Robotics: Science and Systems

Mars Exploration Rover

Overview

This course provides an introduction to robotic systems from a computational perspective. A robot is regarded as an intelligent computer that can use sensors and act on the world. We will consider the definitional problems in robotics and look at how they are being solved in practice and by the research community. The emphasis is on algorithms, probabilistic reasoning, optimization, inference mechanisms, and behavior strategies, as opposed to electromechanical systems design. This course aims to help students improve their probabilistic modeling skills and instill the idea that a robot that explicitly accounts for its uncertainty works better than a robot that does not.

Course Details

Instructor
Florian Shkurti
x@cs.toronto.edu, x=florian
Office: DH3066, UTM
Office Hours: Thu 4-5pm
Teaching Assistant
Nan Liang
y@mail.utoronto.ca, y=nan.liang
Office: TBA
Office Hours: Tue 2-3pm
Lectures: Thursdays, DH4001, UTM, 5-7pm
Tutorials and Practicals: Wednesdays, DH2020, UTM, 1-2pm
Discussion board and announcements will take place on Quercus
Anonymous feedback form for suggested improvements
Course Syllabus

Course Description

This course will broadly cover the following areas:

  • Kinematics and Dynamics: how can we model robotic systems using approximate physical models that enable us to make predictions about how robots move in response to given commands?
  • Feedback Control and Planning: how can we compute the state-(in)dependent commands that can bring a robotic system from its current state to a desired state?
  • Mapping: how can we combine noisy measurements from sensors with the robot’s pose to build a map of the environment?
  • State Estimation: the state of the robot is not always directly measurable/observable. How can we determine the relative weighs of multiple sensor measurements in order to form an accurate estimate of the (hidden) state?
  • The Geometry of Computer Vision: how can modeling pixel projections on an RGB camera help us infer the 3D structure of the world? How can we triangulate points seen from two cameras? How can we estimate the camera’s pose (and therefore the robot’s) while it is moving in the environment?

Schedule

Week Date Lecture Tutorial/Practical Slides Reading
1 Sep 5 Introduction
Motivation, logistics, rough description of assignments, sense-plan-act paradigm.
Syllabus, Quiz 0 (Introduction, Background, Expectations)

Sensors and Actuators
Camera, LiDAR, tactile, IMU, depth, GPS, Hall-effect sensors, encoders, RGBD. Pulse-Width Modulation. Motors.

None



pdf, pptx
Dudek & Jenkin 3.1.1,4, 3.2-3, 4.1-8, 4.10, 5.1.1
Optional: Mike Langer's notes
2 Sep 12 Kinematics
Frames of reference. Rotation representations. Homogeneous coordinates and transformations. Rigid body motion.

Dynamics
Dynamical systems and control. Examples: Dubins car, differential drive car, unicycle, pendulum, cartpole, quadcopter. Holonomic vs. non-holonomic systems.

Intro to ROS pdf, pptx



pdf, pptx

Paul Furgale: robot pose
Lavalle 13.1
Dudek & Jenkin 3.1.5,6
3 Sep 19 PID Control
Tuning, cascading PID, advantages and drawbacks.

Artificial Potential Fields and Obstacle Avoidance
Implementation issues, navigation functions. Vector-field histogram (VFH), dynamic window approach (DWA).

Linear algebra refresher pdf, pptx



pdf, pptx
Optional: Astrom and Hagglund, Ch. 2

Lavalle Ch. 8.4
Dudek & Jenkin 6.3.4
Optional: Howie Choset's notes
4 Sep 26 Linear Quadratic Regulator (LQR)
Computing optimal actions for linear dynamical systems with quadratic cost-to-go functions.


Probability refresher pdf, pptx, code Optional: Stephen Boyd's LQR notes and examples
5 Oct 3 Planning
Dijkstra, A*, Rapidly-exploring Random Trees (RRT), Probabilistic RoadMaps (PRM)
Intro to numpy, Implementing LQR pdf, pptx pdf, pptx Blog post on A*
Udacity Lesson 4
Lavalle 5.5, 5.6
6 Oct 10 Map Representations and Map Alignment
Occupancy grids, Octrees, Voronoi Graph, Homotopy Classes. Map alignment with known or unknown correspondences. Iterative Closest Point (ICP).


Occupancy Grid Mapping With Known Robot Poses
Log-odds ratio, Probabilistic dynamics and measurement models, Bayesian estimation.

Function approximation with numpy pdf, pptx



pdf, pptx
Pieter Abbeel's notes Pieter Abbeel's notes
Probabilistic Robotics Ch. 2 and Ch. 9
Oct 17 Reading week



7 Oct 24 Maximum Likelihood, Least Squares Estimation, Maximum A Posteriori Estimation
Least squares as a special case of maximum likelihood estimation on Gaussian models.

GraphSLAM
Expectation and Covariance. Geometric interpretation of the covariance matrix. Nonlinear Least Squares formulation of the Simultaneous Localization And Mapping (SLAM) problem.

Demonstrating gMapping pdf, pptx


pdf, pptx
Udacity Lesson 6
Probabilistic Robotics Ch. 11
8 Oct 31 Kalman Filter
Bayes' rule on Gaussian distributions. Example of 1D Kalman Filter.

Bayes' Filter and Kalman Filter
Kalman Filter as a special case of Bayes' Filter. Examples of 2D and 4D Kalman Filter. General prediction and update equations.

pdf, pptx Udacity Lesson 2
Kalman Filter, Illustrated, Probabilistic Robotics Ch. 2,3
9 Nov 7 Extended Kalman Filter (EKF)
Bayes' Filter and nonlinear transformations. Monte Carlo sampling vs. Linearization. EKF prediction and update equations. Examples: EKF Localization and EKF SLAM.


Basic Kalman Filter implementation pdf, pptx Cyrill Stachniss' intro to EKF
Cyrill Stachniss' intro to EKF-SLAM
Probabilistic Robotics Ch. 2,3
10 Nov 14 Particle Filter
Representing multimodal distributions. Particle propagation and resampling. Pathologies of particle filter. Importance Sampling. Examples: Markov localization in a known map. FastSLAM.

pdf, pptx Udacity Lesson 3
Optional: Thrun's paper on PF
11 Nov 21 Camera Optics and Multi-view Geometry
Pinhole cameras, lenses, perspective projection. Aperture, focal length, exposure time, depth-of-field. Structure from Motion.
pdf, pptx Optional: James Tompkin's notes
12 Nov 28 Visual odometry and Visual SLAM
Epipolar constraints. Depth from stereo disparity for parallel cameras. Triangulation as a least-squares problem. Scale issues in visual odometry with a single camera. Visual SLAM vs. structure from motion.
pdf, pptx Optional: James Tompkin's notes on stereo and SfM.
Sanja Fidler's notes on depth from stereo
13 Dec 5-6 Study break, beginning of exams
Review for final exam

Assignments

Marking scheme

Recommended, but optional, textbooks

Self-Driving RC Cars

We are in the process of incorporating 5 RC-cars with navigation sensors (Intel Realsense RGBD cameras, Hokuyo 2D LiDAR, IMU) and onboard computing (NVIDIA Jetson Xavier) into the course assignments. We bought these cars from the RACECAR/J team, and we are currently assembling them. We will very likely have them ready by the second half of the semester. Stay tuned!



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