This paper presents an innovative guidance and control method for a space manipulator that actively maneuvers its base to hold a tumbling object stationary relative to the base during proximity operations. This simplifies motion planning, reduces collision risk, and enables impact-free capture using single- or multi-arm configurations, with or without predefined grasping interfaces. The proposed approach involves two phases. In the pre-grasping phase, a synchronization control aligns the target's center of mass (CoM) with the system's instantaneous center of rotation (ICR), virtually rigidizing the target-servicer system to keep the object stationary for reliable grasping. In the post grasping phase, a control strategy based on Hamiltonian dynamics and optimal control stabilizes the combined system by minimizing time, fuel, or energy, while respecting base torque limits and multiple grasping constraints. For structured targets, applied forces and torques stay within their bounds; for unstructured ones, friction constraints prevent slipping. A case study demonstrates the method's effectiveness in enabling both the subsequent grasping and detumbling phases.

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