Some features of vectored thruster autonomous underwater vehicle control.
Key words: underwater vehicle, vectored thruster, forming trajectory.
An improvement in the characteristics of autonomous underwater vehicles (AUV) is possible not only because of the use of the more advanced control systems, but also the development of new approaches to the construction of these AUV. One of such promising approaches is concept AUV with one vectored thruster (Cavallo et.all, 2004). The use only of one vectored thruster will make it possible to create small high-speed AUV. However, because of the limited orientation angles of AUV thruster on the AUV maneuverability also is set the same limitations. This leads to the need for considering its limitations at the forming of AUV motion trajectory.
In the work (Michelini et.all, 2004) was partially already examined a question of trajectory forming for vectored thruster AUV. However, was not developed the algorithm of the arrival of this AUV into the target point independently from it position relative to AUV in the vertical plane. And also were not obtained conditions of arrival AUV into the target point depending on the limitations, superimposed on the orientation angles of its thruster.
2. TASK SETTING
Thus, in this work is set and solve the problem of the trajectory forming of vectored thruster AUV during its motion in the terminal mode (motion to the target point). For the solution of this task it is necessary to develop the algorithm of AUV motion in the vertical plane, which makes it possible to increase its maneuverability in this plane. And also to obtain the conditions, which allow determining the possibility of the approach of this AUV to the target point, with the presence of limitations to the thruster orientation angle.
3. MOTION IN THE VERTICAL PLANE
As was shown in the work (Michelini et.all, 2004) vectored thruster AUV it has substantial limitations during the motion in the vertical plane, which can not allow it to arrive into the arbitrary target point. The following approach is proposed for the solution of the described problem. Let us designate in the vertical plane of AUV motion the point C, which has the following coordinates ([[??].sub.c], [y.sub.b]) in the vertical plane, where [[??].sub.c] = [[??].sub.a] + [k.sub.z]([[??].sub.b] - [[??].sub.a]), 0 < [k.sub.z] < 1 is a certain constant coefficient, [??] = [square root of ([x.sup.2] + [z.sup.2])] is coordinates AUV and target point (point A([[??].sub.a], [y.sub.a]) and B([[??].sub.b], [y.sub.b]) in fig. 1) in the vertical plane [??]Oy.
In the process of AUV motion we will consider target point not point B, but point C. Thus, the desired value of the pitch [[psi].sup.*] it will be calculated by the expression:
[[psi].sup.*] = arctg(([y.sub.b] - [y.sub.a])/([k.sub.z] [absolute value of [[??].sub.b] - [[??].sub.a]])). (1)
Furthermore, for the faster arrival on the assigned depth to the AUV desired velocity value, calculated on the basis of the distance to the target point, is added a certain additional value, which depends on the [[psi].sup.*]:
[v.sup.*] = [k.sub.l]r + [k.sub.v[psi]] [absolute value of sin([[psi].sup.*])], (2)
where [k.sub.v[psi]] > 0, [k.sub.l] > 0 are some positive coefficients, r is distance from AUV to the target point B, [v.sup.*] is desired AUV velocity.
This approach will make it possible to ensure motion with the increased angle of pitch and velocity in the initial stage, which will lead to the quick AUV moving in the vertical plane. When AUV arrive to the target point B the angle of pitch equal zero, which will ensure approach AUV to the target point without the overshot on the coordinate y. This explains by the fact that in the process of motion to the target point B, the desired value of the pitch [[psi].sup.*] it will decrease and it will become equal to 0 with the approach AUV to the point B.
The formation of the values [[psi].sup.*] and [v.sup.*] by the expressions (1), (2) ensures the increased maneuverability vectored thruster AUV. This algorithm proposed makes it possible to automatically work out approach to the target point, located vertically up (down) these AUV. In this case AUV move on the spiral to the target point with the increased speed. It is obvious that with the helical motion the course angle [phi] will change over wide limits, since AUV can complete several turnings around the vertical axis. This can require the use of special logical conditions for the correct formation of the desired value of this angle.
[FIGURE 1 OMITTED]
In this case it is proposed to use the algorithm, which makes it possible without the additional logical conditions to obtain the correct value of the desired course angle, which takes the following form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The results of the modeling work of developed algorithm are shown in fig. 2. This figure show the vectored thruster AUV motion trajectories in the vertical plane in different cases: moving to the target point, located vertically above AUV (curve 1), moving to the target point in the vertical plane without the helical motion (curve 2), mixed motion (curve 3). As can be seen from represented figures, the formation of the desired values [[psi].sup.*], [v.sup.*] and [[phi].sup.*] by algorithm (1), (2), (3) makes it possible to ensure approach AUV to the target point, is independent from it location in the vertical plane relative to AUV.
