Reorientation of Space Mu Ltib

The problem of reorientation of planar multibody systems in space with angular momentum preserving controls is studied. We consider rest-to-rest maneuvers for the absolute orientation of a multibody system which maintains zero angular momentum. We propose a control strategy for a system which is composed of (1) N planar rigid bodies interconnected by ideal pin joints in the form of an open kinematic chain, (2) joint torque motors which actuate the motions at the joints. The control strategy uses holonomy or geometric phase relationships. A key observation is that the holonomy, the extent to which a loop in the shape space (relative angle space) fails to be lifted t o the configuration space (absolute angle space), depends only on the path traversed in the shape space and not on the time history of the joint angular velocities. The control strategy first transfers a given initial condition to the origin of the shape phase space. The control strategy then causes the state to track a loop in the shape space that achieves the desired holonomy. A feedback controller which implements this strategy thus accomplishes the desired objective. The proposed strategy is demonstrated by computer simulations of a three-link example. The theory developed in the paper is applicable to a variety of multibody control problems in space, including space robotics, astronaut maneuvers, satellite antenna deployment, etc., which are briefly described.