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Motion Control of a Hovering Biomimetic 4-finUnderwater Robot

Taavi Salumae, Ahmed Chemori, and Maarja Kruusmaa

Abstract—U-CAT is a highly maneuverable biomimetic 4-finunderwater robot for operating in confined spaces. Because of itsnovel mechanical design and specialized purpose, the traditionalautonomous underwater robot control methods are not directlyapplicable on U-CAT. This paper proposes a novel modularcontrol architecture that can be adopted for different applicationscenarios. Within this framework we implement and test several 2degrees of freedom (DOF) controllers and discuss the test results.Next, we describe and implement an actuation coupling methodby prioritizing the selection of DOF with fuzzy membershipfunctions and demonstrate the approach for 3-DOF control.The results show that DOF prioritization approach helps todecrease tracking errors both in the case of human in the loopand automatic control. Finally, we describe long duration fieldexperiments in realistic environmental conditions.

I. INTRODUCTION

AUTONOMOUS underwater vehicles (AUVs), such asIver-2 [1], Bluefins [2] and Remus [3], are nowadays

widely used in many research areas and industries. For exam-ple the oil and gas industry uses them for surveys to locate de-posits and to inspect pipelines or rigs [4], navies use them forintelligence and mine countermeasures [5]; and archaeologistsuse them to locate historical shipwrecks [6]. The large varietyof applications of AUVs motivates researchers to develop moreand more advanced control systems and technologies for thesevehicles. The more advanced control systems in turn shiftAUV application towards even more complex underwater en-vironments. In many of these environments, traditional vehicledesigns are no longer optimal. Traditional AUVs are actuatedby propellers and they are relatively large to accommodatehigh-tech suites. Such vehicles are not well suited to be usedin shallow waters, confined areas, in proximity of divers andanimals or close to bottom.

The use of biomimetic underwater robots presents an alter-native to traditional propoller driven vehicles by using novelthrust creating mechanisms, such as fins, paddels and flippers.Some recent examples of bio-inspired underwater locomotioninclude mimicking the swimming of fish to create AUVsfor mariculture monitoring [7], mimicking the locomotionof snakes in water to develop amphibious vehicles [8] andstudying the diving of birds to build aerial-aquatic robots [9].One class of fin-actuated AUVs consists of multi-fin vehiclesthat are often referred to as ”turtle-like robots”. These vehiclesuse multiple oscillating fins that are actuated either in 1 DOF

Taavi Salumae and Maarja Kruusmaa are with Centre forBiorobotics, Tallinn University of Technology, Tallinn, Estonia,taavi.salumae@ttu.ee

Ahmed Chemori is with LIRMM UMR CNRS/Univ. of Montpellier, 161rue Ada, 34392 Montpellier, France, ahmed.chemori@lirmm.fr

Fig. 1. U-CAT biomimetic 4-fin AUV.

[10]–[13], 2DOFs [14]–[18] or 3DOFs [19]. Most of themuse 4 fins, but in some cases the number of actuated fins isdifferent [13]. Some of the studies have a goal to preciselymimic the turtle-like motion [14]–[16], [19], [20] while inothers the biological similarity has lower priority comparedto practical feasibility [10]–[13], [18], [21]. With differentmulti-fin underwater vehicle designs, researchers mostly hopeto achieve high maneuverability, quiet and efficient thrustgeneration as well as reliable or even amphibious locomotion[11], [13], [15]. Alternative locomotion approaches mightwork better in difficult conditions, such as close to the bottom,next to shore or near water plants and animals.

As the locomotion principle of multi-fin vehicles is verydifferent from that of propeller-actuated vehicles, traditionalunderwater vehicle motion control methods often cannot bedirectly applied. One main peculiarity of fin-based actuationis the oscillating thrust generation - it is not possible tocreate constant thrust and this has a strong impact on thecontrol stability. The thrust vector of fins is also much lessreactive. While the rotation speed of the propeller can usuallybe changed in a fraction of a second, the thrust of a fin dependson the oscillation amplitude and frequency which cannot bechanged equally fast. Moreover, the thrust of fins can not beas easily and precisely estimated as it is a complex functionbetween oscillation parameters, bending modes and harmonicoscillations of fins and other variables. Next, and likely thebiggest difference between highly maneuverable traditionalAUVs and multi-fin AUVs, is that the former usually usea separate actuator for controlling each degree of freedomwhereas the latter are mostly under-actuated. Multi-fin AUVsinstead use different combinations of actuator configurationsin order to achieve motion in the available DOFs. They usedifferent combinations of fin motions to achieve different types

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of motions. This creates strong coupling between the control ofdifferent DOFs. For example, when such a vehicle is diving atfull speed, the fins are pointed straight up. This configurationcompletely prevents a surge action to be done at the sametime, as this requires the fins to be horizontal.

In this paper we propose a motion control system forbiomimetic vehicles actuated by 4 pitching fins. We demon-strate the implementation and functionality of the motioncontrol system on a novel biomimetic AUV U-CAT (Fig.1). U-CAT is an agile 6-DOF maneuverable vehicle that isdeveloped for autonomous and semi-autonomous inspectionof confined spaces, such as shipwrecks, caves, submergedbuildings etc. With regards to the mechanical locomotionprinciple, U-CAT presents a slight departure from previousworks; in task/mission directive, the vehicle is fully novel. Wepropose a control architecture suitable for semi-autonomousand autonomous control of the vehicle, more specifically:

• a modular, easily extensible control architecture thatallows rapid and simple implementation and testing ofdifferent controllers for different control scenarios.

• comparison of four controllers for simultaneous controlof 2 DOFs

• a method for dealing with actuation coupling by priori-tizing the action of different DOFs

• simultaneous control of 3 DOFs in 1) manual control with2 DOF autopiloting, i.e. remotely operated vehicle (ROV)mode; 2) fully autonomous control (AUV mode)

• demonstration and validation of the performance for areal underwater mission

This paper build upon our previous work published in [22]and [23] which have outlined our approach to the controlarchitecture along with partial test results. This paper extendsthe conference articles by adding:

• more detailed description of the implementation andvalidation of the whole control architecture

• model identification of the U-CAT robot• description, implementation and experimental compari-

son of different model-based controllers for selecting themost suitable one for U-CAT

• experimental validation of the whole system on realunderwater robot missions

The article is structured as follows: section II gives anoverview of multi-fin vehicles and their control systems.Section III describes the U-CAT vehicle, its modeling andthe model identification. Section IV describes the proposedcontrol architecture including the priority management. Sec-tion V compares 4 different controllers to choose the mostsuitable one for controlling U-CAT. Section VI shows theimportance of DOF priority management and validates thecontrol system for remotely operated vehicle mode and fullyautonomous mode. Section VII validates the system on tworeal-life missions. Conclusions are presented in Section VIII.

