  Many day-to-day activities involve people working collaboratively toward
reaching a desired outcome. Previous research in motor control and neuroscience
have proposed inter-personal motor synergy (IPMS) as a mechanism of
collaboration between people, referring to the idea of how two or more people
may work together "as if they were one" to coordinate their motion. In motor
control literature, uncontrolled manifold (UCM) is used for quantifying IPMS.
According to this approach, coordinated motion is achieved through
stabilization of a performance variable (e.g., an output in a collaborative
output tracking task). We show that the UCM approach is closely related to the
well-studied consensus approach in multi-agent systems that concerns processes
by which a set of interacting agents agree on a shared objective. To explore
the connection between these two approaches, in this paper, we provide a
control-theoretic model that represents the systems-level behaviors in a
collaborative task. In particular, we utilize the consensus protocol and show
how the model can be systematically tuned to reproduce the behavior exhibited
by human-human collaboration experiments. We discuss the association between
the proposed control law and the UCM approach and validate our model using
experimental results previously collected from an inter-personal finger force
production task.
