Underwater Robots - Gianluca Antonelli.pdf

204 8. Interaction Control of UVMSs
Fig. 8.1. Snapshot of the two seven-link Ansaldo manipulators during awet test
in apool (courtesy of G. Casalino, Genoa Robotics And Automation Laboratory,
Università diGenova and G. Veruggio, National Research Council-ISSIA, Italy)
f e,d = M d ¨˜x + D d ˙˜x + K d ˜x (8.1)
where M d ∈ IR 3 × 3 , D d ∈ IR 3 × 3 and K d ∈ IR 3 × 3 are positive definite matrices.
In other words it is required toassign adesired impedance at the
end effector expressed as adesired behavior of the linear e.e. force in the
earth-fixed frame.
Let recall eq. (2.75)
M ( q ) ˙ ζ + C ( q , ζ ) ζ + D ( q , ζ ) ζ + g ( q , R I B )=τ + J T pos( q , R I B ) f e
that, by defining
τ n = C ( q , ζ ) ζ + D ( q , ζ ) ζ + g ( q , R I B )
can be written as
(2. 75)
M ( q ) ˙ ζ + τ n = τ + J T pos( q , R I B ) f e . (8.2)