Underwater Robots - Gianluca Antonelli.pdf

joint torques [Nm]
200
0
−200
−400
7.9 Virtual Decomposition Based Control 195
τ q 1 ,τq 4 ,τq 5 ,τq 6
τ q 3
τ q 2
−600
0 10 20 30
time [s]
Fig. 7.30. Virtual decomposition control. Time history of the joint torques
frame-based, model-based controller presented inSection 3.6) gets improvement
inthe tracking error by considering the proper adaptation onthe sole
persistent terms, i.e., the current and the restoring forces. It is worth noticing
that the rigid bodies ofthe manipulator are subject toafast dynamics and
thus the effects numerically shown in Chapter 3for asingle rigid body (the
vehicle) are magnified for afast movement ofone of the arm.
It is advisable,thus, to merge these two approaches as done by G. Antonelli
et al. in [15] in order to get benefit from both of them. The resulting control
scheme has amodular structure which greatly simplifies its application to
systems with alarge number of links; furthermore, it reduces the required
computational burden by replacing one high-dimensional problem with many
low-dimensional ones, finally allows efficient implementation ondistributed
computing architectures.
Numerical simulations have been performed toshow the effectiveness of
the discussed control law with the same model used for the virtual decomposition
approach; the simulation, thus, uses ≈ 400 dynamic parameters. The
overall number of parameters ofthe controller is 9 ∗ ( n +1)=63. Moreover,
the software to implement the controller is modular, the same function
is used to compensate for all the rigid bodies, either the vehicle or links of
the manipulator, with different parameters as inputs. This makes easier the
debugging procedure.
The desired end-effector path is astraight line with length of 35 cm, to be
executed 4times according to a5th order polynomial time law; the duration
of each cycle is 4s.The desired end-effector orientation is constant along the
commanded path. The vehicle is commanded to keep its initial position and
orientation during the task execution. Therefore, the inverse kinematics is
needed to compute the sole joint vectors q d ( t ), ˙q d ( t )and ¨q d ( t )inreal time,