  Haptic upper limb exoskeletons are robots that assist human operators during
task execution while having the ability to render virtual or remote
environments. Therefore, the stability of such robots in physical
human-robot-environment interaction must be guaranteed, in addition to
performing well during task execution. Having a wide range of Z-width, which
shows the region of passively renderable impedance by a haptic display, is also
important to render a wide range of virtual environments. To address these
issues, in this study, subsystem-based adaptive impedance control is designed
for having a stable human-robot-environment interaction of 7 degrees of freedom
haptic exoskeleton. The presented control decomposes the entire system into
subsystems and designs the controller at the subsystem level. The stability of
the controller in the presence of contact with the virtual environment and
human arm force is proved by employing the virtual stability concept.
Additionally, the Z-width of the 7-DoF haptic exoskeleton is drawn using
experimental data and improved using varying virtual mass element for the
virtual environment. Finally, experimental results are provided to demonstrate
the perfect performance of the proposed controller in accomplishing the
predefined task.
