Site of the previous year (2024/25) 

News

• The course is planned to start on the Monday September 29 2025

Abstract

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. 

Prerequisites

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.

Exam

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:

• TBD

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

TBD

Project Enrollment Form

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.

Exam Results

• TBD

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.

Preliminary Program

• 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) 

Tentative schedule of the lectures

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

Extras : C++ course by Igor Bogoslavskyi, University of Bonn

Link

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.