Title :
An intrinsic approach to the control of rolling bodies
Author :
Agrachev, Andrei A. ; Sachkov, Yuri L.
Author_Institution :
Steklov Math. Inst., Moscow, Russia
Abstract :
We apply the principal tools of geometric control theory to an intrinsic geometric model of a pair of rolling rigid bodies. The controllability problem is solved completely: in particular, the system is globally controllable if the bodies are not isometric. We also construct a canonical nilpotent approximation of the system, describe its symmetries and express extremals of the corresponding optimal control problem via elliptic functions
Keywords :
control theory; controllability; elliptic equations; functions; geometry; optimal control; rolling; symmetry; canonical nilpotent approximation; controllability; elliptic functions; extremals; geometric control theory; globally controllable system; intrinsic geometric model; nonisometric bodies; optimal control; rolling body control; rolling rigid bodies; symmetry; Bismuth; Control systems; Control theory; Controllability; Motion control; Optimal control; Solid modeling; State-space methods;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.832815
