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In this paper, the interaction control schemes suitable for implementation on industrial robot units are presented. In particular, the focus is on impedance control and parallel control, which are conceived to manage the interaction with a more or less compliant environment without requiring an accurate model thereof. All the considered schemes are based on an inner motion control loop, which can be the usual independent joint control of PID type or an advanced model-based motion control law with superior tracking performance. The inner motion control loop is in charge of tracking the reference trajectory computed by the outer interaction control loop. Special emphasis is given to controlling 6-degrees-of-freedom (DOF) interaction tasks involving the end-effector position and orientation when a contact force and moment are applied.