One minute in to the first lecture: "We do theorems and proofs every single day, even today, and we never see anything practical on a robot."
Robotics 501: Mathematics for Robotics
21–30 of 64 posts
Re: Robotics 501: Mathematics for Robotics
#22Honest 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…
Pay attention to all of the answers you're receiving. It's like they're coming from the University itself! Not one single concrete example of where someone has used GJ in the field, just a bunch of the same excuses and hypotheticals regurgitated in different ways.
Re: Robotics 501: Mathematics for Robotics
#23This may be a fine course, but there seems to be nothing specific to robotics here. Not even control theory.
This is a class in the Robotics program at University of Michigan, which has a long and deep history in control theory and related topics. The detail you're missing is that the control theory classes are for both Robotics students and general EE's, ME's, Aerospace Engineers, etc, so they're not going to get combined with this. The thing this lets people avoid is the EE linear systems theory class, which broadly covers the same topics, probably along with the EE intro to probability class, since that's more for full on signal processing or stochastic control. It fits in nicely with the other curriculum components, just not as a general purpose math for robotics for a non-program student.
Re: Robotics 501: Mathematics for Robotics
#24This may be a fine course, but there seems to be nothing specific to robotics here. Not even control theory.
This is my disappointment as well. Mathematics for robotics is quite challenging due to control theory and non-linear optimization, which do not seem to be the focus of this course.
I suspect this is a prerequisite course for the ones that are more topical.
I'm not familiar with this particular department approach, but scanning the syllabus it seems like a pretty standard introductory "leveling" course you use in a graduate program taking in students from lots of different undergrad degrees.
Re: Robotics 501: Mathematics for Robotics
#25See 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?
Re: Robotics 501: Mathematics for Robotics
#26One minute in to the first lecture: "We do theorems and proofs every single day, even today, and we never see anything practical on a robot."
Prof Grizzle is very much about practical learning and has a pretty good sense of humor too.
When I did undergrad at Michigan, I got the sense he was one of those exceptional profs who knows what they're doing + truly cares about the non-academics.
Re: Robotics 501: Mathematics for Robotics
#27Honest 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…
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
Re: Robotics 501: Mathematics for Robotics
#28See 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?
Id say by leaps and bounds DH
software in companies needs to be as easy to explain as possible to the widest audience.
very few people have a firm understanding of exponential maps
Re: Robotics 501: Mathematics for Robotics
#29Honest 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…
*Replying to the answers received as of 17:02 20220127 GMT+1.*
Thanks A HUGE LOT to all and sundry for taking the time.
I am the first one to understand that theory is the only way to really grasp a problem (this is why differential equations and calculus and linear algebra are key in the education of an Engineer). This is something I guess all of you agree on (as a matter of fact, I am a pure mathematician by education).
My problem with *specific algorithms* is that they are deemed to be obsolete, unless they are inherently theoretical. In this sense:
a) Gauss reduction method (some of you have mistaken this for the iterative Gauss-Jordan method, I guess): this is not just a method but a way to understand a linear map (and a system of equations) in a much simpler way, and of getting information by itself (i.e. the eigenvalues). Same for the Jordan decomposition result (but this is a bit overkill to me).
b) Newton-Raphson: the most important use of the "derivative as approximation" that exists, apart from showing the importance of iterations and stability.
c) The condition number, and (in)stability of linear systems: this is a pure theoretical notion (nobody computes the condition number because if you can, then you can also invert the matrix) which has very important *applications as understanding*.
However:
a) Gauss-Jordan (i.e. the iterative method): I understand that it may be good to teach it as a tool to understand convergence and iterations but (you won't believe this): here they ask the students to *perform* iterations of this method BY HAND WITH A CALCULATOR...
b) QR: I never understood teaching this to undergrad engineers (it is just the Gauss reduction method with a little care when your matrix is symmetric). What interest does this have in general for an engineer?
Etc...
Compare the two above with, for instance, the method of integration of rational functions in its most general form, which was taught in Spain in schools of engineering until twenty years ago. Nobody sees this as relevant any more, as it adds absolutely nothing to the understanding of the integral, and is just a waste of time (Wolfram|Alpha does it for free)...
By the way, and you will not believe this either (I have been teaching this course several years by now). Where I work it is *in the first year*. This hurts a lot, as my students have absolutely no way to apply any of this to any engineering problem.
Re: Robotics 501: Mathematics for Robotics
#30Honest 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…
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?