21/10/2024: OPIS CODE for in-class course evauation: 153J9L9T
23/09/2024: Due to health reasons, the start of the course is delayed by one week. The lessons will start on Monday September 30 2024
The course is planned to start on the Week of September 22 2024
This course aims at providing the students with the necessary mathematical background and the practical guidelines to tackle complex problems in state estimation and model identification for robots. At the end of this course the student will possess the necessary background to approach fundamental problems in robotics including, but not limited to localization, simultaneous localization and mapping (SLAM), calibration and tracking.
Monday, 14:00-16:00
Tuesday 14:00-16:00
Wednesday 12:00-14:00
Room B2, Via Ariosto
Room B2, Via Ariosto
Room A6 Via Ariosto
This course in the "manifesto" is scheduled for both the first and the second year of the MARR/AIRO studies. Since it requires reasonably solid notions of Linear Algebra, Robotics 1 (or their italian versions Geometria and Robotica 1 which are taught on the 1st year of the master, we recommend the students to put Prob Rob in the second year of the study plan.
ECTS Credits: 6
How to complete the credits for this module: After attending classes, students should:
develop a project.
sustain a written exam.
Next Exams:
17.1.2025 14:00, Room 204, Marco Polo
18.2.2025 09:00, Room 204, Marco Polo
4.4.2025, 17:00, Room A3, Via Ariosto
25.6.2025, 9:00, Room 105 Marco Polo
24.7.2025, 9:00, Room 108 Marco Polo
05.9.2025, 14:00, Room 105 Marco Polo
10.10.2025, 14:00, Room A3, Via Ariosto
A reminder on what a mark means
The grade is on the test not on the student: a brilliant student can make a test that scores poorly, and a lucky student can make a test that scores high.
We evaluate the tests. We do not judge the students.
Anxiety sucks.
If you (after looking at the solutions) don't feel your mark is correct we might have misunderstood something (or you wrote hieroglyphs). Come and ask for explanations.
Total grade
Written test is 3/4 (max mark 30), project takes 1/4 (max mark 8) and the total grade is 32
Example:
Written part 27/30
Project grade 6/8
Total grade: 27*24/30 + 6 = 27,6 => 28
Projects 2024/2025
Please fill the following form to choose a project.
Project Submission
Prepare a readme file in your repo with some explanation about your project, what did you do and how did you solve it. Embed plots (if required, this depends on the project), some tables with numerical errors and output files required (for this create a folder called `output`) for us to evaluate independently the quality of your work.
Send us an email when you complete the project.
If you wish to discuss the exam, send an email to Omar, Lorenzo, Leonardo and Giorgio, with subject [PR-[date_of_exam]-discussion]. We will try to clarify the correction by email, and should this not be sufficient we will schedule an individual meet/zoom/whatsoever.
Probability Primer
Axioms of probability
Bayes Rule, Chain Rule, Marginalization and Conditioning
Statistical independence
Manipulating pdf representations: marginalizing, conditioning, applying a function
Discrete
Gaussian
Particles
Dynamic Systems
System Model (state, observations, controls)
Filtering (Discrete , Kalman and Particle)
Geometry and Linear Algebra Refresher
vectors, matrices and their operations, SO(X) groups, SE(X) groups
computation of gradients (symbolic, numerical and automatic differentiation)
Applications of Filtering
Localization (Kalman and Particle)
SLAM (Kalman and Particle)
Least Squares Estimation
Gauss-Newton and Levenberg/Marquardton Euclidean Spaces
Probabilistic Interpretation
Manifolds
Robust Kernels
Applications of Least Squares Estimation
Calibration
Sensor Registration (ICP, Bearing-only, Range-Only)
Sparse Least Squares
Structure of the problem
Factor Graphs
Sparse Solvers
Applications of Sparse Least Squares
Graph-SLAM
Simultaneous Localization, Calibration and Mapping
Data Association
Mahalanobis Distance
Voting and Consensus Methods (RANSAC and variants)
Week 1: Intro, Sensors, Mobile Platforms, Probability
Week 2: Manipulating PDF
Week 3: Dynamic Systems, Filtering, Discrete Filters
Week 4: Kalman Filters
Week 5: Gaussian Filters
Week 6: Wrapup on Filtering and Applictions: Localization and SLAM
Week 7: Least Squares Estimation
Week 7: Least Squares Estimation, Applications: Calibration, Sensor Registration
Week 8: Sparse Least Squares
Week 9: Applications of Sparse Least Squares: Graph-SLAM
Week 10: Data Association
Week 11: Wrapup and Applications
We remind that the knowledge of C++ is not mandatory for the exam. Still, we believe that this programming skill might be useful for your career in Robotics.