II. MULTI-FIN UNDERWATER VEHICLES AND THEIRCONTROL SYSTEMS

Most multi-fin vehicles aim to mimic aquatic locomotion ofturtles. Marine turtles produce thrust with a complex motion

of their forelimbs by using them as rolling and pitchingwings creating lift-based forces, as paddles or rows creatingmainly drag-based forces, or as a combination of both of them[24]. One of the earliest examples of mimicking such thrustgeneration can be seen on Turtle 2005 [14] of Kogakuin Uni-versity that uses rolling and pitching fore-fins for propulsionand pitching hind-fins for control. The same configuration isused by the robot turtle of Nanyang Technological University[15]. Some other examples are Finnegan the RoboTurtle [16]which uses 4 fins instead of 2 giving the robot a hoveringcapability, Naro-tartaruga [19] robot whose fins also includeadditional yaw motion and Gen series robots of Naval Re-search Laboratory [20] which use slightly different so calledactive shape deformation fins [17]. Turtle-like motion has evenbeen mimicked using smart soft composite materials [25].Some of these robots have better maneuverability than mostof the traditional AUVs. However, due to the specifics of theturtle-like actuation, all these robots perform much better insurge motion than in other degrees of freedom. They havenone or poor hovering capability and are thus not well suitedfor tasks such as wall-following or close-up inspection andinvestigation of confined spaces, in which the vehicle mustperform well along each DOF. Another major disadvantageof turtle-mimicking robots is the complexity of multiple-DOFfin actuators. Due to their complex mechanical design suchactuators are usually large and less reliable.

U-CAT generates thrust by using only the pitching motionof fins. This allows us to reduce complexity and size of thefins as each fin is driven only by a single motor. Pitchingfins have previously been used also on Madeleine of NektonResearch [10], [26], its commercial successor, an amphibianROV Transphibian of IRobot [11] and a vehicle developedby Robotics Institute of Beihang University [12]. All thesevehicles have 4 pitching fins whose rotation axes are parallel[10] or very close to parallel [11], [12]. Such fin configurationallows to control the robots in maximum 5 DOFs, leaving outthe sway motion i.e. they can not move sideways. U-CAT, onthe contrary, has a different mechanical configuration that alsomakes the sideways motion possible, thus giving the vehicleall 6 controllable DOFs.

There are also some other, slightly different vehicles thatuse pitching fins. An amphibious robot of Peking University[21] uses fins that are actuated by two parallel motors throughspecial five-bar link mechanism. The mechanism allows thefins to be used for thrust generation or as legs for walkingon the ground. Another vehicle of Peking University [18] hasfins whose rotation axes can be reoriented using an additional4 motors. This vehicle is extremely highly maneuverable andcan be used to control 6 DOFs, but this comes at a price ofdoubling the number of motors. The amphibious Aqua vehicleof McGill University [13] uses 6 pitching fins instead of 4. Theadditional two fins help to improve the crawling performance,but are excessive when only aquatic locomotion is desired.

The motion control systems of most of the multi-fin ve-hicles are not as profoundly developed as their mechanicaldesigns, however, there are some exceptions. Many of theauthors have only presented open-loop or manual control[12], [14], [15], [18], [21]. Their main contribution has been

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in the development and analysis of the gait generation, forexample using central pattern generators [12], [18], [21]. Somestudies have been conducted about the control of non- hovercapable turtle-like vehicles during dominant surge motion. [20]demonstrates model free control only for 1 DOF at the sametime, [19] presents model free control of the angular rate forforward swimming stabilization. [16] concentrates mostly onmimicking the fin kinematics and maneuvering of a biologicalturtle on Finnegan the RoboTurtle, but it presents also resultson pitch, roll and yaw control for different dynamically stableand unstable turning maneuvers. To the best of our knowledge,there are no studies that concentrate on the automatic positioncontrol of 4-fin hover-capable vehicles. Although [10] claimsto have a simultaneous control of different DOFs of theMadeleine vehicle, the authors have not published the controlapproach or any experimental or simulated results yet.

Advanced position control has been developed for a 6-finamphibious Aqua vehicle [13]. It is somewhat similar to theU-CAT in terms of using only pitching fins and being hover-capable. [27] and [28] present modeling and model-basedcontrol of Aqua, but only for a single simultaneous DOF.In [29] authors also demonstrate multi-DOF control using acombination of model-free PD and PI controllers for yaw, roll,pitch and heave. They avoid coupling problems by using gainscheduling depending on the surge speed. Even though authorshave reported good trajectory following, this was achievedby tuning an array of 45 control parameters, making thedeveloped control approach inextensible and complex. Authorshave tried to simplify the process by using online gain adaptionalgorithms [30], however the presented results show largedeviations from desired attitude.

As can be seen from the background overview, manydifferent fin-actuated vehicles have been developed in recentyears. However, the control of these vehicles, especially theposition control of hover-capable vehicles is relatively littlestudied.

III. U-CAT VEHICLE

U-CAT is a biomimetic underwater vehicle designed forautonomous and semi-autonomous inspection of confined ar-eas, such as shipwrecks, caves and man-made underwaterstructures. It was developed in the framework of EuropeanCommission funded research project ARROWS [31]. The aimof the ARROWS project was to adapt and develop low-cost AUV technologies to significantly reduce the cost ofarchaeological operations. U-CAT was designed specificallyto meet archaeologists’ requirements for unmanned shipwreckpenetration. It uses fin-based locomotion to achieve highmaneuverability and for quiet and safe locomotion. One uniquefeature of U-CAT compared to other mentioned 4-fin vehicleslies in its fin placement. The fins are placed such that a thrustforce can be created in all the 6 DOFS. This includes sway,which cannot be controlled with other vehicles using 1 DOFpitching fins, but which is extremely useful for various videoinspection tasks such as wall following. More detailed designjustification and the description of vehicle are presented in[32]. Some preliminary control results for 1 degree of freedomusing non-model-based controllers are published in [22].

zb

xb

ϑ

ψ

ϕ

yb

xe ze

ye xyz

Fig. 2. Coordinate systems used in this study. {xb, yb, zb} is the body-fixed coordinate frame and {xe, ye, eb} is the earth-fixed coordinate frame.Robot’s position is presented as a vector of positions in earth-fixed frameη = [x, y, z, ϕ, ϑ, ψ]T

U-CAT is 56 cm long and weights approximately 19 kg. Itsfour fins are actuated by 60 W Maxon brushless DC motorsdriven by Maxon Epos motor drivers using sensorless back-EMF feedback control. The vehicle has an internal batteryallowing at least 6 hours of autonomous operation. The wholecontrol architecture is developed on an internal single-boardcomputer with ARM Cortex A9 quad-core 1Ghz processor. Weuse a modular development approach with ROS middleware.The on-board computer communicates with a remote PCthrough a custom connectorless tether mounted on top ofthe vehicle. In the end of the tether there is a waterproofedWiFi router, creating an ultra short range underwater WiFilink. We use the remote PC only for forwarding remotecontroller actions in ROV mode, and accessing the on-boardcomputer for debugging. As a remote controller we used aSony Playstation DualShock 3.

In this paper we use the following sensors of U-CAT:• Invensense MPU-6050 IMU for measuring attitude. In the

current study only yaw measurement is directly used asa feedback in control loop. The roll and pitch measure-ments are used only for coordinate transformations. Thesampling frequency is 5 Hz.

• GEMS 3101 analog output pressure sensor with 18-bitDAQ for measuring depth. The sampling frequency is 10Hz and the resolution is 0.6 mm.

U-CAT has some additional devices not used in this study,but which will be used in further developments: Appliconacoustic modem for underwater communication and localiza-tion; two active buoyancy control modules; custom-developedhydrophone array for acoustic beacon localization; custom-made echosounder array for close-distance obstacle avoidance;Point Grey Chameleon camera; and various system healthmonitoring sensors.

