welcome to introduction to robotics - university of...
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Welcome to Introduction to Robotics
Prof. Katie Driggs-Campbell
Jan. 21, 2020
Introduction to Course Staff
Prof. Katie Driggs-
Campbell
Lab Manager: Dan Block
TA: Mario Perez
TA: Peixin Chang
TA: Chuyuan
Tao
TA: Ben Walt
TA: Shuijing
Liu
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 11-14Planning + Decision-Making
Weeks 15-16Projects
Course Components
– 10% Participation– 20% Homework– 25% CBTF Quizzes– 20% Group Projectx 25% Laboratory
+ Extra Credit
ParticipationParticipation is graded for positive course contributions (50%) and guest lecture reflections (50%)
• Guest Lectures: Attendance required. You will submit a 1pg reflection.• 2.06 Prof. Joohyung Kim (ECE, formerly Disney Research)
• 2.27 Prof. Wendy Rogers (Kinesiology, Human Factors and Aging Lab)
• 4.07 Dr. Aadeel Akhtar (PSYONIC)
• 5.05 Chris Walti (Tesla)
• Positive contributions: Include attending lecture, being active on Piazza, helping others in office hours and/or lab, actively participating in homework parties, etc.• Homework Parties on Fridays from 3:00-6:00pm in ECEB2017 (except 2/28)
• Two self-assessments throughout the semester
• Shout-out forms available all semester
Homework and Quizzes
• Weekly assignments will be completed online through PrairieLearn• Homework will be due every Friday at 8pm
• One week after the deadline, you may submit an assignment for up to 50% credit
• No homework assignments will be dropped
• There will be three one-hour, closed-book quizzes, with access to python and MATLAB, taken in the CBTF• The first two quizzes will have re-takes, the third will be treated as a final (no
re-take)
Extra Credit Opportunities
No homework or quizzes will be dropped, but you will have two opportunities for extra credit:
1. Optional CBTF Orientation – sign up now!• ~1% (roughly one homework)
2. Tutorial video on some robotics topic • Up to 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)
Vectors (4)
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
Summary
• Introduced course content
• Reviewed Vector and Matrix representations and operations
• Rotation matrices are an example of orthogonal matrices that have many practical uses in robotics
• The Jacobian contains the partial derivatives for a vector valued function