The effective use of robotics in realistic environments requires robots capable of adapting to different task requirements and in terms of motion tracking performance, interaction forces, payload conditions as well as in uncertainties that may occur during the task execution. While impedance control represents an effective control tool to adapt to the different requirements and uncertainties, the online modulation of impedance during the task execution represents a critical prerequisite, yet it remains an open research topic today. In this work, we present a new method, which permits a robot to modulate online the parameters of its impedance taking into account of the requirements of the task to be performed. The method considers the motion tracking performance requested by the task as well as the expected task payload or interaction forces to derive the stiffness parameter that can ensure the desired performance under the required motion and payload conditions. Appropriate damping levels are also derived to ensure the stability of the modulated impedance on the robot. The method is successfully verified on the CENTAURO robot while performing a number of manipulation tasks with different motion requirements, payload, and interaction settings, showing its function in modulating online the impedance parameters of the robot for ensuring the requested performance.