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A full-pose, position and orientation, trajectory-tracking control of kinematically redundant flexible-macro-rigid-micro manipulators is proposed. Redundancy is resolved such that the forces exciting the lowest-frequency 'modal coordinates' of the system are minimized, while imposing a proportional damping on the flexural dynamics, rendering it stable under certain conditions. The simulation results show that the initial posture of the manipulator plays an important role in satisfying the foregoing stability conditions. [DOI: 10.1115/1.1870039]

The work reported here was motivated by the development of manipulator systems comprising one long-reach, flexible-link subsystem, termed the macromanipulator, and a short-reach, rigid-link subsystem, called the micromanipulator. The flexural states of the macromanipulator, needed for controlling such systems effectively, are not usually measurable directly. For this reason, a state-estimation algorithm is proposed which uses the velocity and angular-velocity data of the micromanipulator base to estimate the flexural states of the macromanipulator. The velocity data are inferred from the acceleration signals delivered by a kinematically redundant set of triaxial accelerometers. The accelerometer signals are also utilized to calculate the translational and angular accelerations of the micromanipulator base, which are, in turn, used along with the dynamics equations of the micromanipulator to obtain the reaction force and moment acting between the two subsystems. Treating the force and the moment as inputs, the dynamics equations of the macromanipulator alone are used in the observer, thus reducing the order of the dynamics model. The state-output relations, on the other hand, are linearized in closed form to lower the computational cost. The relations thus obtained are then used in an extended Kalman filter to estimate the flexural states of the system. Index Terms--Flexible manipulator, flexural coordinates, linearized kinematics, macro-micro manipulator, state estimation, twist vector.

Using an order N Lagrangian formulation, the paper studies attitude control of a rigid platform supporting a flexible tether connected to a rigid satellite. The system, in an arbitrary orbit, is free to undergo three-dimensional motion in both rigid and flexible degrees of freedom. As can be expected, the governing equations of motion, in general, are highly nonlinear, nonautonomous, and coupled, and are amenable only to numerical integration. The control is achieved through time dependent offset of the tether attachment point, as determined through the Liapunov method, thus providing regulated amount of tether tension induced damping moment. Results suggest that the controller is quite successful in stabilizing the platform about its nominal equilibrium position in a few orbits, even in the presence of relatively large disturbances. Furthermore, extensive parametric study suggests that the controller is quite versatile in imparting any desired orientation to the platform. This would enable the system to undertake diverse missions aimed at communications, launch and retrieval of spacecraft, monitoring the Earth's environment, planetary, and galactic observations, etc.