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)}.
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 |