Underwater Robots - Gianluca Antonelli.pdf

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7.9 Virtual Decomposition Based Control 183
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Fig. 7.21. Output feedback control; third case study. Comparison between
the control laws (7.43),(7.44) and (7.63): joint control torques. Left: control
law (7.43),(7.44). Right: control law (7.63)
nion [246]— is used inthe control law; this allows overcoming the occurrence
of representation singularities.
The discussed control scheme is tested in anumerical case study. Amanipulation
task isassigned in terms of adesired position and orientation
trajectory for the end effector of a6-DOF manipulator mounted on a6-DOF
vehicle. Then, the system’s behavior under the discussed control law isverified
in simulation.
Control law. The dynamics of an UVMS isrewritten in away to remark
the interaction between the different rigid bodies, i.e., between the links and
between links and the vehicle. Consider an UVMS composed ofavehicle and
of a n -DOF manipulator mounted on it.
The vehicle and the manipulator’s links are assumed to be rigid bodies
numbered from 0(the vehicle)to n (the last link, i.e., the end effector). Hence,
the whole system can be regarded as an open kinematic chain with floating
base.
Areference frame T i is attached to each body according tothe Denavit-
Hartenberg formalism, while Σ i is the earth-fixed inertial reference frame.
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