Probabilistic Robotics

A.Y. 2018/19


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.

Office (DIAG)







Every Wednesday: 14.00-17.00


Despite this course in the "manifesto" is scheduled for the first year of the MARR/AIRO studies, it requires reasonably solid notions of Linear Algebra, Robotics 1 (or their italian versions Geometria and Robotica 1) and Autonomous and Mobile Robotics. For this reason, we recommend the students to sustain the exam on the second year.

Time and Location of the Lectures

When: Fall semester (about 12 weeks), Start: Wednesday, 26/09/2018

Wednesday 09:00-12:00, Room A4

Thursday 14:00-16:00, Room A4

Where: Dipartimento di Ingegneria informatica automatica e gestionale Antonio Ruberti (DIAG) , Sapienza University of Rome.

Via Ariosto 25, I-00185, Rome, Italy.


ECTS Credits: 6

How to complete the credits for this module: After attending classes, students should:

  • develop a small project. Work is individual.
  • sustain an oral interview (that will contain also written exercises)

IMPORTANT NOTE: from this academic year it will NOT be possible to sustain Probabilistic Robotics as 2 modules of Elective in AI or Elective in Robotics.

Next Exams:

  • Jan 29, 2019. 10.30am Room A3
  • Feb 21, 2019. 11am Room A6
  • Mar 27, 2019. 2pm Room B101

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

The images in the title banner are courtesy of Dellaert et al., Agarwal et al. and Cremers et al.