Biomimetic Robotics - Engineered Biomimicry - page 100

such as dead band and hysteresis. However,
both tendons cannot be allowed to be slack
simultaneously if the limb is to maintain its ori-
entation. When the nonlinear model was used
only for the tendon that was less stressed, the
results resembled the case of the UKF without
adaptation of the process covariance.
In this section the successful application of
the UKF and the adaptive UKF to the identifica-
tion of model parameters of a typical nonlinear
muscle-limb dynamic system is illustrated. It
has been shown by example that UKF-based and
adaptive UKF-based state estimation and
parameter identification are an option that is
particularly well suited for the dynamic systems
associated with muscle-limb interactions.
Although the generic case of a limb actuated by
a pair of antagonistic muscles was considered,
the identification method could be fine-tuned
and applied to any specific pair of antagonistic
muscles actuating a particular limb. The method
is currently being employed to design nonlinear
control laws that can be used to control smart
prosthetic limbs.
An adaptive UKF is used to estimate the
unmeasurable state variables and kinetic param-
eters of the muscle-limb model. Although the
UKF has a simple structure, the tuning of these
estimators is a relatively difficult task. The use
of the adaptive approach eliminates the need for
the tuning of the covariance parameters of the
UKF estimator. However, the estimates of the
process covariance matrices obtained adap-
tively can vary widely depending on the adap-
tation scheme adopted. For this reason, the
adaptive algorithm is recommended to be used
only in the initial stages as a tuning method.
One of the features of the parameter-identi-
fication problem considered here is the pres-
ence of internal parameters in the definition of
the applied moment. These internal parame-
ters, such as the distances to the two muscle
distal and proximal anchor points from the
center of rotation, d d and d p , constitute a set of
weakly identifiable parameters since they may

in some cases be inaccessible for observation.
Although formal identifiability analysis of the
model has not been carried out, the problem of
weakly identifiable parameters has been dealt
with by the use of optimal state estimation of
nonlinear dynamic systems. Moreover, physi-
cally meaningful, coupled models of the inter-
nal tendons' length dynamics facilitate the
identification of the weakly identifiable
parameters.

4.4 P ROGNOSIS FOR THE FUT URE

Biomimetic roboticists will continue to develop
the field so as to mimic physiological dynamic
models of human limbs and the manner in
which they are controlled. These developments
will lead to the routine use and implementa-
tion of sophisticated and complex systems. In
particular, these developments are expected to
be in the area of the design and implementation
of compliant robot limbs and hands with excep-
tional sensory and control capabilities so that
they can be interfaced to the human brain and
controlled by it.

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