Underwater Robots - Gianluca Antonelli.pdf

2.11 Identification 43
f e = K ( x − x e ) , (2.76)
where x is the position of the end effector expressed in the inertial frame, x e
characterizes theconstantposition of theunperturbed environment expressed
in the inertial frame and
K = k nn T , (2.77)
with k>0, is thestiffness matrix being n the vector normal to the plane [194].
nn T x e
x e
f e
( I − nn T ) x e
x
Fig. 2.5. Planar view of the chosen model for the contact force
In our case it is x = η ee1 ;however, in the force control chapter, the
notation x will be maintained.
2.11 Identification
Identification of the dynamic parameters of underwater robotic structures is a
very challengingtask.The mathematicalmodel shares its main characteristics
with the model of aground-fixed industrial manipulator, e.g., it is non-linear
and coupled. In case of underwater structure, however, the hydrodynamic
terms are approximation ofthe physical effects. The actuation system of the
vehicle is achieved mainly by the thrusters the models ofwhich are still object
of research. Finally, accurate measurement ofthe whole configuration is not
easy. For these reasons, while from the mathematical aspect the problem
is not new, from the practical point ofview it is very difficult toset-up
asystematic and reliable identification procedure for UVMSs. At the best
of our knowledge, there isnosignificant results in the identification of full