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<title>Ch. 24 - An Optimization
Playbook</title>
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<h1><a href="index.html" style="text-decoration:none;">Underactuated Robotics</a></h1>
<p data-type="subtitle">Algorithms for Walking, Running, Swimming, Flying, and Manipulation</p>
<p style="font-size: 18px;"><a href="http://people.csail.mit.edu/russt/">Russ Tedrake</a></p>
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© Russ Tedrake, 2022<br/>
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<p><b>Note:</b> These are working notes used for <a
href="http://underactuated.csail.mit.edu/Spring2022/">a course being taught
at MIT</a>. They will be updated throughout the Spring 2022 semester. <a
href="https://www.youtube.com/channel/UChfUOAhz7ynELF-s_1LPpWg">Lecture videos are available on YouTube</a>.</p>
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<chapter class="appendix" style="counter-reset: chapter 3"><h1>An Optimization
Playbook</h1>
<p>Coming soon... a collection of tips and formulations that can make
seemingly non-smooth constraints smooth, seemingly non-convex constraints
convex, etc.</p>
<todo>PQ trick from LQR</todo>
<todo>Hongkai's smooth non-penetration constraints for polygons</todo>
<todo>"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))
</todo>
<todo>Barrier function for friction cones in Grandia 2019, Feedback MPC for
Torque-Controlled Legged Robots.</todo>
<todo>Linearization of the rotation matrix in Real-time Model Predictive
Control for Versatile Dynamic Motions in Quadrupedal Robots</todo>
<todo>Briat15 chapter 1 has some good modeling tricks for LPV systems</todo>
</chapter>
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