In this paper, we address the challenge of performing non-prehensile pushing operations with a compliant robotic manipulation system. To ensure safe operations in human-populated environments, robots must comply with external physical interactions and exhibit a passive behavior. To achieve this, we extend a state-of-the-art pushing model to integrate it with impedance-controlled robots. We develop a model predictive control framework built upon this model that enables performing compliant pushing through optimal modulation of the robot's position/velocity set-point, jointly realizing the required pushing force and contact point adaptation to obtain a desired object motion. However, external interactions may induce tracking errors causing a consequent potentially indefinite increase of the pushing force. To prevent this, we integrate an energy tank passivity filter that further modulates the robot velocity set-point to guarantee passivity and avoid uncontrolled energy buildup. The proposed method has been rigorously tested in simulation and validated through experiments on two different robotic systems, demonstrating passive compliance during human-robot interactions, and assessing trajectory tracking performance and robustness to variations in the object's physical parameters.

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