Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Robotics 501: Mathematics for Robotics

github.com

Post reply on HN
Print view View original

31–40 of 64 posts

Re: Robotics 501: Mathematics for Robotics

#31

Post by pfortuny »

PennRobotics wrote: post #13
pfortuny wrote: post #6

Honest question (am a prof. of Maths for engineering at a Spanish Univ. and am wondering about this a lot): What is the point of explaining, say the QR factorization or iterative methods like Gauss-Jordan to engineers ? I think of them as the method of integration of rational functions (the complete method, not the basic cases): totally useless today ... I understand, for example, the Jordan decomposition theorem in…

The most mathematically-relevant stuff I remember was inverse kinematics and using numerical approximation to really cut down on computation when switching between coordinate spaces. This gets more important as the degrees of freedom increase. For instance, you'd like to know that when a state-space matrix is not full rank, you lose some control. In practical terms, a robot arm can usually move in any arbitrary Carte…

Yes, of course, but those are not specific algorithms (except possibly the Gauss reduction method which deserves a special treatment because it is not "just a method of computing" but "a way of understanding" by itself).

Re: Robotics 501: Mathematics for Robotics

#32

Post by pfortuny »

Archit3ch wrote: post #14
pfortuny wrote: post #9

Earlier quoted context omitted.

Yes, that is exactly my issue. It is unlikely you are going to use the Gauss-Jordan method (if you find a linear problem of huge size, you are just going to plug it into Matlab or whatever) and it does really not give you any information on the problem. On the other hand, eigenvectors (and the principal components theorem) do give you an idea. I reckon (as of now) that Theory is much more important than methods : the…

> if you find a linear problem of huge size, you are just going to plug it into Matlab or whatever It depends on your viewpoint. Are you going to be the user who calls the MATLAB function, or the engineer who implements a specific iterative method, optimizes it for new hardware, and so on? I am trying to make the jump into the second category.

No: the person who implements the method is certainly working alongside (or has handy) a say, mathematician/physicist/specialist in numeric computation. I would not ask "just an Engineer" (no offense) to understand how to properly implement such type of methods (mostly because they are full of special cases which require a specialist).

Hope you make the jump to that job, which is surely interesting (and pretty hard).

Thanks.

Re: Robotics 501: Mathematics for Robotics

#33

Post by pfortuny »

slingnow wrote: post #20
pfortuny wrote: post #6

Honest question (am a prof. of Maths for engineering at a Spanish Univ. and am wondering about this a lot): What is the point of explaining, say the QR factorization or iterative methods like Gauss-Jordan to engineers ? I think of them as the method of integration of rational functions (the complete method, not the basic cases): totally useless today ... I understand, for example, the Jordan decomposition theorem in…

The answer is simple: this course is taught at a university, so they have to fill the time with _something_. And if that something is a rote method that lends itself well to testing, even better! It matters little if actual engineers in the field use it (I've done robotics for years, and knowing that Gauss-Jordan exists has helped me precisely zero times).

Come on, do not simplify like this (I am teaching it and precisely because I am worried, I try to fill the course with relevant topics).

Re: Robotics 501: Mathematics for Robotics

#34

Post by gmadsen »

pfortuny wrote: post #30
gmadsen wrote: post #27

Earlier quoted context omitted.

Just want to point out, this is a graduate course(although 1st year). Many students taking it are phd students, who at Michigan can do quite theoretical research. Its not uncommon to take graduate math and cs courses as an engineering phd at Michigan

Yes, I understood that from the 5 at the beginning. OK, so it is not a Masters but something directed to PhD students then?

I wouldn't say that, it is a mix of masters/phd. the robotics department is quite new, the overall curriculum is pretty rigorous mathematically, but also a lot of lab work.

this is more of a catch all to make sure everyone is able to handle the rest of the program, since depending on undergrad school and country, mathematical maturity seems to be a large spectrum for incoming robotics students

Re: Robotics 501: Mathematics for Robotics

#35

Post by biotinker »

hcrisp wrote: post #25
erwincoumans wrote: post #5

See also the Modern Robotics course videos: https://youtube.com/playlist?list=PLggLP4f-rq02vX0OQQ5vrCxbJ... and free book: http://hades.mech.northwestern.edu/index.php/Modern_Robotics It also has a github repo: https://github.com/NxRLab/ModernRobotics

Modern Robotics adopts the Product of Exponentials (PoE) mathematical approach (also known as screw-theoretic) over Denavit-Hartenberg (D-H) for forward kinematics . Do robotics companies use PoE in their written software or is D-H still the practical choice?

I work for Viam[0] and while all of our actual calculations are made using Spatial Vector Algebra[1], inputs can be made in a number of different ways and supporting DH is crucial for allowing pre-existing configurations to be easily brought over to our platform. SVA can also conveniently be easily used for both kinematics and dynamics.

Personally I find SVA way more intuitive than DH or PoE.

[0] https://www.viam.com/

[1] https://link.springer.com/chapter/10.1007/978-1-4899-7560-7_...

