In this paper, we present an integrated robotic arm with a flexible endoscope for laparoscopy. The endoscope holder is built to mimic a human operator that reacts to the surgeon's push while maintaining both the incision opening through the patient's body and the center of the endoscopic image. An impedance control algorithm is used to react to the surgeon's push when the robotic arm gets in the way. A modified software remote center-of-motion (RCM) constraint formulation then enables simultaneous RCM and impedance control. We derived the kinematic relationship between the robotic arm and line of sight of the flexible endoscope for image center control. Using this kinematic model, we integrated the task control for RCM and surgeon cooperation and the endoscope image centering into a semi-autonomous system. Implementation of the control algorithm with both matlab simulation and the HIWIN RA605-710 robotic arm with a MitCorp F500 flexible endoscope demonstrated the feasibility of the proposed algorithm.