A. Kinematics

U-CAT has four fins placed at 30 degree angle with respectto the vehicles center-line on the horizontal plane. Each fin i isseparately actuated using a sinusoidal input with parameters:Ai - oscillation amplitude; fi - oscillation frequency and Φi

- oscillation offset. The oscillation amplitude and frequency

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a) b) c)

d) e) f)

Fig. 3. Motions of the U-CAT in the hovering mode: a) surge; b) sway; c)heave; d) roll; e) pitch; f) yaw.

modify the magnitude of thrust while the oscillation offsetmodifies the direction of thrust. By combining the motions ofall four fins it is possible to move the robot in all the threedirections and to rotate the robot around all three axes.

We have identified 2 main modes of locomotion which wecall 1) cruise mode and 2) hovering mode. In cruise mode thefins are generally pointing in the same direction (as seen on therobot on Fig. 2). The surge motion in cruise mode is achievedby actuating all the fins at the same time. The robot can beoriented by slightly modifying the offset or thrust of some ofthe fins. The cruise mode is useful when fast forward motion isdesired, however, it is not practical for slow maneuvering andhovering at single spot. The reason is that it is not possible tocreate thrust forces in any direction without reorienting fins.For example when the vehicle is swimming forward and thenneeds to slightly move backwards, it would have to reorientall its 4 fins 180 degrees, making it impossible to preciselykeep station. To avoid this problem during tasks that requireprecise maneuvering, such as close-up inspection of an artifact,we use the hovering mode. During hovering mode the frontand back fins are generally pointing towards each other. Such afin configuration allows for force in any direction and torquearound any axis to be created without fin reorientation (seeFig. 3).

The current article concentrates only on the control of therobot in the hovering mode. The oscillation frequency of thefins is fixed at an experimentally identified optimum value andthe desired thrust is being achieved by actively changing theactuation amplitude. The fin oscillations are synchronized tohave a zero phase shift. Precise synchronization is importantto reduce irregular motions of the vehicle resulting fromoscillating thrust vectors. When the fins are all oscillatingin the same phase, the vehicle oscillates mostly in the heavedirection.

B. Dynamics

We model the rigid body dynamics of the vehicle in 6DOFs using Fossen’s robot-like vectorial model of marinecraft [33]. The Fossen’s model is well suited for computer

implementation and control systems design. Therefore it iswidely used in underwater robotics, but also in submarine andsurface vessel studies. The 6 DOF model is represented as:

Mν +C(ν)ν +D(ν)ν + g(η) = τ (1)η = J(η)ν (2)

where η = [x, y, z, ϕ, ϑ, ψ]T is the vector of positions inthe earth-fixed frame, ν = [u, v, w, p, q, r]T is the vector ofvelocities in the body-fixed frame and J(η) ∈ R6×6 is thetransformation matrix mapping from the body-fixed frame tothe earth-fixed frame. The coordinate systems are presented onFig. 2. M =MRB+MA is the system inertia matrix, whereMRB is the inertia matrix of the vehicle and MA describesthe added mass resulting from the accelerating volume ofwater surrounding the robot. C(ν)CRB+CA is the Coriolis-centripetal matrix which takes into account the rigid bodyand the added mass. D(ν) is the damping matrix, g(η) isthe vector of gravitational/buoyancy forces and moments andτ = [X,Y, Z,K,M,N ]T is the vector of control inputs. τcan be represented as a resultant force composed of forces Fi

with which each fin i acts on the rigid body.

C. Fin forces

To successfully control the vehicle using model-based ap-proaches, we need to know the relationship between thefin actuation parameters and the generated thrust force. Theforces generated by the fins depend on complex interactionsbetween the viscoelastic body and the hydrodynamics of thesurrounding water. We have previously studied the analyticalmodeling of these interactions [34], however, due to complexnature of the system, analytical models are either too impreciseor not suitable for using in real-time control. Therefore, wecreate an empirical model of the fin thrust.

The average magnitude Fi of thrust Fi of each fin i isdescribed as

Fi = ξ(,Ai , fi) (3)

where Ai is the oscillation amplitude and fi is the oscillationfrequency. We identified the relationship experimentally bymounting the U-CAT’s fin module on a waterproof 4-axisforce/torque sensor and actuating it with different amplitudesand frequencies. Fig. 4 plots the average thrust during 10 sexperiment period. We fitted the experimental results to gainthe relation 3.

To illustrate the strong oscillating nature of the fin lo-comotion, Fig. 5 plots the example of forces generated bythe fins over 2 oscillation periods. The plot shows that thefins do not generate fluctuating forces only in the desireddirection. They also generate lateral forces whose amplitude isoccasionally exceeding the amplitude of thrust. Large lateralforces are the main reason why the fin motion has to beprecisely synchronized. The oscillating motion also has to betaken into consideration during controller implementation asit can initiate strong instability.

5

Amplitude, deg0 10 20 30 40 50 60

Mea

n Th

rust

, N

0

1

2

3

4 2.3 Hz

0.5 Hz

1.4 Hz

0.8 Hz

1.1 Hz

2.6 Hz1.7 Hz

2.0 Hz

Fig. 4. Mean fin thrust at different actuation parameters. Red marks thefrequency of 2 Hz which we used in our control experiments.

Time, s0 0.5 1 1.5 2

Forc

e, N

-10

0

10

ThrustLateral Force

Fig. 5. Thrust and lateral forces generated by the fin while actuated at 2.0Hz with the amplitude of 30 deg

D. Model identification

The initial dynamic parameters in Eq. 1 were found usingboth analytical and computational methods. Using experimen-tal model identification, the most important of these parameterswere adjusted.

The geometrical properties of the vehicle are found from adetailed 3D model drawn in SolidWorks CAD software. Themodel includes all the internal and external components of therobot and also the density of the larger components. The 3Dmodel allowed us to precisely calculate all the componentsof the U-CAT’s inertia matrix MRB , the Coriolis-centripetalmatrix CRB , and the gravity and buoyancy vector g(η).The damping is modeled as a hydrodynamic drag. The dragcoefficients in the damping matrix D(ν) are found usinga computational fluid dynamics package called SolidworksFlow Simulation. The inertia MA and Coriolis-centripetalmatrix CA of the added mass are calculated with the helpof strip theory using simplified geometrical representation ofthe vehicle. Strip theory is a widely used approach in marineengineering. It can be used to find an added mass of closed2D contours. The added mass of contours is summed to findthe added mass of the whole body.

To achieve higher modeling precision along the most im-portant DOFs, we experimentally identified surge, sway, heaveand yaw related components of the added mass inertia matrixMA and drag matrix D(ν). We actuated the robot with aconstant known force in a single DOF at the same time andmeasured the response. To measure the depth response we usedthe pressure sensor, and for yaw, surge and sway response weused the experimental setup described in Fig. 6. The robot wasmounted on a highly buoyant bar to constrain its depth, roll

3 m 5 m

1.8 m

1

2

Fig. 6. Experimental setup for model identification and validation. Experimentwas conducted in a 25 m swimming pool. The robot was mounted on a floatingbar (2) which was tracked by the overhead camera (1).

and pitch motions. On the bar there were two contrast markerswhich were automatically tracked from the video recorded bythe calibrated over-head camera. The custom-made trackingsoftware implemented in LabVIEW calculated the vehicle’scoordinates on the x-y plane. The robot itself was preciselytuned to be neutrally buoyant to minimize the effect of the baron the system dynamics. The bar was only slightly touchingthe water surface.

