In human-robot interaction, the robot must behave safely, especially when an operator is present in its workspace. Even higher safety levels must be attained when physical contact occurs between the two. To this end, standards such as the ISO10218 define the requirements for a robot to be considered safe for interaction with human operators in an industrial environment. In this paper, we propose an adaptive damping controller that fulfills the ISO10218 requirements by limiting the tool velocity, power and contact force online (and only when needed). The controller is experimentally validated on a hand-arm robotic system, in a mock-up collaborative application. For the hand, safe interaction is enhanced by using tactile sensing, both to regulate grasp forces and to provide an intuitive interface for the operator.