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kiuhnm

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*popular*way (e.g. from Boothby's book)?

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- Geometry
- Thread starter kiuhnm
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kiuhnm

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May I ask how differential geometry is needed for robotics?(I need it for robotics)

- #3

kiuhnm

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Anyway, I don't like Vargas's book. It's almost unreadable because the author refers to concepts before defining or explaining them. I'm reading Victor Guillemin's notes right now and I like them.

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May I ask how differential geometry is needed for robotics?

There could be a few ways- motion of a jointed arm (for example), involves coordinate transformations. Trying to move a tool along a prescribed path is another. I've seen differential geometry appear in gear theory as well:

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19900010277.pdf

- #6

kiuhnm

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May I ask how differential geometry is needed for robotics?

I'm focusing on underactuated robotics which is related to nonholonomic mechanics. I've been ignoring the dynamics part so far because I've been using Reinforcement Learning, which is basically an approach where an agent figures out on its own how to maximize a reward signal. If the reward signal indicates how fast an agent is running, then the agent will learn how to run (with mixed results because of bad local minima).

That approach is very promising but I think it's not enough so I want to learn about dynamics and see if dynamics and mechanics can inform the RL algorithms in a useful way.

Here's the most recent and complete book I could find about nonholonomic mechanics: https://www.amazon.com/dp/1493930168/?tag=pfamazon01-20

It looks pretty advanced so I need to do some background study. Goldstein's book is a classic but I think that José & Saletan or Fasano & Marmi are better suited for my purpose, being more mathematical.

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In my experience (I am a theoretical physicist) "more mathematical" usually means more abstract, and hence less applicable. Abstraction is good for understanding the big picture, but not for solving specific practical problems. Nevertheless, you certainly know better what is better suited for you.Goldstein's book is a classic but I think that José & Saletan or Fasano & Marmi are better suited for my purpose, being more mathematical.

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- #8

kiuhnm

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In my experience (I am a theoretical physicist) "more mathematical" usually means more abstract, and hence less applicable. Abstraction is good for understanding the big picture, but not for solving specific practical problems. Nevertheless, you certainly know better what is better suited for you.

I think one should learn enough math to be able to read and understand most papers and books relevant to its field. For instance I had to learn some measure theory just to be able to read some overly mathematical papers and that certainly paid off.

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