Proceedings of the 2000 IEEE International Conference on Robotics & Automation San Francisco, CA • April 2000

Guidance of unmanned underwater vehicles: experimental results M.Caccia, G.Bruzzone, G.Veruggio Consiglio Nazionale delle Ricerche

Istituto Automazione Navale Via De Marini, 6

16149 Genova

Abstract This paper addresses the problem of guidance of unmanned underwater vehicles. In the framework of a two layered hierarchical architecture uncoupling the system dynamics and kinematics, a couple of guidance laws for approaching a target with the desired orientation and following an environmental feature has been designed with Lyapunov-based techniques. Suitable acoustic-based estimators of the corresponding operational variables have been designed and integrated with the guidance and control system. Experimental results of pool trials of a prototype UUV executing free-space maneuvering and wall-following tasks are reported and discussed.

1. Introduction Guidance systems for marine vehicles have traditionally been designed separately from control systems, adopting simple strategies such as line of sight (LOS) between way points, generating the reference heading and, sometimes, surge velocity. See (Healey and Lienard, 1993) and (Fossen, 1994) for the case of unmanned underwater vehicles (UUVs) and ships respectively. When trajectory­tracking is required, these approaches lead to finite steady-state errors depending on the trajectory parameters. In order to guarantee the steady-state trajectory tracking error be zero, a combined gain­scheduling based guidance/control system has been proposed in (Fryxell et aI., 1996), relying on the observation that the trimming trajectories for autonomous underwater vehicles are helices, parameterized by the AUV's body axis speed, yaw rate and flight path angle. On the other hand, the adoption of Lyapunov-based guidance laws, which do not require any (re)planning, proved its feasibility in controlling the motion of an under-actuated UUV in the presence of a high uncertainty in position estimates, typical of underwater robotics (Caccia et aI., 1998).

Figure 1: Guidance and control architecture.

On the basis of this experience, a dual-loop hierarchical guidance and control architecture for UUVs, uncoupling the management of the vehicle's kinematics and

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Italy

dynamics, has been designed as shown in Fig. 1, where X, � and 41 represent the operational variables, the vehicle's linear and angular velocities, and the control actions respectively. As discussed in (Caccia and Veruggio, 2000), the vehicle's dynamics has locally been reduced to a set of second order systems with fixed characteristic equations by suitable gain-scheduling velocity controllers. The Lyapunov-based synthesis of the guidance laws, generating the desired velocities, has enabled the implementation of a library of basic task functions performing conventional autopilot tasks, e.g. autoheading and autodepth, hovering control, and environment-related tasks such as autoaltitude. The problem of extending the library of the task functions for the UUV guidance on the horizontal plane both in free space and nearby underwater structures is addressed in the following focusing on the tasks of approaching a target with a desired orientation and following a sensor-detected environmental feature. In particular, the possibility of transferring the smooth control laws for unicycle-like vehicles presented in (Aicardi et aI., 1995) to UUV guidance applications has been experimentally verified with the prototype UUV Romeo maneuvering in a pool. The problem of following an environmental feature has then been reduced to the task of approaching with a suitable orientation a target moving along the tracked object. A detailed description of these tasks and the corresponding guidance laws is given in section 2, together with a brief overview of free-space guidance task functions. Section 3 deals with the estimate of the vehicle's motion combining internal (compass) and external (profiling sonar) sensor data with a priori knowledge of the system dynamics. In particular, the basic ideas of sonar-based motion estimation in structured environments with a priori known maps presented in (Caccia et aI., 1997) are shortly summarized. On this basis a combined dynamic estimator of the vehicle's motion with respect to a sonar­tracked surface and the surface orientation is synthesized. Finally, experimental results of pool trials, carried out with Romeo, the prototype UUV developed by CNR­IAN, are reported and discussed in section 4, after a short description of the vehicle and its sensor configuration. Experiments have shown that Romeo can also execute the task of approaching a target with desired orientation without controlling the sway velocity (torpedo-like motion) and use this guidance law to follow a pool-wall.

