Underwater Robots - Gianluca Antonelli.pdf

7.9 Virtual Decomposition Based Control 189
Table 7.5. Masses, vehicle length and Denavit-Hartenberg parameters [m,rad] of
the manipulator mounted on the underwater vehicle
mass (kg) length (m) a d θ α
vehicle 5454 5.3 - - - -
link 1 80 - 0 . 150 0 q 1 − π/2
link 2 80 - 0 . 610 0 q 2 0
link 3 30 - 0 . 110 0 q 3 − π/2
link 4 50 - 0 0. 610 q 4 π/2
link 5 20 - 0 − 0 . 113 q 5 − π/2
link 6 25 - 0 0. 103 q 6 0
matter of fact, the code would be exactly the same, just reading the parameters’
values from different data files, with obvious advantages for software
debugging and maintenance.
Notice, that, for all the simulations the following conditions have been
considered:
• full degrees-of-freedom dynamic simulations;
• detailed mathematical model used inthe simulation;
• inaccurate initial parameters estimates used by the controller (about 15%
for each parameter);
• reduced order regressor used in the control law;
• digital implementation of the control law (at asampling rate of 200 Hz);
• quantization ofthe sensor outputs and measurement noise.
Theonly significantsimplificationisthe neglect of thethruster dynamics that
causes limit cycle in the vehicle behavior [300]. Itisworth remarking that the
adaptive control law uses areduced number of dynamic parameters for each
body: body mass and mass of displaced fluid (1 parameter), first moment
of gravity and buoyancy (3 parameters). Those are the parameters that, in
absence of current, can affect asteady state error. Thus, each vector ˆ θ i is
composed of 4elements. In Chapter 3, adetailed analysis of adaptive/integral
actions in presence of the ocean current isdiscussed.
The desired end-effector trajectory is astraight line the projection of
which onthe inertial axis isasegment of0. 2m.The line has tobeexecuted
four times, with duration of the single trial of 4swith a5th order polynomial
time law. Then, 14s of rest are imposed. The attitude of the end effector
must be kept constant during the motion.
The initial configuration is(see Figure 7.22):
η =[0 0 0 0 0 0] T
m, deg
q =[0 180 0 0 90 180 ] T deg