The paper present results of the Ukrainian-French scientific activity between Donetsk National Technical University and French partners in the field of human-robot and robot-environment interactions. The first part of the research shows adaptation of robotic arm movements to the dynamics of interacting person who imposes its own rhythmicity. The adaptation algorithm is based on rhythmic oscillator inspired by biology. The second part of the research considers adaptation of a biped robot internal vibration modes to the environment during flexion-extension vertical movements. These vibrations are extremely unwanted; they appear during robot motion by reason of internal flexibilities in articulations, backlashes and friction and can cause the fall of the robot. It is shown that their efficient attenuation can be achieved by using auto-adaptive oscillator that acts on the robot’s knee articulations.