Underwater Robots - Gianluca Antonelli.pdf

7.5 Non-regressor-Based Adaptive Control 149
the manipulator’s motion. For this reason the additional control action ∆ τ � v
is required. In[67], arobust control isdeveloped for the vehicle in order to
counteract the coupling effects.
Simulations are carried out considering a dry weight of 150 kg and a
length of 1m for the vehicle and adry weight of40kgand alength of 1m
for the manipulator. Moreover, the natural frequencies have been chosen as
ω 0 v = 1. 5rad/s and ω 0 q = 15rad/s leading toavalue of ε = 0. 1.
7.5 Non-regressor-Based Adaptive Control
In 1999 reference [185, 252] extend to UVMSs the non-regressor-based
adaptive control developed by J. Yuh [316] and experimentally validated
in [83, 216, 320, 323] with respect to AUVs. In [322], this controller is integrated
with adisturbance observer to improve its tracking performance
and simulated on a1-DOF vehicle carrying a2-DOF manipulator.
The main idea is to consider the vehicle subsystem separate from the manipulator
subsystem and to develop two controllers with different bandwidth,
independent one from the other. Itisworth noticing that the controller has
been developed together with akinematic control approach (see Chapter 6).
The vehicle generalized force τ � v ,thus, can be computed by considering
the controller
τ � v = K 1 ,v ¨η d + K 2 ,v ˙η + K 3 ,v + K 4 ,v ˙˜η + K 5 ,v ˜η =
already defined and discussed in Section 3.3.
The manipulator iscontrolled with the following
τ q = K 1 ,q¨q d + K 2 ,q ˙q + K 3 ,q + K 4 ,q ˙˜q + K 5 ,q˜q =
5�
K i,vφ i,v ,
i =1
5�
K i,qφ i,q ,
i =1
where ˜q = q d − q ,the gains K i,q ∈ IR n × n are computed as
where
� s q � � �
� φ �
i,q
K i,q = ˆγ i,qs q φ T i,q
s q = ˙˜q + σ ˜q with σ>0 ,
i =1,...,5 ,
and the factors ˆγ i,q’s are updated by
˙ˆγ i,q = f i,q � s q � � �
� φ �
i,q with f i,q > 0 i =1,...,5 .