This dissertation is concerned with a space robot consisting of a rigid platform, two articulated flexible arms and a rigid end-effector. The task is to ferry some payload and to dock smoothly with an orbiting target whose motion is either known or not known a priori. The dynamical equations for planar motion of the space robot are derived by means of Lagrange’s equations. They are then separated into two sets of equations suitable for rigid-body maneuver control design and vibration suppression control design. A perturbation method is used when the target motion is known a priori and direct partitioning is used when the target motion is not known. Both approaches are under the assumption that maneuver motions are much larger than elastic motions. As far as the rigid-body maneuver control is concerned, optimal trajectory planning is carried out off-line by means of the global optimization method under the assumption that the target motion is known a priori. In contrast, when the target motion is not known a priori, on-line feedback tracking control is carried out by means of an algorithm based on Liapunov-like methodology and using on-line measurements of the target motion. As far as the vibration suppression control is concerned, the use of the piezoelectric sensor/actuator pairs dispersed along the flexible arms is proposed. Collocated sensors/actuators for vibration control exhibit good performance. The actuators are designed to compensate for the disturbances caused by the rigid-body maneuver and to realize the LQR feedback control. Assuming that the number of actuators along each flexible arm is equal to the number of modes used to model the beam, the LQR control design is based on a linear time-varying system without persistent disturbances. Problems related to the digital implementation of the control algorithms are also discussed. Some undesirable effects, such as the bursting phenomenon and even system instability, can occur if the control algorithms are realized in discrete-time. To prevent these problems, the modified discrete-time control schemes are developed. Numerical examples are used to demonstrate the control algorithms. / Ph. D.