As during each experiment the robot is moving only alonga single axis, the dynamics can be written in a single DOF.For example for the x-axis

(MRBx +MA

x )u+Dxu = τx (4)

The velocity u and acceleration u are taken from the experi-mental results, total fin thrust τx in x-direction known from thefin characterization experiment and vehicles inertia matrix’sfirst diagonal component MRB

x is equal to the vehicle’s mass.The parameters MA

x and Dx can be found using the least-squares method over the full experimental data set. We re-peated the process with various different actuation parametersand and selected the average of the found coefficients.

To validate the precision of the model we compared the ex-perimentally measured motion and the model-predicted motionin each degree of freedom. The results for a single actuationamplitude and frequency are presented on Fig. 7. It can beseen that the model-predicted position of the robot matchesthe actual position with a high precision.

IV. CONTROL ARCHITECTURE

We present a modular, easily extensible control architecturethat allows rapid and simple controller implementation andtesting, but which also can be used during a wide range

6

0 5 10

Surg

e, m

0

1

2

3

4

0 5 10

Sway

, m

0

0.5

1

1.5

Time, s0 5 10 15

Hea

ve, m

0

0.5

1

1.5

2

2.5

Time, s0 5 10 15

Yaw

, rad

0

5

10

15

20PredictedMeasured

Fig. 7. Model validation for four main degrees of freedom. Plots showthe model predicted (solid line) and experimentally measured (dashed line)position in different degrees of freedom when the fins are actuated at constantparameters (frequency of 2 Hz and amplitude of 50◦)

of different real mission scenarios (see Fig 8). The controlarchitecture is implemented fully in general matrix form.Matrix form implementation allows to quickly work withdifferent DOF’s without the need to reimplement any parts ofthe architecture if additional DOF’s need to be added to thecontrol. The second feature, which simplifies the testing andimplementation, is that the control architecture is composed ofdifferent modules, which all are implemented as independentROS nodes. Each node can be easily replaced or modifiedfor different scenarios. Also, additional nodes can be addedfor new control scenarios. In the current study the core ofthe control architecture is composed of the following nodes:Automatic Control for different DOFs, Dynamical Model, Pri-ority Management, Force and Torque Calculation, Actuation,Odometry Estimation, Trajectory Management, and HumanIntervention.

The general idea behind the proposed control is that eachdegree of freedom is separately and independently controlledby the best controller chosen for this DOF. The output ofeach controller is then prioritized using smooth functions, de-pending on the desired control action, to reduce the actuationcoupling problem. The controllers can be individually tunedand replaced with a different control method or with manualinputs from the remote controller.

A. Automatic control

The automatic control node includes the controller imple-mentations for each DOF. To choose the most suitable controlapproach we have experimentally tested different model-freeand model-based controllers. In section V we present thecomparison of following controllers:

• PID• Inverse dynamics (ID)

IMU

Pressure sensorOdometry node

Trajectory manager

Wrench driver

𝜂, ν

𝜂 , νd d

𝝉

Saturation

Rate limiter

Priority management

Yaw and depth priority

Surge priority

1-1 0

1

0

0.5

𝛼₁

Prio

rity

𝝉 �𝜶

M1 M2 M3 M4

𝝓, 𝑨, 𝒇

𝝉 �

Joystick

Dynamics nodeAutomaticcontrol

DOF-wise controller selection

𝜶

C(ν), D(ν)

g(𝜂)

𝜂, ν

Fig. 8. Motion control architecture

• Inverse dynamics with nonlinear feedback gains (IDNL)• Adaptive inverse dynamics (AID)

B. Human intervention

In addition to the automatic control, all DOFs can be con-trolled manually using a joystick. Joystick outputs axis valuesbetween 0 to 1. These values are proportionally mapped tomanual control input τm. For each DOF, operator can choosewhich control input the vehicle uses, manual or automatic.

C. Priority management

The priority management node offers a solution to the DOFactuation coupling problem. It was proposed and demonstratedon U-CAT in our previous work [23]. Previously, task prioritycontrol has been used in robotics to prioritize between differenttasks [35] but as opposed to task priority control, DOF prioritycontrol is implemented to solve the problem of actuationcoupling. We demonstrated experimentally that using our DOFprioritization approach significantly reduced the tracking er-rors. DOF prioritization approach works by assigning prioritiesto the control actions using smooth functions. To prioritizethe DOFs, control input vector τ elements are multipliedby priority vector p = [px, py, pz, pϕ, pϑ, pψ] elements. Thepriority of each DOF varies from 0 to 1. To assign priorities,different sets of laws could be created. Our tests show that on

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U-CAT it is best to use laws that assign priorities depending onthe control action of a single DOF. We created laws that givehighest priority to yaw and depth control when surge action issmall. When surge action increases, the priority of depth andyaw decreases. In principle, the control is modified dependingon what motion the vehicle is about to perform. When thevehicle is close to its desired x , y position, it can preciselyhover and orient itself towards the desired direction. When anew waypoint is commanded or when the operator wants tomove forward, surge action increases and the action of depthand yaw decreases. The laws we use are the following:

pz = pψ = c1|αx|3 + c2|αx|2 + c3|αx|+ c4

px = 1− pz(5)

where αx = τx/τxmax is the normalized control input.Constants ci are such that 0 < α1 < 1 → 0 < pz < 1.The rules are plotted in Fig. 8.

D. Wrench driver

The wrench driver converts the generalized, priortized con-trol input τp into fin actuation parameters Ai, fi and Φi . Ituses a set of simple rules to convert forces and moments ofdifferent DOFs to corresponding fin thrust forces Fi. Theserules are implemented to achieve motions presented on Fig. 3.The conversion from fin thrust forces to actuation parametersis found from (3). We use a fixed frequency of 2 Hz andonly vary the oscillation amplitudes Ai and directions Φi .Wrench driver forwards the actuation parameters to Maxonmotor controllers who handle the position control of fins.

E. Odometry and trajectory

Odometry node calculates the positions and velocities of thevehicle using the feedback from IMU and pressure sensor. Italso estimates the position of the vehicle in the world-fixedframe using the dynamics of the vehicle. However, we do notuse this estimation in the current study due to the lack of agood state observer.

The trajectory manager creates smooth position and velocitytrajectories. In the current study it uses predefined timedsetpoints written in a file. It then uses hyperbolic tangentfunctions to calculate smooth transitions between setpoints.The trajectory manager is also able to read setpoints fromother sources. For example, a remote controller can be usedto modify the desired depth and yaw.

V. 2-DOF CONTROL

The Automatic Control Unit in Fig. 8 is responsible forautomatically controlling the specified degrees of freedom.This control unit can work in combination with the manualcontrol by joystick, leaving the control of some DOFs for ahuman operator. An automatic control of some DOFs wouldtake some cognitive load from the human operator and letthe operator concentrate on better completing the misson. Atypical scenario may be a human operation guiding the vehiclealong a desired trajectory by visual feedback on x-y planewhile the depth and yaw of the vehicle are automatically

controlled. In order to select the most suitable controllerfor automatic control, we present the implementation andcomparative experiments of four different feedback controllers(one non-model-based and three model-based controllers) at3 different implementation scenarios with a varying degreeof complexity. All the proposed controllers are tested andcompared at the following scenarios:

• Nominal case in a controlled environment• External disturbance rejection• Robustness towards uncertainties

A. Controllers1) Proportional Integral Derivative (PID): The PID is a

well known and well established non-model-based controller[36]. The control law can be expressed by:

τττ = KP ηKP ηKP η +KI

∫ t

0

ηKI

∫ t

0

ηKI

∫ t

0

η dtdtdt+KD˙ηKD˙ηKD˙η (6)

ηηη = ηηη − ηdηdηd is the tracking error, and ˙ηηη is its first derivative.KPKPKP ,KIKIKI ,KDKDKD are positive definite matrices representing theproportional, the integral, and the derivative feedback gainsrespectively.

