Robot manipulators are designed to interact with their surroundings. Even if a task does not specifically involve interaction, the robot may collide with unknown obstacles during its motion. To overcome these problems, it is necessary to consider possible interactions inside the control system. This paper aims to design a controller that allows the manipulator to reach a final pose, even if it interacts with an unforeseen object during its trajectory. This design is composed of two stages: A feedback linearization system that allows to eliminate intrinsic nonlinearities of the robot, and the imposition of a dynamic behavior to keep delicate interactions without using external 6D force/torque sensors. The proposed controller was tested on an UR5 robot, but can be extended to any robotic manipulator. The results show the comparison between the behavior achieved by a standard feedback-linearized position controller, and a sensor-free impedance controller, both for environments with and without unknown obstacles, in which the proposed controller generated smoother and more precise trajectories.