A Hybrid Control Framework Using Reinforcement Learning for Dynamic Robotic Manipulation and Sim-to-Real Transfer This paper presents a hybrid control architecture for dynamic robotic picking tasks. The framework combines a Deep Reinforcement Learning policy for high-level interception with a dedicated Inverse Kinematics controller for precise terminal grasping, while mitigating precision limitations of monolithic learning-based approaches. The framework utilizes a Proximal Policy Optimization agent to approach moving targets, seamlessly transitioning to an Inverse Kinematics solver that reduces terminal orientational and positional errors while minimizing cumulative control effort. To facilitate deployment on physical hardware, a robust sim-to-real pipeline incorporating system identification, domain randomization, and latency injection is employed. Experimental results on a physical Franka Emika Panda manipulator validate this hybrid architecture. The system achieves an 80% success rate in pick-and-place tasks, compared to 60.8% for unadapted baselines, with no safety-critical violations such as joint limit breaches or collisions observed during testing.