2) Inverse dynamics (ID): The main idea of this controlleris to fully linearize the dynamics of the robot based on anonlinear feedback law to obtain a linear system [33]. Considerthe nonlinear dynamics (1) of the robot, and consider thefollowing nonlinear feedback control law:

τττ = MabMabMab +n(ν, η)n(ν, η)n(ν, η) (7)

with ababab the body frame commanded acceleration, that can becalculated from a simple transformation between the body andthe earth fixed-frames as ababab = J−1J−1J−1(ananan − JνJνJν), and ananan =

ηdηdηd−KP ηKP ηKP η−KI

∫ t0ηKI

∫ t0ηKI

∫ t0ηdtdtdt−KD

˙ηKD˙ηKD˙η, where ηdηdηd is the desired trajectory

and ηdηdηd is its corresponding acceleration. The control law (7),if replaced in the robot’s dynamics (1), leads to:

(JJJννν + JνJνJν) = ηdηdηd −KP ηKP ηKP η −KI

∫ t

0

ηKI

∫ t

0

ηKI

∫ t

0

η dtdtdt−KD˙ηKD˙ηKD˙η (8)

Now consider the robot’s kinematics (2), its first derivativeleads to ηηη = JJJννν + JJJννν, which if combined with (8) gives:

¨ηηη +KD˙ηKD˙ηKD˙η +KP ηKP ηKP η +KI

∫ t

0

ηKI

∫ t

0

ηKI

∫ t

0

η dtdtdt = 0 (9)

With an appropriate choice of the feedback gainsKPKPKP ,KIKIKI ,KDKDKD, the closed-loop dynamics is asymptoticallystable.

3) Inverse dynamics with nonlinear feedback gains (IDNL):This approach has the same control law as the previous one,except that feedback gains are no longer constants. The use ofnonlinear varying feedback gains may improve the trackingperformance of the controller. For instance, the NonlinearComputed Torque [37] and the Nonlinear Augmented PD [38]provided better tracking performance than the conventionalcomputed torque and augmented PD controllers respectively.For our case, let’s consider the following nonlinear propor-tional gain KP (·)KP (·)KP (·):

KPKPKP (e) =

{kp0 |e|α1−1, |e| > δ1,

kp0δα1−11 , |e| 6 δ1.

(10)

8

where kp0 is its maximum values, α1 is the nonlinearitydecreasing parameter and δ1 its activation threshold (as illus-trated in Fig. 9). The derivative gain KD(·)KD(·)KD(·), also illustrated inFig. 9, may be expressed by:

KDKDKD(e) =

{kd0 |e|α2−1, |e| > δ2,

kd0δα2−12 , |e| 6 δ2.

(11)

with kd0 is its minimum value, α2 is the nonlinearity increas-ing parameter and δ2 its activation threshold.

0.65kp0

0.7kp0

0.75kp0

0.8kp0

0.85kp0

0.9kp0

0.95kp0

kp0

1.05kp0

0.95kd0

kd0

1.05kd0

1.1kd0

1.15kd0

1.2kd0

1.25kd0

1.3kd0

1.35kd0

−4 −3 −2 −1 0 1 2 3 4

kp0

kd0

kp(e)

kd(e)

Fig. 9. Typical evolution of the nonlinear proportional KP and derivativeKD gain versus position error e and velocity error e (respectively) with α1 =0.75, δ1 = 1, α2 = 1.25 and δ2 = 1.

4) Adaptive inverse dynamics (AID): The adaptive inversedynamics controller is a state feedback controller with anadaptation control term. It provides an online estimation ofpossible unknown model parameters in order to ensure a goodtrajectory tracking [33]. The control law can be expressed by:

τττ = MabMabMab + n(ν, η)n(ν, η)n(ν, η) (12)

where the hatted variables denote the dynamics matrices basedon estimations, n(ν, η)n(ν, η)n(ν, η) the estimate of n(ν, η)n(ν, η)n(ν, η) in (7). Since thedynamic model is linear in its parameters, the adaptive controllaw (12) can then be rewritten as:

τττ = Φ(ab, ν, η)θΦ(ab, ν, η)θΦ(ab, ν, η)θ (13)

where ΦΦΦ represents the regressor and θθθ is the vector of theonline estimated parameters. ababab and ananan are computed asin the inverse dynamics controller. The vector of estimatedparameters is updated online based on the following adaptivelaw:

˙θ˙θθ = −ΓΦT (ab, ν, η)J−1yΓΦT (ab, ν, η)J−1yΓΦT (ab, ν, η)J−1y (14)

where the diagonal positive definite matrix ΓΓΓ represents theadaptation gain, JJJ the transformation matrix, and yyy is thecombined tracking error given by yyy = c0ηηη+c1 ˙ηηη. c0 and c1 arepositive constant gains, that may be chosen using the algorithmpresented in [33], and based Barbalat’s lemma, it ensures thatyyy converges to zero.

B. Implementation details

The comparative experiments of 2-DOF control have beencarried out in the swimming pool of the University of Mont-pellier in France with the aim of choosing the most suitablecontroller for the automatic control mode of the architecture

of Fig. 8. The 2DOF control experiments where implementedas follows:

• The parameters of each controller are tuned for thenominal case and kept unchanged for the other scenarios.

• All the proposed controllers were implemented on U-CAT using the ROS based control architecture presentedin section 8

• Two degrees of freedom are to be simultaneously con-trolled (namely depth and yaw).

• All the relevant real-time data were saved to ROS log files(rosbags). The use of rosbags enables inspectingthe data exactly in the same form as used by the robotsoftware.

Next we will briefly describe all 3 implementation scenarios,represent the results and discuss the selection of the 2-DOFcontroller. The parameters of the controllers are summarizedin Tables I, II, III and IV.

TABLE ISUMMARY OF THE PARAMETERS OF THE PID CONTROLLER.

Parameter KPKPKP KIKIKI KDKDKD

Value

(200 00 8

) (7.5 00 0.05

) (80 00 6

)

TABLE IISUMMARY OF THE PARAMETERS OF THE ID CONTROLLER.

Parameter KPKPKP KIKIKI KDKDKD

Value

(0.6 00 2.5

) (0.075 00 0.1

) (0.2 00 2.2

)

TABLE IIISUMMARY OF THE PARAMETERS OF THE IDNL CONTROLLER.

Parameter kp0kp0kp0 KIKIKI kd0kd0kd0

Value(1.6 00 6.7

) (0.075 00 0.1

) (0.36 00 6

)Parameter α1α1α1 α2α2α2

Value(1.25 00 0.01

) (1.25 00 0.1

)Parameter δ1δ1δ1 δ2δ2δ2

Value(0.02 00 1.25

) (0.1 00 1.25

)

TABLE IVSUMMARY OF THE PARAMETERS OF THE AID CONTROLLER.

