Showing papers by "N.H. McClamroch published in 2004"

Control of a dumbbell spacecraft using attitude and shape control inputs only

Abstract: An elastic dumbbell spacecraft is assumed to consist of two identical mass particles that are connected by a long elastic link. The motion of the dumbbell spacecraft can be described by orbit, attitude and shape dynamics that arise due to gravitational forces, an elastic restoring force along the longitudinal axis of the spacecraft, and control forces that act to change the attitude and shape of the spacecraft. These control forces have the property that there is no net external force on the dumbbell spacecraft. Since the angular momentum of the spacecraft is necessarily conserved, Routh reduced equations of motion are developed that describe the reduced dynamics of the controlled spacecraft. The reduced equations of motion are developed; relative equilibria are determined, and simplified reduced equations, in a linear form, are obtained. These linear reduced equations demonstrate spacecraft controllability properties. It is shown that certain maneuvers, involving a change in orbit, can be accomplished using only attitude and shape control inputs. The proposed framework can be used to study this propulsion force approach to orbital maneuvers.

Local equilibrium controllability of multibody systems controlled via shape change

Abstract: We study local equilibrium controllability of shape controlled multibody systems. The multibody systems are defined on a trivial principal fiber bundle by a Lagrangian that characterizes the base body motion and shape dynamics. A potential dependent on an advected parameter, e.g., uniform gravitational potential, is considered. This potential breaks base body symmetries, but a symmetry subgroup is assumed to exist. Symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter. Based on these properties, sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed. These results are applied to two classes of shape controlled multibody systems in a uniform gravitational field: multibody attitude systems and neutrally buoyant multibody underwater vehicles.