Wondering how many LMR's are doing the coursera " Control of mobile robots" course. I have been blown away with the global response to the course. It's my first involvement with such a course.I last attempted matices & eigenvalues over 45 years ago. Bit of a challenge now but managing 90 % at the moment. Really adds another dimension to thinking about projects.
Me there as well 
Guys, you’re not alone! :))
I’m there too, and my brain hurts whenever they show all this formulae and matrices and stuff. Also I’m, similarily as Ladvien, taking Calculus One course at the same Coursera. I still find the course very informative and helpfull!
I’m enrolled, but…
Thought I got it - until I made the first test. Now I am a watchmen - like TinHead, Isotope and Ladvien.
I must admit that whenever you want to build a robot that has kinematic abilities it is very useful to have calculus and higher order differential equations at hand to roll-your-own PID controllers. I still want to get better interpreting and inventing these formulaes.
But the level of mathematics in this course is very high. No time to work from simple calculus basics. You must be fluent in calculus and equation solving to be successful. Second order Taylor Aproximation. Laplace Transformation. Binominal Series of higher order differential equations. Quadratic extensions and other tricks to make an implicit formulae to an explicit formulae. The list of necessary skills goes on and on.
There’s been plenty of worry
There’s been plenty of worry about the math on the discussion forum for the class. I’m in the same boat. I forgot all about this stuff years ago.
Still, I took this class to shake the cobwebs off my grey matter, so I’m sticking with it. Just completed the week 4 quiz and got 100% on the 2nd try. The professor said the math will get lighter from here. I hope so.
In other news, I’ve decided to use a Rocket Brand Studios Tadpole as a test bed for the class. I should roll up my sleeves and learn MATLAB, but I’m much happier working with real hardware. I just got PID feedback working for the encoders. I totally used trial and error to pick the gains. Maybe one day I’ll be able to figure the calculations out to do it “right”.
I will post posted my code on a Robot page soon for anyone who wants to follow along.
You don’t really need the math for PID controllers
You can adjust the parameters of a PID controller for simple things like steering by trial and error. Typically, start with P and find a value that gets a response. Usually, whatever you’re controlling will overshoot and oscillate aboout the target position. Introduce a small negative D component and increase it until the oscillations stop. Everything should now work well, except that your device doesn’t quite reach the target position, there’s always a small offset. Fix that by introducing a small I coefficient. Try a few values.
When adjusting the parameters, at first, don’t use small steps. Double or halve whatever you’re adjusting.
You need to be able to dump a trace of what the controlled parameter (heading or whatever) is doing, compared with what it should be doing. Plot the results in Libreoffice or Excel. It’s much easier to sort out what’s happening by looking at a chart than by watching a robot careering all over the place. If you can dump some of the intermediate results at the same time, that will help with debugging.