Abstract¶
A large part of the recent progress in robotics has sided with advances in machine learning, optimization and computer vision. The objective of this course is to introduce the general conceptual tools behind these advances and show how they have enabled robots to perceive the world and perform tasks ranging, beyond factory automation, to highly-dynamic saltos or mountain hikes. The course covers modeling and simulation of robotic systems, motion planning, inverse problems for motion control, optimal control, and reinforcement learning. It also includes practical exercises with state-of-the-art robotics libraries, and a broader reflection on our responsibilities when it comes to doing research and innovation in robotics.
Materials¶
Assignment notebooks for this class are available on GitHub:
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Assignments |
Lecture materials marked below with an open-book icon 📖 link directly to the corresponding lecture page on this site. Those marked with a closed-book icon 📕 are password-protected for enrolled MVA students. To request those, you can reach out to the corresponding lecturer directly.
1. Introduction to robotics¶
This first lecture is a general introduction of modeling robotic systems. We review basic notions of control theory to describe the evolution of dynamical systems and introduce standard robot dynamics concepts.
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Slides: Introduction to robotics |
Lecturer: Justin Carpentier.
2. Kinematics and rigid transformations¶
Robotics is about producing motion. We now dive into the mathematical representation of robots (articulated systems of rigid bodies) and their motions (relative transforms and generalized velocities of these rigid bodies).
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Materials: Kinematics and rigid transformations |
Lecturers: Silvère Bonnabel and Stéphane Caron.
Topics:¶
- Rotations: SO(3)
- Angular velocities: so(3)
- Rigid-body transforms: SE(3)
- Rigid-body velocities: se(3)
References:¶
- A mathematical introduction to robotic manipulation, Murray, Li and Sastry (2017).
- Lie Groups for 2D and 3D Transformations, Ethan Eade (2017).
- Modern Robotics: Mechanics, Planning, and Control, Lynch and Park (2017).
- To go further: A micro Lie theory for state estimation in robotics, Solà et al. (2021).
- To go even further: An introduction to optimization on smooth manifolds, Boumal (2023).
3. Simulation¶
In this course, we will introduce optimal control and dynamics simulation. We will review the fundamuntal principles (Prontryagin maximum principle and Hamilton-Jacobi-Bellman equations) and their derivation in the context of numerical applications (constrained optimization, differentiable dynamic programming).
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Slides: Simulation |
Lecturer: Justin Carpentier.
Topics:¶
- Optimal control and calculus of variations
- Prontryagin principles and Hamilton-Jacobi-Bellman equations
- Trajectory optimization
- Differential dynamic programming
- Model predictive control
- Distinction between OC and MPC?
References:¶
- Calculus of variations and optimal control theory: a concise introduction, Liberzon (2011).
- Contrôle optimal: théorie & applications, Trélat (2005).
- Model predictive control: theory, computation, and design, Rawlings, Mayne & Diehl (2017).
4. Perception and estimation¶
In this lecture, we will start by briefly describing the sensors that are used by robots to perceive their environment and self-localize in it, namely IMUs, cameras, point clouds, and absolute position measurements (GPS outdoors, motion capture indoors). We will introduce the sensor fusion problem for dynamical systems and its optimal solution in the linear case: the Kalman filter. We will then turn to the nonlinear case and its tools: EKF, Invariant EKF, factor graphs.
As praticle exercises, we will first start with simple wheeled robot localization in 2D, and then move to the principles behind the recent contact-aided invariant EKF for legged robot, and also simultaneous localization and mapping (SLAM) and the MSCKF for visual inertial odometry (VIO).
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Slides: Perception and estimation |
Lecturer: Sivlère Bonnabel.
Topics:¶
- Estimation theory
- Kalman filtering, Invariant Kalman filtering
- SLAM, visual inertial odometry
- Sensors (inertial, visual)
References:¶
- State Estimation for Robotics, Barfoot (2017).
- Bayesian filtering and smoothing, Särkkä (2013).
5. Motion planning¶
This lecture is about motion planning, the problem of finding feasible continuous motions between two robot configurations that may be quite far away or require careful execution, such as navigating between obstacles. We will recall the concepts of configuration space and workspace, then discuss state-of-the-art sampling-based algorithms. We will cover the cases of non-holonomic vehicles and manipulation. In the tutorial session, we will implement motion planning algorithms on a robotic arm scenario.
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Slides: Motion planning |
Lecturer: Stéphane Caron.
Topics:¶
- Configuration space
- Randomized algorithms: PRM and RRT
References:¶
- Robot Motion Planning and Control, Laumond (Ed.) (1998).
- Planning algorithms, LaValle (2006).
6. Optimal control¶
In this course, we will introduce optimal control and dynamics simulation. We will review the fundamuntal principles (Prontryagin maximum principle and Hamilton-Jacobi-Bellman equations) and their derivation in the context of numerical applications (constrained optimization, differentiable dynamic programming).
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Slides: Optimal control |
Lecturer: Justin Carpentier.
Topics:¶
- Optimal control and calculus of variations
- Prontryagin principles and Hamilton-Jacobi-Bellman equations
- Trajectory optimization
- Differential dynamic programming
- Model predictive control
- Distinction between OC and MPC?
References:¶
- Calculus of variations and optimal control theory: a concise introduction, Liberzon (2011).
- Contrôle optimal: théorie & applications, Trélat (2005).
- Model predictive control: theory, computation, and design, Rawlings, Mayne & Diehl (2017).
7. Reinforcement learning for legged robots¶
In this lecture, we will outline recent breakthroughs of reinforcement learning in real-robot locomotion and manipulation. We will step through the technical decisions in training pipelines, and describe the state-of-the-art toolbox for transferring simulation-trained policies to real robots.
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Materials: Reinforcement learning for legged robots |
Lecturer: Stéphane Caron.
Topics:¶
- Partially-observable Markov decision process (POMDP)
- Goal of reinforcement learning
- Model, policy, value function
- Policy optimization: REINFORCE, policy gradient, PPO
- Application to robotics: domain randomization, Markov property, "rewArt"
References:¶
- Reinforcement learning: An introduction, Sutton & Barto (2018).
- Learning quadrupedal locomotion over challenging terrain, Lee, Hwangbo, Wellhausen, Koltun & Hutter (2020).
8. Responsible robotics¶
What is Ethics, how does it work and what are your obligations when it comes to doing research and innovation in robotics? After a bit of history and a review of major aspects related to responsible robotics, we'll work through examples such as self-driving vehicles.
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Slides: Responsible robotics |
Lecturer: Pierre-Brice Wieber.
Topics:¶
- Human agency and oversight
- Technical robustness and safety
- Environmental and societal well-being
- Accountability
Discussion ¶
You can subscribe to this Discussion's atom feed to stay tuned.
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Alouane
Posted on
Hello I wonder wether it is possible to have copy of the courses you are providing in this website. Actually, i need those courses to widen my knowledge in robotics Thanks
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Stéphane
Posted on
Thank you for your interest. The materials marked with the open-book icon 📖 are accessible directly on this site, while the ones marked with the closed-book icon 📕 are password-protected for enrolled MVA students. If you'd like access to those, you can reach out to the corresponding lecturer directly. (I have updated the Materials section at the top to reflect this, thank you for your feedback.)
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