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2. Guidance task functions A mobile robot follows a trajectory or approaches a target by maneuvering in the free space according to some guidance law. When an unforeseen obstacle or a target feature is detected, the robot follows its profile until a suitable detaching condition is verified, and then continues its free-space maneuver. As discussed in (Caccia et aI., 1998), basic free-space maneuvers for unmanned underwater vehicles can be defmed as: long-range maneuvering (LRM): approaching the target area, regardless of the vehicle orientation; medium-range maneuvering (MRM): guiding the vehicle up to the target, with the required orientation; short-range maneuvering (SRM): hovering above the target even in the presence of disturbances, which demands high-precision movement. Since experimental applications ofLRM and SRM can be found in (Caccia et at, 1998) and (Caccia arid Veruggio, 2000) respectively, in the following, attention will focus on MRM and feature-following, which is the basic external sensor-based guidance task function. 2.1 Medium Range Maneuvering The task of reaching the point �* = [x * y *Y with orientation 1jI* is suitably described by the task function � = [e 8 a]T, where y = atan2( y*-y , x*-x ). The operational variables {e=�(X*-X)2 +(y*-yY

8=Y-IjI* a=Y-1jI

are defmed as depicted in Figure 2.

(1)

Fig. 2. Medium Range Maneuvering task nomenclature

Being the fIrst time derivatives of the operational variables equal to

e = -ucosa-vsina e=usina_�

e e (2),

yaw velocities respectively, the choice of the desired vehicle's speeds 1 u·=Ae cos�

v* = o * , cos a sina ( he) r =/.1a+ ,.. a+ a

makes the positive definite function V=V +V 8 =.!..e2 + .!.. 'a2 +he2) e n, 2 2 �

(3)

(4) a Lyapunov function and � converges to zero for increasing time. 2.2 Feature-following Representing a sensor-detected feature in terms of its orientation 0 and range d from the robot, the task of following it at constant range d* can be reduced to follow a way point moving along the feature itself.

Fig. 3. Feature-following and tracking task nomenclature

As shown in Figure 3, being n the unit vector normal to the tracked feature, a desired target position and orientation are computed at each time as follows: �*=!+(d-d*)g+bTrot!!. (5)

with

and

_jleft: [� -01] Trot - [ 0 1] right:

-I 0 { left: 0 + 1t 12 'l'*= right: B - 1t ! 2

(6),

(7),

according to the vehicle is requested to maintain the feature on its left or right. Then the target ! * is followed by applying the MRM guidance law presented in the previous section. 3. Environmental-based motion estimators . . u sina v cos a a = -r + a = -r + -- - --- The motion of an underwater vehicle in the direction e e perpendicular to a locally linear surface can be estimated where u, v and r represent the vehicle's surge, sway and on the basis of range measurements collected through

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sweeping the surface itself with a profiling sonar (Cristi et aI., 1998). The motion of a vehicle moving in a known structured environment can be alternatively estimated by tracking a set of surfaces with different orientations, while, in case an unknown surface is tracked, a local estimate of the tracked feature and the vehicle's relative motion is possible. Estimator's performances are increased by the knowledge of the vehicle's dynamics. 3.1 Map-based motion estimation Consider a UUV moving in a known structured environment modeled as a collection of linear elements, characterized by orientation 0, position (xL,i) and extremes, (xLI,il) and (xL2,i2). The UUV motion on the horizontal plane is described by the following state equations: {X = u cos 'If - vsinljf

y = usinljf + v cos Ijf I I �) mu

.u =myvr-kuu-kululuu+Fu

my v =- mu ur-kv V-kvlyIVlvl+Fy

where mu and my represent the vehicle's mass (included added masses), Fu and Fy the control forces, and the hydrodynamic drag is modeled by uncoupled linear and quadratic terms. When the s-th linear element is tracked by a range and bearing sensor, e.g. a profiling sonar positioned in (dx, dy ) in the vehicle-fixed reference frame, the vehicle

kinematics [x y u v]T can be updated on the basis of the measurement equation

P_ cosOs (x-x;)+sinos (y - y; ) + -

cos(Ijf+ �-li. ) d. cos(1jf - os) -dysin('If - as)

cos(1jf + 13 - 0.) where 13 is the sonar bearing (see Figure 3).

