The present study deals with a trajectory control of a space-based variable geometry manipulator interconnected by an arbitrary number of modules, each with two flexible links: one of them free to slew (revolute joint); and the other deployable (prismatic joint). The mobile character provides some additional versatility to the system: favorable obstacle avoidance, small inertia coupling effects, no singular configurations, and so on. First, the outline of derivation procedure of the dynamical equations for the system is explained using the Lagrangian principle. The obtained equations are highly nonlinear, nonautonomous and coupled equations in recursive form. This is followed by showing a method of solution for the inverse kinematics using the dynamical equations. Finally, some numerical simulations for the trajectory control of the end-effector are executed using the resolved acceleration control. The simulation results show that the control strategy based on the flexible manipulator model is quite better than the strategy based on the rigid manipulator model.