49:35 Can someone teach me why a fully-actuated system can be equivalent to a double integrator (q''=u) ? This means the input u (torque) can directly equal to the second differential of output q (position)? Thanks!
As I understood, If you have a fully-actuated system, that means you can get u from q'' = f1(q,q',t) + f2(q,q',t)u in form u = f2^-1(q,q',t)(q'' - f1(q,q',t)). And now, taking the last equation, you can "change" q'' to any control you want (f.e u*) and passing u to the first equation get q'' = u*, meaning you can fully control accelerations. You can find more info in lecture notes (underactuated.csail.mit.edu/intro.html#section3)
This class (Underactuated Robotics) is officially a grad class; the other class I teach (Robotic Manipulation) is both undergrad and grad, so starts more slowly. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-v04rn86Dehg.html .
@@rtedrake I see, Thank you! Also, do you think you could recommend some textbooks that are for total beginners (from scratch) that are either PDF or available on amazon now
