Underactuated Robotics

Algorithms for Walking, Running, Swimming, Flying, and Manipulation

Russ Tedrake

© Russ Tedrake, 2021
Last modified .
How to cite these notes, use annotations, and give feedback.

Note: These are working notes used for a course being taught at MIT. They will be updated throughout the Spring 2021 semester. Lecture videos are available on YouTube.

Previous Chapter Table of contents Next Chapter

An Optimization Playbook

Coming soon... a collection of tips and formulations that can make seemingly non-smooth constraints smooth, seemingly non-convex constraints convex, etc.

PQ trick from LQR Hongkai's smooth non-penetration constraints for polygons "Soft" absolute value: $|x|_epsilon \approx \sqrt{x^2 + \epsilon}$. import numpy as np import matplotlib.pyplot as plt x = np.linspace(-2.,2.,101) plt.plot(x, np.sqrt(np.power(x,2) + 0.01)) Barrier function for friction cones in Grandia 2019, Feedback MPC for Torque-Controlled Legged Robots. Linearization of the rotation matrix in Real-time Model Predictive Control for Versatile Dynamic Motions in Quadrupedal Robots Briat15 chapter 1 has some good modeling tricks for LPV systems
Previous Chapter Table of contents Next Chapter