Robot Dynamics and Model-based Control

MIT 6.832: Underactuated Robotics

Spring 2022, Lecture 1

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Course Info

Instructor: Russ Tedrake









Alexandre Amice

Lujie Yang

Cassie by Agility Robotics

T-HR3 by Toyota

ANYmal C by ANYbotics

Spot by Boston Dynamics

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)

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

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

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