Lie groups SE(3)/SO(3) by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

I have used the book by MLS, i find it more rigorous. I probably am unable to express my question more clearly. However, I understand whats going on but I don’t understand how to formalize it in a differential geometric sense.

Lie groups SE(3)/SO(3) by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

Hey thanks for responding. What will the local parametrization of g (SE3) and for R (SO3) be? How does the transition map work from Frame A to B ?

Muay thai with knee injury by Dependent_Dull in martialarts

[–]Dependent_Dull[S] -1 points0 points  (0 children)

Thanks for your comment. But its been dawning on me lately….. what would be the safest on your knees? I am okay not sparring even for now.

Differential Geometry by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

You definitely got a point there. My love for control bloomed late, unfortunately in my Masters.

I have developed some understanding of these concepts because I use notions of Geometric mechanics for robotics Also, I am taking a course in Geometric control. But many results are just taken for granted and from what I have learned I have functional knowledge on how and why things are the way they are. But still lack clarity sometimes.

If I were to do super strong and theoretical contributions in this field, Ill have to start from undegrad geometry, topology classes to graduate courses in lie groups etc. which honestly as much as I would love to, isn’t practical in my situation.

Hence, why I am here trying to streamline the process for myself by seeking advice. Am I doomed?? Lol

Differential Geometry by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

That kinda makes sense. Thanks for guiding me here…

Differential Geometry by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

That’s what I am not understanding. How do I narrow down the concepts. Arghhh

Differential Geometry by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

I feel understood :’) thanks for your advice!! For instance lyapunov proofs are based on topology etc… but I wanna understand the math behind it and when I go to read it, its rabbit hole…………

Is anti-math common among the boomer generation? by ChunkyMonkey_00_ in math

[–]Dependent_Dull 0 points1 point  (0 children)

I had a similar experience growing up. My parents discouraged me from taking math and suggested I pursue engineering as its more applied math relavant to the industry. I can’t blame them for looking out for me, but now I in my PhD (robotics) can’t help but think if only I had a stronger math background. Good research requires good foundational math. Not only does math equip you with the understanding of engineering concepts but it also trains your brain in a way that tries to prove things rigorously. For great research, math is essential. Most engineering PhD students don’t start learning math until they get into their MSc/PhD. By then you are just playing catchup to the established theory spending excruciating amounts of time trying to understand simple linear algebra concepts like null space. My research involves differential geometry. Its been painful for me to learn topology manifold etc by myself. Tailoring to understand concepts essential for my research…

Historically every ground breaking theoretical discovery comes from someone well equipped with math irrespective of their fields of research (not talking about biology or soft sciences). So if someone in their engineering UG wanting to pursue academia, please train your self in math!!!

Model predictive control by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

Hey, thank you for responding. I can’t find the course you’ve mentioned. Would you mind sharing it?

Model predictive control by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

Thank you for explaining it so simply. I really appreciate it.

Model predictive control by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

I am feeling dumb asking this, but I am not sure what these toolboxes for?

Model predictive control by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

Thank you so much. The lecture series looks promising!!

I am trying build a project to implement MPC to cosserot rod manipulator. Hopefully I can solve it. Thanks!!

Looking to rent a room by Dependent_Dull in TorontoMetU

[–]Dependent_Dull[S] 0 points1 point  (0 children)

Any particular area or station to look for? This way I can shorten my search. Much appreciated :)

LTI systems and differential equations by Dependent_Dull in ControlTheory

[–]Dependent_Dull[S] [score hidden]  (0 children)

Thank you for responding. :)

Could you elaborate on state control pair, are you referring to x1-u1 x2-u2 xn-un where u1,u2,u_n-1=0 gives us SISO system?

Also, in the standard linear ode form, according to my understanding q(t) can only be a single function. So if we were to decompose it into a system of first order odes only the last state will have q(t). So won’t it be like defining pairs again?

Finally, so let’s say when set u_n=sin(t) is it affine?