This paper presents a kinematically constrained planar hybrid cable-driven parallel robot (HCDPR) for warehousing applications as well as other potential applications such as rehabilitation. The proposed HCDPR can harness the strengths and benefits of serial and cable-driven parallel robots. Based on this robotic platform, the goal in this paper is to develop an integrated control system to reduce vibrations and improve the trajectory accuracy and performance of the HCDPR, including deriving kinematic and dynamic equations, proposing solutions for redundancy resolution and optimization of stiffness, and developing two motion and vibration control strategies (controllers I and II). Finally, different case studies are conducted to evaluate the control performance, and the results show that the controller II can achieve the goal better.