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Robotics 501: Mathematics for Robotics
- amelius 5y agoThis may be a fine course, but there seems to be nothing specific to robotics here. Not even control theory.
- quanto 5y agoThis 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.
- ska 5y agoI 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.
- ianai 5y ago“ local vs global convergence in nonlinear optimization”?
- wcunning 5y agoThis 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.
- Ostrogodsky 5y ago
- overkalix 5y agoSeems a pretty standard linear algebra course, nothing that justifies the title...
- funnym0nk3y 5y agoIt seems very shallow too.
- erwincoumans 5y agoSee also the Modern Robotics course videos: https://youtube.com/playlist?list=PLggLP4f-rq02vX0OQQ5vrCxbJrzamYDfx https://youtube.com/playlist?list=PLggLP4f-rq02vX0OQQ5vrCxbJ... and free book: http://hades.mech.northwestern.edu/index.php/Modern_Robotics http://hades.mech.northwestern.edu/index.php/Modern_Robotics It also has a github repo: https://github.com/NxRLab/ModernRobotics https://github.com/NxRLab/ModernRobotics
- hcrisp 5y agoModern 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?
- gmadsen 5y agoId 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
- biotinker 5y agoI 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/ https://www.viam.com/ [1] https://link.springer.com/chapter/10.1007/978-1-4899-7560-7_2 https://link.springer.com/chapter/10.1007/978-1-4899-7560-7_...
- erwincoumans 5y agoBTW, we use Featherstone algos too (ABA, RNEA, CRBA etc) but use URDF to describe our robots.
- 5y ago
- pfortuny 5y agoHonest 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 a Linear Algebra course because it gives a clear-cut description of a linear map and the meaning of eigenvalues/eigenspaces, etc. Anyone cares to share? Thanks in advance.
- funnym0nk3y 5y agoWell, I'm currently in my masters in electrical engineering in Germany and we are taught the same stuff. We even have a mandatory course about basic numerical algorithms. What exactly I can do with that I don't know
- pfortuny 5y agoYes, 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: these are going to become obsolete very fast, whereas the geometric/qualitative/quantitative insights of theoretical results are what give you understanding. Thanks for the feedback.
- Archit3ch 5y ago> 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.
- 5y ago
- baking 5y agoOne 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."
- mishftw 5y agoProf 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.
- addcninblue 5y agoGenuinely curious: How does real analysis apply to robotics?
- pfortuny 5y agoThe very notions of continuity and extrema allow you to, for instance, tell if a mechanism is in general position or in a special case.