(9),

In order to reduce localization errors due to wrong data associations, a candidate tracked surface s is computed as s=minp· (10) ie.5' I where Pi is the predicted range for the i-th surface, and S=�:C'I nC'2 nC'3} is the set of linear elements satisfying the constraints: C'1 : Pi is an admissible range; C'2: the angle of incidence between the sonar direction and the linear element is admissible; C'3: the intersection between the sensor's observation direction and the line is inside the linear element extremes. Then if Ip - P. I:;; e:r then s is assumed to be tracked and the vehicle's position and speed updated on the basis of equations (8) and (9). 3.2 Feature-based motion estimation

tracked surface range d and orientation Ii and the UUV velocities, u and v, can be defined. The system dynamics and measurement equation are respectively (see Figure3) 1 d=-u cos(ljf-:o)+v sin(Ijf-O)

0=0 mu u =my vr-ku u-k ulululul+Fu

mv\>' =-muur-kyv-kvlvlvlvl+Fy

and

(11)

d d, cos(ljf-li)- dysin(ljf-o) P=

cOS(Ijf+I3-S) - cos('If+I3-a) (12).

The state [d Ii u v y can be estimated by extended Kalman filtering techniques, considering that the vehicle speed is only observable through range and bearing measurements in the direction orthogonal to the tracked surface and has to be predicted on the basis of the model in the direction parallel to the feature itself. 4. Experimental results

Trials have been performed in a pool using Romeo, the last prototype UUV developed by CNR-IAN (see Figure 4). In particular, MRM tests have been carried out by estimating the vehicle's motion as shown in section 3.1 alternatively tracking two orthogonal pool walls with a profiling sonar, while wall-following tests have been executed by integrating the combined feature and motion estimator of section 3.2 with the feature-following guidance law of section 2.2.

In case the operating environment is not known and a Fig. 4. Romeo: horizontal motion trials configuration surface is tracked by a profiling sonar, a local model of the vehicle-environment interactions, consisting of the

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MRM (tway tomrDlled): Romeo PiIlh -2 MRM (SWilY not controlled): Romeo Path -2

-4 -4

oS oS

-8 -8

!-10 I.,o -12 ·12 -14 ·14 -16 -16

_18 2 10 12 14 16 18

-18 2 10 12 14 16 18 rlml Jlm\

Fig. 5.1. Romeo estimated path 'l'=FfFffj CI • I • I • • , I , I , • •

� � � � � � � :lIlJ . . .

- I • • !t�Et:t:Lb - "". -100 ' , , , •

� � � m � m �

�l4mtm� � -60 - - ___ � ___ � ____ � __ r-, ____ l ________ • - -_ : ______ _

-100 " " � � � m � m �

limalsj

!}�nnJ IlftitHmJ -= I I • I , , ... I I • I I • - " I • • • -200 • • , • • ,

73) 740 750 750 770 700 7!lO SOD i:[---- -r------j------_j ____ n -f- j------j----J 73) 740 750 750 770 700 7!lO SOD

lime lsi Fig. 5.2. Estimated task variables

.� - }If' - '"

� � ! 0 \tt , , _ _� � � � .

685 � !ll5 70D 1lJ5 710 715 720 725 73) 736 740 time Is! tIme Is)

Fig. 5.3. Reference and estimated linear and angular velocities MRM (sway controlled): Path and Vehicle Orientation MRM (sway not controlled): Path and Vohicle Orientation

2OOr---�--�----�---r----�--'----. lID

150 100

100 100

50

1: 0

-&I

-tOO

-t50

-200 � 6!IJ 740 760 790 time(sJ

Fig. 5.4. Comparison between the vehicle heading and the path tangent Fig. 5. Medium Range Maneuvering experimental results with enabled and disabled sway control (left and right column).