Parameter KPKPKP KIKIKI KDKDKD

Value

(0.6 00 2.5

) (0.075 00 0.1

) (0.2 00 2.2

)Parameter c0c0c0 c1c1c1 ΓΓΓ

Value

(0.1 00 0.1

) (0.075 00 0.075

) (1.5 00 3

)

9

0 20 40 60 80

Dep

th, m

-0.6

-0.4

-0.2

0

Nominal case

Time, s0 20 40 60 80

Yaw

, rad

0

0.5

1

0 50 100-0.6

-0.4

-0.2

0

External disturbance

Time, s0 50 100

0

0.5

1

0 20 40 60 80-0.6

-0.4

-0.2

0

Increased buoyancy

Actual valueDesired value

Time, s0 20 40 60 80

0

0.5

1

20 40 60 80

Dep

th, m

-0.6

-0.4

-0.2

0

Nominal case

Time, s20 40 60 80

Yaw

, rad

0

0.5

1

0 50 100-0.6

-0.4

-0.2

0

External disturbance

Time, s0 50 100

0

0.5

1

0 20 40 60 80-0.6

-0.4

-0.2

0

Increased buoyancy

Actual valueDesired value

Time, s0 20 40 60 80

0

0.5

1

0 20 40 60 80

Dep

th, m

-0.6

-0.4

-0.2

0

Nominal case

Time, s0 20 40 60 80

Yaw

, rad

0

0.5

1

0 50 100-0.6

-0.4

-0.2

0

External disturbance

Time, s0 50 100

0

0.5

1

0 20 40 60 80-0.6

-0.4

-0.2

0

Increased buoyancy

Actual valueDesired value

Time, s0 20 40 60 80

0

0.5

1

PID

IDID

NL

Fig. 10. 2DOF controller comparison results in three different test scenarios. Part 1 - PID, inverse dynamics and inverse dynamics with nonlinear feedbackgains

10

0 20 40 60 80

Dep

th, m

-0.6

-0.4

-0.2

0

Nominal case

Time, s0 20 40 60 80

Yaw

, rad

0

0.5

1

0 50 100-0.6

-0.4

-0.2

0

External disturbance

Time, s0 50 100

0

0.5

1

0 20 40 60 80-0.6

-0.4

-0.2

0

Increased buoyancy

Actual valueDesired value

Time, s0 20 40 60 80

0

0.5

1

AID

Fig. 11. 2DOF controller comparison results in three different test scenarios. Part 2 - Adaptive inverse dynamics controller

C. Experimental scenarios

1) Experimental scenario 1 : Nominal case: We first test allthe proposed control solutions in the nominal case. This meansthat the tests will be conducted without external disturbancesand without changes in the dynamic parameters of the robot.The main objective is to track predefined time-varying refer-ence trajectories along both controllable degrees of freedom(depth and yaw).

2) Experimental scenario 2 : External disturbance rejec-tion: The main objective behind this experimental scenario isto test the ability of the proposed controllers to reject externaldisturbances. The same predefined time-varying reference tra-jectories, used for the previous scenario, are tracked. Once thesystem outputs (depth and yaw) reach the steady-state value,an external disturbance is applied, the behaviour of the systemis recorded to show the reaction of the controller and its abilityto steer back the system’s outputs to their reference values.

3) Experimental scenario 3 : Robustness towards uncer-tainties: With this scenario we test the robustness of thecontrollers towards parameters’ uncertainties. We change oneof the dynamic parameters of the robot (namely the buoyancy),and check how well the proposed controllers are able tocompensate for such change with respect to the nominal case.It is worth to emphasize that all the parameters of the proposedcontrollers are kept unchanged. Fig. 12 illustrates how thebuoyancy of the robot was changed: piece of a float was fixedon the body of the robot, which will increase its buoyancy. Theproposed experimental scenario consists of tracking referencetrajectories while the buoyancy of the robot is increased.

D. Experimental results

The experimental results are plotted in Fig. 10 (PID, IDand IDNL controllers) and Fig. 11 (AID controller). Theplots show the desired and actual depth and yaw during eachexperiment. To compare the results, we use the root-mean-square tracking error (RMS) calculated over the full lengthof each experiment (from diving to re-surfacing). In additionto the RMS error of depth (RMSdepth) and yaw(RMSyaw)

Fig. 12. View of the robot with increased floatability, a piece of float fixedto the body of the robot increases its buoyancy.

TABLE VRMS VALUES FOR DEPTH / YAW

Scenario 1 Scenario 3depth | yaw depth | yaw

PID 34.5 mm | 30.3 mrad 56.1 mm | 136.6 mrad

ID 22.8 mm | 37.0 mrad 39.6 mm | 76.0 mrad

IDNL 29.6 mm | 29.2 mrad 51.0 mm | 85.3 mrad

AID 21.2 mm | 33.0 mrad 22.2 mm | 68.3 mrad

TABLE VIMEAN RMS VALUES

Scenario 1 Scenario 3

PID 32.4 96.3

ID 29.9 57.8

IDNL 29.4 68.1

AID 27.1 45.2

we use the mean of these two values (RMS) to describe thecombined performance of the whole system. All the depth andyaw RMS values are shown in Table V and all the mean RMSvalues are shown in Table VI.

11

It is important to note that RMS values are comparable onlyin the Scenario 1: Nominal case and Scenario 3: Robustnesstowards uncertainties. RMS value does not give meaningfulinformation in Scenario 2: External disturbance rejection, asthe external disturbance applied to the vehicle was not equal inall the experiments. In this scenario we qualitatively estimatehow well does the vehicle return to a steady state after thedisturbance.

The results show that in the nominal case, all four proposedcontrollers hold the vehicle on the predefined trajectory with-out any major deviations or oscillations. However, the RMSvalues differ significantly. As expected, the mean RMS of PIDis bigger than that of the model based controllers in both thenominal and the increased buoyancy scenario. In the case ofincreased buoyancy the PID is not able to correctly track theyaw trajectory due to the instability in depth control and thecoupled degrees of freedom.

The ID depth controller performs 33.9% better than PID innominal case and 29.4% better than PID in case of increasedbuoyancy. Even though the yaw performance in nominal casewas slightly lower than that of the PID, the combined errorof ID was 7.7% smaller in nominal case and 40.0% smallerin the case of modified buoyancy. The external disturbanceexperiment shows that the ID controller is very well able toreturn the vehicle to the desired values after disturbance. Thereare no oscillations in the depth and yaw values and only slightovershoot in the yaw.

Contrary to our expectations, IDNL does not perform betterthan ID. Even though its combined performance in the nominalcase is 1.6% better than that of the ID, the mean RMS inthe modified buoyancy case is 17.9% higher that of the ID(28.7% bigger depth RMS and 12.2% bigger yaw RMS). Also,the external disturbance experiment reveals strong oscillationsin depth and failure to return to desired yaw value afterdisturbance.

The AID’s mean RMS is 9.3% smaller than that of theID in nominal case and 21.7% smaller that that of the ID inthe case of modified buoyancy. Based on these values AIDhas best performance in the nominal case and in the caseof modified buoyancy (16% better than PID in nominal caseand 53% better than PID in the case of modified buoyancy).However, the external disturbance experiment reveals a majordisadvantage of the adaptive controller. After the disturbance,the controller needs approximately 40 s to take the vehicleback to the desired depth. During these 40 s there is a steadydepth error slowly converging towards zero. The reason forthis error is that as a result of a strong external disturbance theadaptive model parameters diverge from their desired valuesand it takes time until the parameters re-adapt to their correctvalues.

