Underwater Robots - Gianluca Antonelli.pdf

164 7. Dynamic Control of UVMSs
vehicle; this makes the extension of the previous approach toour case not
straightforward.
As amatter of fact, the use of numerical differentiation ofnoisy position/orientation
measurements may lead to chattering ofthe control inputs,
and thus tohigh energy consumption and reduced lifetime of the actuators.
Moreover, low-pass filtering of the numerically reconstructed velocities may
significantly degrade the system’s dynamic behavior and, eventually, affect
the closed-loop stability. In other words, such afilter has tobedesigned together
with the controller so as to preserve closed-loop stability and good
tracking performance.
This is the basic idea which inspired the approach described in the following:
namely, anonlinear filter (observer) on the position and attitude
measures is designed together with amodel-based controller so as to achieve
exponential stability and ensure tracking of the desired position and attitude
trajectories.
ALyapunov stability analysis isdeveloped to establish sufficient conditions
onthe control and observer parameters ensuring exponential convergence
of tracking and estimation errors.
In view of the limited computational power available in real-time digital
control hardware, simplified control laws are suggested aimed at suitably
trading-off tracking performance against reduced computational load. Also,
the problem of evaluating some dynamic compensation terms, to be properly
estimated, is addressed.
Asimulation case study iscarried out to demonstrate practical application
of the discussed control scheme to the experimental vehicle NPS AUV
Phoenix[145]. Theobtained performance is compared to that achieved with a
control scheme in whichvelocityisreconstructed via numerical differentiation
of position measurements.
Controller-observer scheme. The desired position for the vehicle is assigned
in terms of the vector η 1 ,d( t ), while the commanded attitude trajectory
can be assigned in terms of the rotation matrix R I B,d ( t )expressing the orientation
ofthe desired vehicle frame Σ d with respect to Σ i .Equivalently, the
desired orientation can be expressed in terms of the unit quaternion Q d ( t )
corresponding to R I B,d ( t ). Finally, the desired joint motion is assigned in
terms of the vector of joint variables q d ( t ).
The desired velocity vectors are denoted by ˙η 1 ,d( t ), ν I 2 ,d ( t ), and ˙q d ( t ),
while the desired accelerations are assigned in terms of the vectors ¨η 1 ,d( t ),
˙ν I 2 ,d( t ), and ¨q d ( t ).
Notice that all the desired quantities are naturally assigned with respect
to the earth-fixed frame Σ i ;the corresponding position and velocity inthe
vehicle-fixed frame Σ b are computed as
⎡ ⎤ ⎡ ⎤
η B 1 ,d = R B I η 1 ,d, ζ d =
⎣
R B I ˙η 1 ,d
R B I ν I 2 ,d
˙q d
⎦ = ⎣ ν 1 ,d
ν ⎦ 2 ,d .
˙q d