  The ability of animals to interact with complex dynamics is unmatched in
robots. Especially important to the interaction performances is the online
adaptation of body dynamics, which can be modeled as an impedance behaviour.
However, the variable impedance controller still possesses a challenge in the
current control frameworks due to the difficulties of retaining stability when
adapting the controller gains. The fractal impedance controller has been
recently proposed to solve this issue. However, it still has limitations such
as sudden jumps in force when it starts to converge to the desired position and
the lack of a force feedback loop. In this manuscript, two improvements are
made to the control framework to solve these limitations. The force
discontinuity has been addressed introducing a modulation of the impedance via
a virtual antagonist that modulates the output force. The force tracking has
been modeled after the parallel force/position controller architecture. In
contrast to traditional methods, the fractal impedance controller enables the
implementation of a search algorithm on the force feedback to adapt its
behaviour on the external environment instead of on relying on \textit{a
priori} knowledge of the external dynamics. Preliminary simulation results
presented in this paper show the feasibility of the proposed approach, and it
allows to evaluate the trade-off that needs to be made when relying on the
proposed controller for interaction. In conclusion, the proposed method mimics
the behaviour of an agonist/antagonist system adapting to unknown external
dynamics, and it may find application in computational neuroscience, haptics,
and interaction control.
