Welcome to Introduction to Robotics

Prof. Katie Driggs-Campbell

Aug. 27, 2019

Introduction to Course Staff

Prof. Katie Driggs-

Campbell

Lab Manager: Dan Block

TA: Alli Nilles

TA: Peixin Chang

TA: Hang Cui

TA: Ben Walt

TBD

Environment & Agent Models

Compute Platform

Low-level Control

Trajectory Planning

Decision-Making

Perception

Sensors

Simulation & Validation

Topics in Robotics

sense

think act

Weeks 01-03Perception + State Estimation

Weeks 04-10Kinematics + Dynamics

Weeks 11-13Planning + Decision-Making

Weeks 14-15TBD + projects

Course Components

– 10% Participation– 20% Homework– 25% CBTF Quizzes– 20% Group Projectx 25% Laboratory

+ Extra Credit

Course Components

Participation

• You will get credit for positive course contributions (e.g., attendance, Piazza, helping others in office hours,)

• Note that:• You’ll submit a 1pg reflection after guest

lectures (attendance will be taken every guest lecture)

• Helping others at Homework Parties on Fridays from 3:00-6:00pm in ECEB3013

Homework and Quizzes

• Weekly assignments that will be completed online through PrairieLearn• Homework will be due every Friday at 8pm • For one week after the deadline, you may

submit a late assignment for 50% credit• No homework assignments will be dropped

• There will be four one-hour, closed-book quizzes, with access to python and MATLAB, taken in the Computer-Based Testing Facility (CBTF)

Extra Credit Opportunities

No homework or quizzes will be dropped, but you will have two opportunities for extra credit:

1. Optional Quiz 0 in the CBTF this week• ~1% roughly equivalent to one homework

2. Tutorial video on some robotics topic • ~5% roughly one quiz or a few homework assignments

Quick Linear Algebra ReviewInspiration from Lukas Luft and Wolfram Burgard

Vectors (1)

Vectors (2)

Vectors (3)

Matrices

Matrix Operations and RankCommon Matrix Operations

- Multiplication by a scalar

- Sum (commutative, associative)

- Multiplication by a vector

- Product (not commutative)

- Transposition

- Inversion (if square, full rank)

Matrix Rank

- Rank is determined by the maximum number of linearly independent rows (columns)

- If A is 𝑚 × 𝑛, then• rank 𝐴 ≥ 0

• rank 𝐴 ≤ min 𝑚, 𝑛

- rank 𝐴 can be computed by finding the rows that are linearly dependent, Gaussian elimination, and/or by counting the number of non-zero rows

Matrix Vector Products

Matrix Matrix Product

Matrix Inverse

Determinants

Application of the determinant

• Used to compute the eigenvalues, by solving the characteristic polynomial: det(𝐴 − 𝜆 𝐼) = 0

• Is equal to the product of the eigenvalues of 𝐴

• Gives area and volume of the unit square transformed by 𝐴

Orthogonal Matrix

Rotation Matrix

Example of Transformations

• A sensor detects an obstacle at location p, in its own frame

Example of Transformations

• A sensor detects an obstacle at location p, in its own frame

• The sensor is mounted on a robot- Matrix B represents the position of the sensor on the robot

Example of Transformations

• A sensor detects an obstacle at location p, in its own frame

• The sensor is mounted on a robot- Matrix B represents the position of the sensor on the robot

• The robot is moving around in the world- Matrix A represents the pose of the robot out in the world

Jacobian Matrices

Jacobian Matrix

Gives the orientation of the tangent plane to the vector-valued function at a given point

review materials for linear algebra

The Matrix Cookbook

Linear Algebra Done Right

Textbooks on Linear Algebra

by Gilbert Strang