Based on the controller comparison we can say that PIDand ID are the only controllers that show good results inall the three experimental scenarios. However, due to thecompensation of the nonlinear components of the vehicledynamics, the ID controller performs significantly better.IDNL fails to perform well in our case probably because ofa more difficult and less intuitive parameter tuning process.As we are looking for robust and easily applicable control

methods, IDNL is not the best approach. As expected, AIDperforms significantly better than any other controller in thetest of robustness towards model uncertainties. Therefore, thiscontroller would be the best choice for missions where thevehicle dynamics changes during the operation. This includesfor example the case where the robot is operated on a longtether that affects the vehicle’s dynamics. However, AID isnot appropriate for missions in which the vehicle may beexposed to strong external disturbances, such as collision withunderwater objects. Our control architecture allows seamlessswitching between different control approaches even duringthe mission. Either ID or AID can be chosen by the operatordepending on the situation.

VI. 3-DOF CONTROL

This section experimentally validates the control architec-ture with DOF prioritization for 3D motion of the robot.We describe 3 control strategies where some of the degreesare controlled by the operator with the joystick and othersautomatically while using the DOF priority manager in Fig.8. These tests are also compared to the scenario where theDOF priority management is switched off.

The experiments were conducted in a 60 m long, 5 m wideand 3 m deep fresh water tow tank of Tallinn Universityof Technology. In all the experiments the robot followeda lawnmower trajectory at constant depth of 1 m. Eachexperiment started with a dive and ended with a resurface.We chose the lawnmower trajectory because of its wide usein underwater inspection tasks. During the experiments therobot recorded its depth and yaw data into ROS log files. Asthe acoustic positioning methods did not work in a concretetank, we did not have any real-time position feedback fortranslational motions on the horizontal plane. However, weused a calibrated overhead camera for recording the vehicletrajectories. After the experiments we manually tracked theposition of U-CAT from the overhead video frame by frame.

A. Experimental scenarios

We tested the following 5 control approaches:1) Fully manual control: An experienced U-CAT operator

controlled depth, yaw and surge to follow the predefinedtrajectory as precisely as possible while keeping constantdepth. In this scenario the automatic control unit on Fig.8 is switched off and the commands from the joystick areprocessed by the priority manager. The operator used visualfeedback and a depth reading on screen. The lawnmowertrajectory was relatively loosely defined in our experiments,as there was no precise position feedback other than visual.The operator used markers on the poolside to approximatelytravel a same distance with every short leg of the trajectory.For comparative reasons the operator also tried to follow thesame trajectory timing as in other experiments.

2) Depth autopilot: In this experiment the automatic con-trol unit in Fig. 8 controls only depth while the operatorcontrolled other DOFs (yaw and surge) manually.

12

3) Depth and yaw autopilot: In this experiment the opera-tor’s manual control was kept minimal as he only controlledthe surge motion with the joystick to move the vehicle fromone turning point to another while depth and yaw motionwhere controlled automatically.

4) Fully autonomous control: As U-CAT is designed toeventually be fully autonomous, we also tested the extensibilityof our control approach to fully autonomous mode. In this casethe vehicle was untethered and the operator was removed fromthe control loop. The manual surge regulation was replacedby automatic open-loop control. As we did not have anysurge velocity or position feedback, the surge control wasimplemented as a smooth predefined force trajectory.

5) Fully autonomous control without DOF prioritization:In this experiment we repeated the fully autonomous controlscenario, but we disabled the priority manager. All 3 DOF(depth, yaw and surge) where controlled by the Autonomouscontrol unit in Fig. 8 while the Priority Manager was turnedoff.

B. Experimental Results

The desired and actual trajectories for each of the aboveexperiments are shown in Fig. 13. Root mean square (RMS)error values calculated over the full length of experiments aremarked on the graphs.

1) Manual Control: Fig. 13a shows the desired and actualtrajectories of depth, yaw, x and y. From the figure it canbe easily seen that the trajectory following precision is poor(depth RMS error of 27.6 cm and yaw RMS error of 39.8◦).This illustrates the definite need for at least some autopiloting.

2) Depth Autopilot: In this experiment the depth autopilotwas enabled while the operator manually controlled the surgeand yaw. Results show 81% decrease in depth error comparedto the manual control. In addition yaw error decreased 28%as now the operator had to concentrate on controlling only2 DOFs instead of 3. However, the overhead camera imagestill reveals the lack of precision in tracking straight lines.The vehicle turns rapidly. This kind of unsteady motion wouldprobably cause problems in video inspection tasks, especiallywhen using automatic video processing methods such asmosaicking.

3) Depth and Yaw Autopilot: In this experiment we alsoenabled automatic yaw control. This time the operator inter-vention was minimal. He only had to control the surge motionto move the vehicle from one turning point to another. Results(Fig. 13c) show high precision in yaw tracking (RMS errorof 2.5◦ ; improvement of 91%). Also, due to more steadyyaw the depth tracking error decreased by 63% comparedto the scenario with only depth autopilot. More stable yawis also visible from the overhead camera image. It showshow the robot moves in straight lines between turning points.Unfortunately, the short legs of the trajectory (vertical onthe overhead camera images) are not perpendicular to thelong legs. This is caused by the disturbance of the tether,which slowly pulled the vehicle sideways. The disturbances areinevitable and during ROV missions they have to be manuallycompensated for. The compensation can be relatively easily

done as the U-CAT’s fins also allow to actuate the sway motionto move the vehicle sideways. In this article, however, we donot consider sway control.

4) Fully Autonomous Control: The results (Fig. 13d) showthat removing human intervention did not significantly reducethe tracking precision. Also, the tether disturbance is not anymore visible on the overhead image. However, the figurereveals an IMU drift in yaw signal which was not present inour previous experiments. We have noticed that large IMU driftsometimes occurs due to electromagnetic noise emitted by themotor controllers. The drift is small enough (0.9 deg/min)to not affect the controller behaviour. For real missions thedrift will be reduced by minimizing electromagnetic noiseand by using magnetometers and Extended Kalman Filter.Despite the IMU issue the experiment shows that our controlapproach is suitable for simultaneously controlling 3 DOFsof the fully autonomous 4-fin vehicle. Once the vehicle hasa reliable position or surge velocity estimation, the currentsurge controller can be replaced with a suitable closed-loopcontroller.

5) Fully autonomous control without DOF prioritization:The test results without the priority manager in Fig. 13 e)showstrong oscillations of depth value. The oscillations occur whenthe surge action increases and the vehicle tries to moveforward. The figure also displays the roll and pitch anglesin comparison to those during the previous experiment (Fig.13 d). It can be seen that the vehicle is strongly oscillatingin pitch and roll. The oscillations are a result of a couplingbetween the actuation of different DOFs. All the controllerstry to stabilize the vehicle, however the fin configuration doesnot allow to equally control all the DOFs at the same time.The resulting lawnmower trajectory is also different from thatof the experiment 4 as the vehicle can not correctly outputthe predefined surge force. These results clearly show theimportance of DOF prioritization in our system.

VII. VALIDATION IN NATURAL ENVIRONMENT

This section describes two real-life test scenarios in naturalenvironments where the control of the robot was validatedduring a real mission.

A. ROV Inspection Missions of Submerged Machinery

The first testsite is located in Rummu quarry in Estonia(59*22,83122 N,24*22,60113E). Rummu quarry is an aban-doned flooded limestone mine containing submerged buildingand several large mining machines. We inspected a miningexcavator in 11m depth with the U-CAT in an ROV mode.Two missions where carried out on this test site in differentenvironmental conditions:

• 1 - Winter experiment (3.03.2016) - we launched thevehicle through an 1x1 meter hole (see Fig. 15a) cut into20 cm thick layer of ice.