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4.1 Vehicle configuration Romeo is equipped with four horizontal and four vertical thrusters, which guarantee the full controllability of the vehicle's motion . A detailed description, of·the vehicle's mechanical, computer and software design can be found in (Caccia et at, 1999). During the experiments the vehicle moved in a pool at constant depth. Heading and yaw rate measurements were supplied by a KVH­DGCIOO compass and low-cost gyro, while the pool walls were swept by a high-frequency, 1.25 MHz, pencil beam profiling sonar Tritech ST-lOOO, positioned in (0.37,O)m in the vehicle-fixed reference frame and able to rotate mechanically at 0.9 degrees steps. Thanks t6 a set of gain­scheduling velocity controllers, the surge, sway. and yaw vehicle dynamics has locally been reduced to a set of second order systems with fixed characteristic equations s2 + 2s + 1.01:::; 0, i.e. cr=1 and 0>0=0.1 (Caccia and Veruggio, 2000).

4.2 Medium Range Maneuvering The medium range maneuvering guidance task has been tested both in the case of fully controllable UUV s, fixing the sway velocity to be zero according to equation (3), and of torpedo-like vehicles, assuming the vehicle's sway speed uncontrollable and letting it be damped py the hydrodynamic drag forces. As discussed in (Caccia et a!., 1998), where only simulation tests have been presented, the MRM guidance law allows the vehicle to approach a target area with a desired orientation, while the vehicle trajectory gets a spiral around the target when the range error e is almost zero. This behavior, which tries to compensate for the sideways movements of the UUV in proximity of the target and requires the integration of medium and short range maneuvering tasks for approaching and hovering an operating site, is stronger when the vehicle sway is not controlled as shown in Figure 5.2, where Romeo estimated task variables are plotted. In the experiments shown in Figure 5, Romeo was required to reach the point (-8,8) meters with heading equal to 135 degrees. Measuring the angles a and e in degrees, the parameters 'A. and I! were assumed equal to 0.3, h was unitary, and the surge and yaw velocities were

saturated at 0.4 mls and 10 degls respectively. The vehicle estimated paths are plotted in Figure 5.1, which shows the vehicle's position every 5 seconds. The asterisks indicate the corresponding values of the plotted variables in the other pictures of Figure 5. The reference and estimated linear and angular velocities are plotted in Figure 5.3, clearly showing the sideways motion of the vehicle when turning, which the vehicle compensates by heading towards the inner side of the bend. Figure 5 .4, plotting the computed path tangent and the vehicle's heading, points out this behavior: after 750 s, when the vehicle turns left, the UUV heading is more negative than the tangent to the path in the case the sway velocity is not annulled by the controller.

4.3 Feature-following Since, as shown in the previous section, Romeo was able to approach a target area with approximately the desired

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orientation even working in torpedo-like mode, a general purpose feature-following guidance law for UUVs, which does not require the control of the vehicle sway, hll.s been tested. The feature-following algorithm of section 2.2 has been applied to follow a pool wall, generating the reference surge and yaw velocities, While the zero reference sway was not controlled. The pool wall has been tracked by the profiling sonar sweeping a 30 degree sector centered about orthogonal the tracked feature. Experimental results, in the case the vehide had to keep the pool wall two meters at its right, follow. The vehicle's heading and sonar bearing are plotted in the top picture of Figure 6, together with the resulting direction of the sonar beam, while the bottom picture shows the measured sonar range and the estimated range of the vehicle from the wall.

