Underactuated Robotics

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

Russ Tedrake

© Russ Tedrake, 2022
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Note: These are working notes used for a course being taught at MIT. They will be updated throughout the Spring 2022 semester. Lecture videos are available on YouTube.

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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
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