  Robots that physically interact with their surroundings, in order to
accomplish some tasks or assist humans in their activities, require to exploit
contact forces in a safe and proficient manner. Impedance control is considered
as a prominent approach in robotics to avoid large impact forces while
operating in unstructured environments. In such environments, the conditions
under which the interaction occurs may significantly vary during the task
execution. This demands robots to be endowed with on-line adaptation
capabilities to cope with sudden and unexpected changes in the environment. In
this context, variable impedance control arises as a powerful tool to modulate
the robot's behavior in response to variations in its surroundings. In this
survey, we present the state-of-the-art of approaches devoted to variable
impedance control from control and learning perspectives (separately and
jointly). Moreover, we propose a new taxonomy for mechanical impedance based on
variability, learning, and control. The objective of this survey is to put
together the concepts and efforts that have been done so far in this field, and
to describe advantages and disadvantages of each approach. The survey concludes
with open issues in the field and an envisioned framework that may potentially
solve them.
