<p>Laparoscopic surgery is a minimally invasive technique in which internal organs are accessed through small incisions using elongated instruments and an endoscopic camera. The constrained dexterity of the instruments and the absence of direct tactile feedback make precise and safe manipulation challenging, particularly during tool–tissue interaction. This paper develops the dynamic model and a task-space impedance controller for a 4-DOF laparoscopic surgeon robot equipped with a scissor-type grasper and a Leap Motion–based teleoperation interface. A complete Euler–Lagrange formulation is derived for the coupled robot–grasper system, and the corresponding Jacobians are obtained for both translational shaft motion and grasping rotation. The proposed impedance law uses the measured end-effector position to shape the apparent stiffness and damping at the tool tip, aiming to bound interaction forces despite the lack of tactile feedback and thereby reduce the risk of tissue damage. Controller gains are selected using a quantitative performance index that balances trajectory tracking error and joint-torque demand over representative motions. The controller is implemented in MATLAB/Simulink and driven in real time by Leap Motion measurements of hand motion and finger gestures. Simulation and pilot hardware-in-the-loop (HIL) real-time user studies on linear, circular, and rotational trajectories demonstrate improved tracking accuracy and tremor attenuation relative to prior PID-based teleoperation. These preliminary results suggest that the proposed modeling and impedance-control framework may enhance precision and safety in robot-assisted laparoscopic procedures.</p>