Introduction:

Robot Dynamics and Model-based Control

MIT 6.832: Underactuated Robotics

Spring 2021, Lecture 1

Follow live at https://slides.com/russtedrake/spring21-lec01/live

(or later at https://slides.com/russtedrake/spring21-lec01)

Course Info

Instructor: Russ Tedrake

 

TAs:

 

 

 

 

 

Website: http://underactuated.mit.edu

Dongchan Lee

AJ Miller

Eric Chen

Remote Teaching

I want lectures to be interactive.

(synchronous will be better!)

 

Piazza (sign up if you're registered)

Email: underactuated-staff@mit.edu

 

Open to everyone / anywhere:

Remote Teaching

I want lectures to be interactive.

(synchronous will be better!)

 

Please keep your video ON.

Please ask questions!

  • Voice is OK.
  • Chat is OK, too.
  • You will not show up on YouTube.

Remote Teaching

I hope to lecture better than I have before

(by injecting code into your browser!)

 

Simulation experiments during lecture.

 

I'm very open to suggestions / changes

 

Please forgive my experiments, and give me feedback!

The plan for this week (Experiment #1)

  • Right now: Short synchronous lecture (~30 min)
  • Asynchronous:
    • Lecture 1 video + notes
    • Lecture 2 video + notes
  • Thursday: You will each be assigned (via announcement on piazza) to one 30 min slot during normal lecture time.
    • Interactive session (nonlinear dynamics of Hopfield Networks)
    • Ratio will be 5-8 students to one staff
    • If you cannot make the synchronous session, then it will be on your pset.

"It's very impressive, but too bad there is no learning..." 

-- almost every computer scientist that I've talked to.

The plan for this term

Cover most of the core topics from underactuated robotics.

 

But take a deep dive into the topic of learning models and planning / control with learned models.  New lectures on

  • Multibody parameter estimation
  • Learning linear models (subspace identification, DMD)
  • Planning and control with deep network models
  • State estimation / task-relevant models
  • Identification of hybrid systems (e.g. with contact)

The plan for this term

Cover most of the core topics from underactuated robotics.

 

But take a deep dive into the topic of learning models and planning / control with learned models.  

 

a.k.a. "Model-based Reinforcement Learning"

 

  • Particular emphasis on algorithms that exploit structure in your model.

Model-based control

First concern:

Models based on physics may be limited.

 

Second concern:

Robot won't continue to improve.

What is a (dynamic) model?

System

..., u_{-1}, u_0, u_1, ...
..., y_{-1}, y_0, y_1, ...

State-space

Auto-regressive (eg. ARMAX)

input

output

x_{n+1} = f(n, x_n, u_n, w_n, \theta) \\ \quad y_n = g(n, x_n, u_n, w_n, \theta)
y_{n+1} = f(n, u_n, u_{n-1}, ..., \\ \qquad \qquad y_n, y_{n-1}, ..., \\ \qquad \qquad w_n, w_{n-1}, ..., \theta)

state

noise/disturbances

parameters

Lagrangian mechanics,

Recurrent neural networks (e.g. LSTM), ...

Feed-forward networks

(e.g. \(y_n\)= image)

What is a (dynamic) model?

System

..., u_{-1}, u_0, u_1, ...
..., y_{-1}, y_0, y_1, ...

State-space

Auto-regressive (eg. ARMAX)

input

output

x_{n+1} = f(n, x_n, u_n, w_n, \theta) \\ \quad y_n = g(n, x_n, u_n, w_n, \theta)
y_{n+1} = f(n, u_n, u_{n-1}, ..., \\ \qquad \qquad y_n, y_{n-1}, ..., \\ \qquad \qquad w_n, w_{n-1}, ..., \theta)

Model "class" vs model "instance"

  • \(f\) and \(g\) describe the model class.
  • with \(\theta\) describes a model instance.

 

"Deep models vs Physics-based models?" is about model class:

Should we prefer writing \(f\) and \(g\) using physics or deep networks (or both)?

Maybe not so different from

  • should we use ReLU or \(\tanh\)?
  • should we use LSTMs or Transformers?
x_{n+1} = f(n, x_n, u_n, w_n, \theta) \\ \quad y_n = g(n, x_n, u_n, w_n, \theta)

The distinction is not about data...

 

Galileo, Kepler, Newton, Hooke, Coulomb, ...

were data scientists.

They fit very simple models to very noisy data.

Gave us a rich class of parametric models that we could fit to new data.

What if Newton had deep learning...?

Galileo's notes on projectile motion

Model-based control

First concern:

Models based on physics may be limited.

 

Second concern:

Robot won't continue to improve.

 

My view:

Each model class has advantages and challenges.  Let's meet Tuesdays and Thursdays to discuss!

Logistics

  • Students: Make sure you're on Piazza
  • Watch this week's lecture videos (ideally before Thursday)
  • Read/comment on the lecture notes
  • Assignment 1 released tomorrow 
    • Due next Wed. 
    • ~5 PSets throughout the class (approximately biweekly), due Wednesday (any time).
  • Midterm.
  • Final project.  

All details (incl. grading policy) are on the course website.

https://forms.gle/W7mCoKyZnRTmdEJo6