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We incorporate a randomized kinodynamic path planning approach with image-based control of a robotic arm equipped with an in-hand camera. The proposed approach yields continuously differentiable camera trajectories by taking camera dynamics into account, while accounting for a critical set of image and physical constraints at the planning stage. The proposed planner explores the camera state space for permissible trajectories by iteratively extending a search tree in this space and simultaneously tracking these trajectories in the robot configuration space. The planned camera trajectories are projected into the image space to obtain desired feature trajectories which are then tracked using an image-based visual servoing scheme. We validate the effectiveness of the proposed framework in incorporating the aforementioned constraints through a number of visual servoing experiments on a six-degree-of-freedom robotic arm. We also provide empirical results that demonstrate its performance in the presence of uncertainties, and accordingly suggest additional planning strategies to increase robustness with respect to possible deviations from planned trajectories.