture Video

Watch the lecture video. The handout and slides present the same material, but the slides include answers to the in-class questions.

About this Video

Introduction to probability theory, with the goals of making precise statements about uncertain situations and drawing reliable inferences from unreliable observations. A hidden Markov model is then applied to robot navigation.

Recitation Video

These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.

Session Activities

The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

Software Lab

PROBLEM # QUESTIONS
10.1.1 Probability distributions: DDist (PDF)
10.1.2 Conditional distributions (PDF)
10.1.3 Joint distributions (PDF)
10.1.4 Operations on conditional distributions (PDF)
10.1.5 Where are you? (PDF)
10.1.6 Implementing joint distributions (PDF)
10.1.7 Implementing operations on conditional distributions (PDF)

Design Lab

Additional Exercises

PROBLEM # QUESTIONS
10.3.1 A distribution (PDF)
10.3.2 Summing to 1 (PDF)
10.3.3 Truth (PDF)
10.3.4 Equivalence (PDF)
10.3.5 Buying a car (PDF)

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Session Overview

Illustration of the Manhattan distance.

In the last session, we introduced the concept of search. We looked at the 6.01 implementation of a general search algorithm, addressed issues of common sense and dynamic programming, and localized a robot.

In this session, we focus on improving search. We can systematically use information we have about the state space we’re searching, in order to save us time and space.

The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources.

Session Content

Readings

Read sections 8.5-8.6 of the course notes.

Lecture Video

Watch the lecture video. The handout and slides present the same material, but the slides include answers to the in-class questions.

About this Video

Uniform cost search takes into account the cost associated with an action, and can be implemented with a priority queue. Heuristics estimate the cost of the remaining path to the goal; the Manhattan distance is an example of an admissible heuristic.

Recitation Video

These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.

Session Activities

The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

Software Lab

PROBLEM # QUESTIONS
14.1.1 Modeling the world (PDF)
14.1.2 Robot on a grid map (PDF)

Design Lab

PROBLEM # QUESTIONS
14.2.3 Aliasing instances (PDF)
14.2.6 Robot race results [optional] (PDF)

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Session Overview

The eight puzzle in its goal state.

In this session, we introduce the idea of search. We’ve designed systems to tackle static problems and modeled the idea of uncertainty, but we still haven’t developed a way to approach that uncertainty and engage in decision-making that we can codify into our systems.

We can tackle uncertainty through search; if we know the domain of possible solutions to a problem, and know the steps to get from one part of the domain to the other, then we can search the domain until we reach the solution.

The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources.

Session Content

Readings

Read sections 8.1-8.4 of the course notes.

Lecture Video

Watch the lecture video. The handout and slides present the same material, but the slides include answers to the in-class questions.

About this Video

Two search algorithms are introduced, depth-first search and breadth-first search. Pruning rules (including dynamic programming) are also considered, so that the same state is not visited repeatedly.

Recitation Video

These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.

Session Activities

The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

Software Lab

PROBLEM # QUESTIONS
13.1.1 Farmer et al.: Machine (PDF)
13.1.2 Farmer et al.: Search (PDF)

Design Lab

Additional Exercises

PROBLEM # QUESTIONS
13.3.1 Compare searches (PDF)
13.3.2 Compare searches (PDF)
13.3.3 Paths in the map (PDF)
13.3.4 Robot on a grid (PDF)
13.3.5 Obstacles [optional] (PDF)
13.3.6 Knight paths on a chessboard [optional] (PDF)
13.3.7 Two robots on a grid [optional] (PDF)

Check Yourself

Nano-Quiz

Nano-quiz problems and solutions are taken from a previous version of the 6.01 Online Tutor. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

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Session Overview

Diagram of robot estimating its distance from the wall.

In the last session, we introduced probability and the basic tools to interact with probability distributions. We use probability to model degrees of belief, so that we can build systems that are robust in the face of uncertainty.

In this session, we focus on state estimation. We’ll use state estimation to estimate the location of a robot in a hallway, and use it to localize a robot. Later we’ll be able to localize and map at the same time.

The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources.

Session Content

Readings

Read sections 7.5-7.8 of the course notes.

Recitation Video

These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.

Session Activities

The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

This session contains a design lab from week 11 of the MIT course, and a software lab from week 12.

Design Lab

PROBLEM # QUESTIONS
11.1.1 Observation models (PDF)
11.1.2 Transition models (PDF)
11.1.4 Simulating hallways (PDF)
11.1.5 Simulating hallways: the noisy-noisy case (PDF)
11.1.6 Sonar hit (PDF)
11.1.7 Ideal sonar readings (PDF)

Software Lab

PROBLEM # QUESTIONS
12.2.1 Stochastic state machines (PDF)
12.2.2 Faster state estimation (PDF)
12.2.3 Localization (PDF)

Check Yourself

Nano-Quiz

Nano-quiz problems and solutions are taken from a previous version of the 6.01 Online Tutor. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

Homework

PROBLEM # QUESTIONS
11.2.1 Basic distributions: square (PDF)
11.2.2 Basic distributions: triangle (PDF)
11.2.3 Mixture distribution (PDF)

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Course Info

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Spring 2011
Level
Undergraduate
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