# Robot Dynamics

MIT 6.821: Underactuated Robotics

Spring 2024, Lecture 1

(or later at https://slides.com/russtedrake/spring24-lec01)

## Course Info

Instructor: Russ Tedrake

TAs:

• Jaehun Choe
• Savva Morozov
• Peter Werner

Website:

Email:

underactuated-staff@mit.edu

Cassie by Agility Robotics

T-HR3 by Toyota

ANYmal C by ANYbotics

Spot by Boston Dynamics

## Goals for the class

• Bring together tools from:
• Nonlinear dynamics
• Optimization
• Control
• Machine learning

• Rigorous thinking about "model systems"
• Algorithmic toolkit for more complex systems

Current enrollment:

## Prerequisites

Robotics (e.g. kinematics, ...), Dynamics, Control, Optimization, Learning are not explicit prerequisites.

But the course is not easy. We'll make heavy use of:

• Linear algebra
• Differential Equations
• Python
• Neural Network jargon

If you were to add one subject to your reading list, it would be optimization.  References on website FAQ.

## Goals for the class

• Bring together tools from:
• Nonlinear dynamics
• Optimization
• Control
• Machine learning

• Rigorous thinking about "model systems"
• Algorithmic toolkit for more complex systems
\begin{aligned} (m_1 + m_2) l_1^2 \ddot{q}_1& + m_2 l_2^2 (\ddot{q}_1 + \ddot{q}_2) + m_2 l_1 l_2 (2 \ddot{q}_1 + \ddot{q}_2) c_2 \\ &- m_2 l_1 l_2 (2 \dot{q}_1 + \dot{q}_2) \dot{q}_2 s_2 + (m_1 + m_2) l_1 g s_1 + m_2 g l_2 s_{1+2} = \tau_1 \\ m_2 l_2^2 (\ddot{q}_1 + \ddot{q}_2)& + m_2 l_1 l_2 \ddot{q}_1 c_2 + m_2 l_1 l_2 \dot{q}_1^2 s_2 + m_2 g l_2 s_{1+2} = \tau_2 \end{aligned}
{\bf q} = \begin{bmatrix} \theta_1 \\ \theta_2 \end{bmatrix}
\frac{d}{dt}\frac{\partial L}{\partial \dot{q}_i} - \frac{\partial L}{\partial q_i} = Q_i

Troody by Pete Dilworth (MIT Leg Lab)

3D Passive-Dynamic Walker by Steve Collins and Andy Ruina (used w/ permission)

"Tour of the MIT Leg Lab"
(used w/ permission from Marc Raibert)

http://world.honda.com/ASIMO/video/

https://en.wikipedia.org/wiki/Stall_(fluid_dynamics)

http://mendobrew.com

http://www.davewalshphoto.com

J Exp Biol October 2012 vol. 215 no. 20 3603-3611

from George Lauder and Mike Triantafyllou (Liao et al, 2003)

By russtedrake

# Lecture 1: Welcome to Underactuated Robotics

MIT Underactuated Robotics Spring 2024 http://underactuated.csail.mit.edu

• 808