In this paper, a new method to perform time-invariant motion is proposed. The approach uses the advantages of variable impedance control to have full interactivity with the human while tracing a desired path. The path is followed at maximum velocity while the human can disturb the robot at any instant and manipulate it far from the desired path without changing the control law. The method was proven in simulation and on a real torque-controlled serial manipulator (KUKA LWR iiwa). The chosen paths were designed to perform robotic assisted ultrasound scanning for breast cancer diagnosis. Results show that interactivity is allowed while keeping a low kinetic energy of the robot. Despite of human disturbances, the robot can keep tracing the path after the interaction is finished.