4. MOVING IN HORIZONTAL PLAN
As has been mentioned above, in the process of AUV motion the target point can to be in this position relative to this AUV, that the approach to it, in view of the limited maneuverability, becomes impossible. In this case AUV it begins to accomplish circular motions in the horizontal plane around the target point. Therefore in the process of AUV moving it is necessary to determine the situations for averting the ineffective energy consumption indicated.
We will further examine AUV motion in the half-joined coordinate system x'y'z'. Let us assume AUV on the circular arc with a radius [R.sub.c] it accomplishes turning to the target point B, located in horizontal plane (see fig. 3).
Let under the action of force [F.sub.x] AUV it move along the trajectory with speed, and under the action of torque [M.sub.y] it is turned in the horizontal plane with the angular velocity [[omega].sub.y]. It is simple to obtain that the AUV turning radius will be determined by the relationship:
[R.sub.c] = [v.sub.x]/[[omega].sub.y]. (4)
Center of circle (point C([x'.sub.c], [z'.sub.c]) in fig. 3) along which moving AUV will be located in the direction perpendicular to the direction of the AUV motion at a distance equal to [R.sub.c]. Therefore it is possible to write down:
[x'.sub.c] = -[R.sub.c]cos([phi])sign([phi]), [z'.sub.c] = -[R.sub.c]sin([phi])sign([phi]). (5)
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Thus, the possibility of the appearance of circular motions with the approach to the target point is determined by the following expression:
[xi] = [([x'.sub.b] - [x'.sub.c]).sup.2] + [(z'.sub.b) - [z'.sub.c]).sup.2] - [R.sup.2.sub.c], (6)
where [x'.sub.b], [z'.sub.b] is the coordinates of target point B. If [xi] < 0, then target point is located inside the circle of turning and approach to it is imp ble. If [xi] > 0 then target point is located outside the circle of turning and AUV will be able it to approach.
Expressions (4), (5) and (6) make it possible to determine the possibility of approach to the target point in the process of AUV motion. However, for the preliminary planning of the trajectory, when the AUV velocities on different sections are not previously known, it is necessary to estimate value [R.sub.c] only on the basis the AUV parameters. The as a result conducted investigation was obtained this relationship:
[R.sub.c] = [square root of ((cos([[delta].sub.dmax])/ lsin([[delta].sub.dmax]))max([d.sub.[omega]y]/[d.sub.vx]))],
where [d.sub.vx], [d.sub.[omega]y], is the coefficients of hydrodynamic friction according to the linear and rotational degrees of freedom correspondingly, l if the distance from the thruster to the AUV masses center, [[delta].sub.dmax] is the maximally possible thruster orientation angle in the horizontal plane
Thus, are in this work examined the special features of vectored thruster AUV control in the terminal mode of its operation. The algorithms formation of the desired values of its course, pitch angles and the velocity are proposed. These algorithms ensure to this AUV the increased maneuverability in the vertical plane. Furthermore, are obtained the conditions, which make it possible to determine the impossibility of approach AUV into the target point.
This work supported by RFBR (grants 05-07-90027, 05-08-33627), grant of President of Russia Federation.
Cavallo E., Michelini R., Filaretov V.F.(2004). Conceptual design of an AUV equipped with a three degrees of freedom vectored thruster // Int. Journal. Intelligent and Robotic Systems.--2004. - Vol. 39, pp. 365 - 391.
Michelini R., Cavallo E., Filaretov V., Ukhimets D.(2004). Path Guidance and Attitude Control of a vectored Thruster AUV// 7-th Int. Biennial ASME Conf. on Engineering Systems Design and Analysis (ESDA) Manchester, UK, 2004, pp. 1-8.
|Printer friendly Cite/link Email Feedback|
|Author:||Yukhimets, Dmitry; Filaretov, Vladimir|
|Publication:||Annals of DAAAM & Proceedings|
|Article Type:||Technical report|
|Date:||Jan 1, 2007|
|Previous Article:||The Fundamental Concepts of Excellence.|
|Next Article:||Determining machine condition--assessement of dynamic behavior of the high speed milling machine tool spindle.|