Bio-inspired robotic systems are capable of adaptive learning, scalable control, and efficient information processing. Enabling real-time decision-making for such systems is critical to respond to dynamic changes in the environment. We focus on dynamic target tracking in open areas using a robotic six-degree-of-freedom manipulator with a bird-eye view camera for visual feedback, and by deploying the Neurodynamical Computational Framework (NeuCF). NeuCF is a recently developed bio-inspired model for target tracking based on Dynamic Neural Fields (DNFs) and Stochastic Optimal Control (SOC) theory. It has been trained for reaching actions on a planar surface toward localized visual beacons, and it can re-target or generate stop signals on the fly based on changes in the environment (e.g., a new target has emerged, or an existing one has been removed). We evaluated our system over various target-reaching scenarios. In all experiments, NeuCF had high end-effector positional accuracy, generated smooth trajectories, and provided reduced path lengths compared with a baseline cubic polynomial trajectory generator. In all, the developed system offers a robust and dynamic-aware robotic manipulation approach that affords real-time decision-making.