• 2 - Summer experiment (14.07.2016) - we launched thevehicle from a small (4.3 m) rowboat.

During the mission the depth and yaw were autopiloted bythe inverse dynamics controller. The operator used a joystickto modify the controller setpoints and to manually control the

13

0 100 200 300 400

Dep

th, m

-1

-0.5

0

AUV mode

Actual valueDesired value

0 100 200 300 400

Yaw

, deg

-100

0

100

Time, s0 100 200 300 400

Atti

tude

, deg

-10

0

10

0 100 200 300

-1

-0.5

0

Depth and Yaw Autopilot

Time, s0 100 200 300

-100

0

100

0 100 200 300

Dep

th, m

-1

-0.5

0

Manual Control

Time, s0 100 200 300

Yaw

, deg

-100

0

100

0 100 200 300

-1

-0.5

0

Depth Autopilot

Actual valueDesired value

Time, s0 100 200 300

-100

0

100

0 100 200 300 400

-1

-0.5

0

AUV mode without priority functions

0 100 200 300 400-100

0

100

Time, s0 100 200 300 400

-10

0

10

PitchRoll

d) e)

a) b) c)

RMS error: 27.6 cm RMS error: 5.22 cm RMS error: 1.93 cm

RMS error: 2.22 cm RMS error: 4.62 cm

RMS error:39.8º

RMS error:28.6º

RMS error:2.50º

RMS error2.91º

RMS error:3.23º

Fig. 13. Experimental results for 3 DOF control in 5 different control scenarios.

14

0 200 400 600 800 1000

Dep

th, m

-8-6-4-20

Actual valueDesired

0 200 400 600 800 1000

Yaw

, deg

-150-75

075

150

Time, s0 200 400 600 800 1000Su

rge

actio

n, N

-10-505

10

Fig. 14. Sample of position tracking and surge action data during theinspection mission done from the boat in Rummu quarry.

Fig. 15. Validating the control system in the real-life ROV inspection mission.a) U-CAT being launched through a hole in the ice; b) U-CAT hovering abovethe mining machine; c) snapshot of the U-CAT’s on-board camera image.

surge speed of the vehicle. He used the live video feedback(Fig. 15c) from the downward looking on-board camera toinspect the different parts of the machine.

Fig. 14 shows a typical test data of the yaw and depthposition and the surge action during one of the dives. It can beseen that the autopilot is able to track the desired trajectorythroughout the whole mission (depth RMS error of 8.6 cm;yaw RMS error of 5.8◦). According the operators’ feedbackthe vehicle was relatively simple to control. He successfullygathered large amounts of video data of the machine during 2

0 200 400 600 800

Dep

th, m

-10-8-6-4-20

Actual valueDesired

0 200 400 600 800

Yaw

, deg

-150-75

075

150

Time, s0 200 400 600 800Su

rge

actio

n, N

-10-505

10

Fig. 16. Position tracking and surge action data during one of the dives ofthe inspection mission done at the Citadel.

missions.Even though the tracking precision was high enough for

ROV inspection, the mean RMS error is higher than in thecontrolled environment (depth RMS error of 1.9 cm; yaw RMSerror of 2.5◦). This is mostly due to following factors: 1.much longer tether; 2. environmental factors such as wavesand currents; 3. in this experiment the operator modified theset values of depth and yaw using incremental steps of 10 cmand 0.1 rad, while in the pool experiments smooth hyperbolictangent trajectories were used.

B. Underwater Archaeology Mission on Citadel

The second test site, the remains of the coastal defensebattery known as The Citadel, is located near the Tallinnshoreline (59*27.2965’, N, 24*47.6140’E) and was chosen forits relevance to the application domain of U-CAT, underwaterarchaeology. The remains of the fortification are in 8-11 mdepth about 900m from shore. The archaeological interest wasin inspecting the separate standing stone filled cellboxed builtof wooden logs, in particular to document the possible damageby waves, ice and divers to the archaeological site.

As opposed to the sheltered water site in Rummu quarry,Citadel is more exposed to the currents and waves and visibil-ity is poor due to turbidity of water and algae growth is sum-mer. Here, the high maneuverability of U-CAT is particularlyimportant in order to visually follow the complicated contoursof the cell boxes at close distance while compensating for waveand current disturbances by the operator. The mission lasted5 days, resulting in 11 hours of onboard camera footage. Therobot was operated from a RIB (rigid-hulled inflatable boat).Due to the turbidity from the algae blooms and highly volatilesilt rising from the bottom with currents, waves and motionof the robot and its tether, the visibility was only 1m or lessmaking close inspection of the logs of the cell boxes and itsdove-tailed corners particularly challenging. The currents wereestimated to reach about 0.5 m/s (just about the max forward

15

speed of U-CAT in hover mode) and the wave height wasvisually estimated about 0.5m.

Fig. 16 shows an example of a typical tracking data duringone of many inspection dives. From the graph it can be seenthat in the beginning and the end of the dive the operatormodified the desired depth faster than the robot was able tomove. Therefore, we calculate the tracking error only in thetime range from the end of the initial dive to the beginning ofthe final resurface. The RMS value for depth tracking is 61.6mm and the RMS of yaw tracking is 14.54◦). Even though thedepth tracking is slightly more precise and the yaw trackingless precise than in the experiments in sheltered quarry, theerror values are still in similar range. This shows that thedeveloped control system can operate with satisfying precisionin more difficult conditions in the presence of environmentaldisturbances such as waves and currents.

VIII. CONCLUSION

This paper presented a control architecture and its imple-mentation for a biomimetic four-finned underwater robot U-CAT in hovering mode. Finned propulsion has several advan-tages compared to a traditional propeller driven underwatervehicle, in the case of the U-CAT high maneuverability on acost of lower complexity, but it also proposes new challengesfor control, mainly caused by strong motion coupling of theDOFs and delayed response of the fin actuators. We have builta modular control architecture and realised 2DOF and 3DOFcontrol presenting a method of DOF priority selection. Thetests show that this approach decreases the tracking errors ofthe U-CAT. We also subjectively experienced during the trialsthat it makes the control more intuitive for a human operator.Also the modular control architecture has been beneficial inthe development phase allowing us to quickly change thecontrol approaches (for example to switch between different2DOF controllers). We therefore conclude that the architecturemakes the robot easier to operate both in development phaseas well as during real missions. The tests where carried outin controlled underwater environment, in sheltered water andin open water environment with waves, currents and verylow visibility at a difficult inspection task. The tracking errorincreases when moving to more complicated environments,which is expected with any control approach. At the same timethe control of the robot was sufficiently easy and precise evenduring a long real mission in a highly unstable environment.We therefore conclude that the control architecture of the robotis suitable for U-CAT. Our future goal is to extend the controlto more DOFs as well as to extend the motion library of U-CAT to include cruising mode. Again, we expect the modularcontrol architecture to be beneficial in development and testingphase as well as on real underwater missions.

ACKNOWLEDGMENT

This research has received funding from the EuropeanUnions Seventh Framework Programme for Research techno-logical development and demonstration, under grant agreementno. 308724 (The ARROWS Project), from Estonian- Frenchjoint collaboration project PHC-PARROT and from IUT339

grant of Estonian Ministry of Education and Research. Theauthors would like to thank Keijo Kuusmik, Jaan Rebane, RihoMarkna who have helped to develop the UCAT vehicle. Wewould also like to thank TUT Small Craft Competence Centrefor letting us use the tow tank.

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