W.I�Estimalion: Sona, Be.ring and Vehicle Heading

'--

�!0������ - beta

'------'10-----'-20---30-'-----'1 = �::a"'.i

�:

E�

·��:·'··-

�:-;:

'I

o W 20 30 � ro lime's,

Fig. 6. Wall-estimation: sonar range and bearing, and estimated range

It is worth noting that, since the sonar was located at prow on the longitudinal axis, the measured sonar range is minor than the estimated range· in the first phase of the maneuver, when the vehicle is not parallel to the tracked surface.

W.I�Foliowing: Esii;".led Wal�Slope; Refu,ence and ESlimaled Heading

l�t:=�l o W 20 30 � ro .

time Is' Fig.7. Wall-following:

reference and estimated heading and range.

The desired and estimated heading and range from the wall are plotted in Figure 7, together with the estimated wall slope (see the top picture). Since the reinforced concrete structure of the pool induced deformations of the magnetic field, the estimate of the wall orientation, based on the combination of the vehicle dynamics with compass and sonar measurements, presents some small changes even if the tracked surface is linear. The reference and estimated linear and angular velocities are plotted in Figure 8, which points out as the vehicle moved at its saturation surge, which was 0.3 mis, during the whole maneuver.

Wail-FOllowing: Reference and Estimated Velocities

Fig.8. Wall-following: reference and estimated linear and angular velocities.

5. Conclusions This research demonstrated the feasibility of the two layered hierarchical architecture presented in (Caccia and Veruggio, 2000) to support free-space and environment­related guidance task functions for unmanned underwater vehicles. In particular, a Lyapunov-based guidance law for approaching a target with the desired orientation has been integrated with suitable sonar-based motion estimators to perform medium range maneuvering and wall-following tasks. In any case, the proposed guidance laws can also work with different motion estimators such as, for instance, video-based pipeline tracking systems for pipeline-following applications. Next research step will consist in developing a system for automatic supervision and co-ordination of guidance and motion estimation tasks in order to execute complex missions including free-

water maneuvering at different precision, obstacle detection and feature-following.

Acknowledgments The author wish to thank all the staff of the Robotics Department for support in pool trials execution. The authors acknowledge Prof. Giuseppe Casalino and Prof. Roberto Cristi for their seminal ideas in Lyapunov­based motion control and acoustic-based motion estimation.

References Aicardi M., G. Casalino, A. Bicchi, A. Balestrino (1995). Closed-loop steering of unicycle-like vehicles via Lyapunov techniques. IEEE Robotics and Automation Magazine, vol. 2, no. 1, pp. 27-35 Caccia M., R. Cristi, G. Veruggio (1997). Acoustic Motion Estimation in a Structured Environment for an Unmanned Underwater Vehicle. IFAC Fifth Symposium on Robot Control (SYROCO '97), Vol. 2, pp. 339-344. Nantes, France. Caccia M., G. Casalino, R. Cristi, and G. Veruggio (l 998). Acoustic motion estimation and control for an unmanned underwater vehicle in a structured environment. Control Engineering Practice, vol. 6, no. 5, pp. 661-670 Caccia M., R. Bono, G. Bruzzone, G. Veruggio (1999). Variable configuration UUVs for marine science applications. IEEE Robotics and Automation Magazine, Vol. 6, No.2, June 1999, pp. 22-32 Caccia M., G. Veruggio (2000). Guidance and control of a reconfigurable unmanned underwater vehicle. IF AC Control Engineering Practice, Vol. 8, No. 1, January 2000, pp. 21-37, Elsevier Science Ltd., England Cristi R., M. Caccia, G. Veruggio (1998). Motion estimation and modeling of the environment for underwater vehicles. International Journal of System Science, vol. 29, No. 10, pp. 1135-1143, Taylor & Francis Ltd., London Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles; John Wiley & Sons, England. Fryxell, D., P. Oliveira, A. Pascoal, C. Silvestre and I. Kaminer (1996). Control Engineering Practice, vol. 4, no. 3, pp.40 l-409 Healey, A.J., and D. Lienard (1993). Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. IEEE Journal of Oceanic Engineering, vol. 18, no. 3, pp. 327-339

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