Re: Robotics 501: Mathematics for Robotics

#36

Post by Tainnor »

neel_k wrote: post #18
pfortuny wrote: post #6

Honest question (am a prof. of Maths for engineering at a Spanish Univ. and am wondering about this a lot): What is the point of explaining, say the QR factorization or iterative methods like Gauss-Jordan to engineers ? I think of them as the method of integration of rational functions (the complete method, not the basic cases): totally useless today ... I understand, for example, the Jordan decomposition theorem in…

It sort of depends upon the course. This particular syllabus looks like a really standard linear algebra course (I have no idea what is robotics-specific about it), and so of course Gauss-Jordan would show up there. More generally, though, I think there are two main reasons to put algorithms like Gauss-Jordan in the engineering curriculum. 1. While it would be nice to treat linear algebra solvers as a perfect black b…

> 2. Personally, though, I find the topic of numerical stability to be a little bit depressing, since it focuses on all the ways computers don't work!

Maybe a way to more positively reformulate this would be: There is no a priori reason to assume that floating point numbers are well behaved. The fact that we were able to come up with a structure so that it approximates real numbers adequately, that arithmetic operations on it are fast (which they aren't for infinite precision) and that, if we design the algorithms correctly, errors are well-behaved, is an astonishing feat of engineering.

Re: Robotics 501: Mathematics for Robotics

#37

Post by BeetleB »

Archit3ch wrote: post #14
pfortuny wrote: post #9

Earlier quoted context omitted.

Yes, that is exactly my issue. It is unlikely you are going to use the Gauss-Jordan method (if you find a linear problem of huge size, you are just going to plug it into Matlab or whatever) and it does really not give you any information on the problem. On the other hand, eigenvectors (and the principal components theorem) do give you an idea. I reckon (as of now) that Theory is much more important than methods : the…

> if you find a linear problem of huge size, you are just going to plug it into Matlab or whatever It depends on your viewpoint. Are you going to be the user who calls the MATLAB function, or the engineer who implements a specific iterative method, optimizes it for new hardware, and so on? I am trying to make the jump into the second category.

> Are you going to be the user who calls the MATLAB function, or the engineer who implements a specific iterative method, optimizes it for new hardware, and so on?

99% of engineers will be in the former.

Of the remaining 1% who would like to be the ones implementing this stuff, about 90% will not get the job that lets them do it.

Of those who do get that job, likely over 50% of them will hate it.

Speaking as one who's been through all of this.

Re: Robotics 501: Mathematics for Robotics

#38

Post by BeetleB »

pfortuny wrote: post #6

Honest question (am a prof. of Maths for engineering at a Spanish Univ. and am wondering about this a lot): What is the point of explaining, say the QR factorization or iterative methods like Gauss-Jordan to engineers ? I think of them as the method of integration of rational functions (the complete method, not the basic cases): totally useless today ... I understand, for example, the Jordan decomposition theorem in…

Although I agree with your general point, but...

Just recently I solved a problem in two different ways (i.e. two methods that led to an equation of the form Ax=b), and after I'd done that, I wondered if they were merely equivalent. The first thing that popped into my head was to reduce to Row Reduced Echelon Form.

There are probably other ways to show equivalence, but here is one engineer who did use it.

(Albeit for a hobby, not a job).

Sadly, most engineers (including me) do not use on the job over 90% of the math we learn in university. And when I actively did, there were disincentives to do so (e.g. no rewards for using them, culture just doesn't value them, etc).

Re: Robotics 501: Mathematics for Robotics

#39

Post by pfortuny »

BeetleB wrote: post #38
pfortuny wrote: post #6

Honest question (am a prof. of Maths for engineering at a Spanish Univ. and am wondering about this a lot): What is the point of explaining, say the QR factorization or iterative methods like Gauss-Jordan to engineers ? I think of them as the method of integration of rational functions (the complete method, not the basic cases): totally useless today ... I understand, for example, the Jordan decomposition theorem in…

Although I agree with your general point, but... Just recently I solved a problem in two different ways (i.e. two methods that led to an equation of the form Ax=b), and after I'd done that, I wondered if they were merely equivalent. The first thing that popped into my head was to reduce to Row Reduced Echelon Form. There are probably other ways to show equivalence, but here is one engineer who did use it. (Albeit for…

Yes, but that method is much more than “a method”, as I explain in my other reply.

Thanks though!

Re: Robotics 501: Mathematics for Robotics

#40

Post by pfortuny »

gmadsen wrote: post #34
pfortuny wrote: post #30

Earlier quoted context omitted.

Yes, I understood that from the 5 at the beginning. OK, so it is not a Masters but something directed to PhD students then?

I wouldn't say that, it is a mix of masters/phd. the robotics department is quite new, the overall curriculum is pretty rigorous mathematically, but also a lot of lab work. this is more of a catch all to make sure everyone is able to handle the rest of the program, since depending on undergrad school and country, mathematical maturity seems to be a large spectrum for incoming robotics students

OK, thanks!
Post reply on HN