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

© 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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This chapter is intended to provide a collection of tips and formulations that can make seemingly non-smooth constraints smooth, seemingly non-convex constraints convex, etc. (It's very much a work in progress...)

Imagine an ellipsoid centered at the origin: $E = \{x | x^T S x \leq
1\}$ with $S=S^T\succ0$. The volume of this ellipse is proportional to
$\left(\det S^{-1} \right)^\frac{1}{2}$. We know that $\log\det(S)$ is a
concave function in the elements of $S$

maximizing volume.

minimizing volume.

volume of a semi-algebraic set. (via a contained ellipsoid)

- "Convex Optimization", Cambridge University Press , 2004. ,

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