Bergerman, M.; Xu, Y. "Robust control of underactuated
manipulators: analysis and implementation."
IEEE Systems, Man and Cybernetics Conference,
San Antonio, USA, October 1994, pp. 925-930.
Underactuated manipulators are robot manipulators composed
of both active and passive joints. The advantages of using such systems
reside in the fact that they weight less and consume less energy
than their fully-actuated counterparts, thus being useful for applications
such as space robotics. Another interest reside in the reliability
or fault-tolerant design of fully-actuated manipulators. If any of the
joint actuators of such a device fails, one degree of freedom of the
system is lost. It is usual in this situation to simply brake the failed
joint and try to resume the task with less degrees of freedom available.
Following the methodology proposed in this work, the passive (failed)
joint can still be controlled via the dynamic coupling
with the active joints, and so the system can still make use of all of
its degrees of freedom originally planned. The methodology proposed
in this paper uses the dynamic coupling between the passive
and the active joints in order to bring the passive joint angles to a
desired set-point. Therefore, the control law and the performance of
the system are completely dependent on the dynamic model. Since
it is difficult to obtain the exact dynamic model of the system in general,
considerable position errors and even instability can result in
some cases. In this paper, we propose a variable structure controller
to provide the system with the robustness necessary to perform tasks
regardless of the modelling errors. Case studies are provided as a
mean of illustration.