×

Stabilization of relative equilibria. II. (English) Zbl 1056.70514

Summary: We obtain feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We use a notion of stability ‘modulo the group action’ developed by G. W. Patrick [J. Geom. Phys. 9, No. 2, 111–119 (1992; Zbl 0761.58017)]. We deal with both internal instability and instability of the rigid motion. The methodology is that of potential shaping, but the system is allowed to be internally underactuated, i.e., have fewer internal actuators than the dimension of the shape space.
Part I, IEEE Trans. Autom. Control 45, No. 8, 1483–1491 (2000; Zbl 0985.70015)}.

MSC:

70Q05 Control of mechanical systems
70K20 Stability for nonlinear problems in mechanics
93D15 Stabilization of systems by feedback
PDFBibTeX XMLCite
Full Text: DOI