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Safe operation of an autonomous underwater towed vehicle: Towed force monitoring and control
Automation in Construction 20 (2011) 1012–1019
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Automation in Construction j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a u t c o n
Safe operation of an autonomous underwater towed vehicle: Towed force monitoring and control Jin-Kyu Choi a,b,⁎, Tetsuya Shiraishi a, Toshinari Tanaka a, Hayato Kondo b a b
Port and Airport Research Institute, 3-1-1 Nagase, Yokosuka, Kanagawa 239–0826, Japan Tokyo University of Marine Science and Technology, 2-1-6 Etchujima, Koto-ku, Tokyo 135–8533, Japan
a r t i c l e
i n f o
Article history: Accepted 5 April 2011 Available online 8 May 2011 Keywords: Towed vehicle AUV Safe operation Towed force monitoring Towed force control
a b s t r a c t On underwater towed systems, the towing cable plays an important role in transmitting electric signals and towing forces. Hence, it is strongly recommended to monitor the towed force for preventing cable breaks and making use of it more efficiently; however, most existing underwater towed systems do not have such a capability. This paper discusses towed force monitoring and control for safe operation of an autonomous towed vehicle that is a kind of autonomous underwater vehicle (AUV). We first overview the autonomous towed vehicle and describe our related previous works. We then present our towed force measuring and monitoring manners and an experimental methodology for obtaining the feasible range of the towed force. In addition, towed force estimation only with vehicle dynamics is presented for the case when the towed force sensor became useless. Finally, we discuss towed force control to keep the towed force inside its feasible region. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Underwater towed vehicles (UTVs) [1–4] make use of a towing cable for transmitting towing forces and electric signals and have been frequently used for high-speed exploration and online monitoring of the sea-bottom or underwater resources. Generally, UTVs have less risk of being lost than autonomous underwater vehicles (AUVs) by virtue of the connection with the mother ship through the towing cable; however, it was reported in the literature [5] that “about ten percent of remotely operated vehicles (ROVs) are lost because of broken tethers.” Thus, it is strongly recommended to monitor the towed force information for preventing cable breaks and making use of it more efficiently. Meanwhile, we have developed an autonomous towed vehicle (see Fig. 1) that has three different navigation modes (autonomous, towed, and kite modes) to accomplish a given observation work regardless of the speed of sea currents [6,7]. Specifically, as shown in Fig. 2, when the current speed is below 2 knots, the vehicle can carry out a given work without the cable constraint (autonomous mode), and when the current speed is greater than 2 knots and less than 3 knots, it can do the work using the towing force exerted by the mother ship (towed mode). When the current speed is over 3 knots, the winch mounted on the moored mother ship can be used for generating kite-like motion (kite mode). Like this, the autonomous ⁎ Corresponding author at: Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Yokosuka, Kanagawa 237-0061, Japan. Tel: +81 46 867 9354; fax: +81 46 867 9343. E-mail address: [email protected] (J.-K. Choi). 0926-5805/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2011.04.002
towed vehicle makes use of towing forces in two navigation modes (towed and kite modes), and therefore, towed force monitoring is essential to raise the safety level during operation. Section 2 of this paper first overviews our autonomous towed vehicle and describes previous works to realize the three navigation modes with an AUV. Then, we will deal with towed force monitoring and control for safe operation in the remaining sections. Two towed force monitoring methods are considered in this paper: one is by direct measuring using a sensor(s) and the other is by estimation based on math models. Many oceanic engineers commonly point out that it is difficult to attach a towed force sensor to a part of the towing cable (or towing device) and to understand a sensed data due to external disturbances, e.g., waves and air friction, etc., even though it was installed (the sensor is usually attached near the mother ship). In Section 3, we describe our towed force measuring manner, for which a towed force sensor is attached near the underwater towed vehicle. We then present an experimental methodology called “stepby-step depth control” in order to define the feasible range of depth control and the safety range of the towed force in relation to the cable length and towing speed. The obtained ranges play a role as indexes when determining the cable length for a given task and judging whether the present towed force is normal. The direct measuring method using a physical sensor is obviously simple and practical; however, it is desirable to prepare for the case when the towed force sensor became useless because underwater environment is severe and unexpected. To this end, towed force estimation based only on vehicle dynamics is also presented in Section 3. State estimation is generally carried out with the input– output relationship, and if such a relationship of the towed system is
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Table 1 Principal components of the autonomous towed vehicle.
cable anchor
Dimension (L × W × H) Weight Actuators OS Communications
towing cable
Equipment
Batteries Duration Maximum depth Towing cable Fig. 1. Autonomous towed vehicle. It is an autonomous underwater vehicle (AUV) with two thrusters at the tail-wings for surge and yaw motions, two elevators at the forewings for pitch and roll motions, and sensors for its motion control.
well defined, the towed force can be estimated. However, this method is difficult to be implemented for the existing UTVs because they commonly have no sensors to identify their motions (the outputs). Moreover, the cable model is very complex and its parameters vary with operational conditions for the estimation using the vehicle-cable dynamics,whereas our autonomous towed vehicle has motion sensors (see Tables 1 and 2) as other AUVs have [8] and this property makes the towed force estimation only with vehicle dynamics possible. After obtaining the towed force information, the operator and/or the towed vehicle can take an appropriate action against an abnormal situation, e.g., over-loosened or over-tensioned case. Section 4 discusses towed force control for maintaining a steady towed force to be remained in the safety region. Four control methods are considered. The first one is to control it by changing the cable length instantaneously using the winch mounted on the mother ship, the second is by changing the towing speed (the speed of the mother ship), the third is by changing the thrusts of the towed vehicle (the speed of the towed vehicle), and the fourth is by changing the elevator angles of the towed vehicle (depth control). Note that the third and fourth methods are another merits produced from the employment of an AUV as a towed vehicle.
3.187 m × 1.469 m × 1.357 m 300 kgf (approximately) Thruster, ×2;elevator ×2 V × Works Acoustic links (autonomous mode) Optical fiber cable (towed mode) Digital camera, ×1;stroboscope, ×2;light, ×2; DVL, ×1; depth sensor, ×1;magnetometer, ×2 (one is for the mother ship); accelerometer, ×2;ceramic gyro, ×3; SSBL transponder, ×1; SSBL transmitter/receiver, ×1; GPS, ×1 Lithium-ion batteries 12 h (autonomous mode) 3.4–8.5 h (towed mode ) 100 m Optical fiber (single mode) Outside diameter, 7 mm Weight, 36 kg/km (in the air) Weight, −3 kg/km (underwater) Working load, 180 kgf Margin load, 450 kgf Rupture strength, 500 kgf
2.1. Overview [6] The autonomous towed vehicle has been developed for underwater observation in the Tokyo bay. The given mission is to take still and moving images to understand the underwater situation around the Tokyo bay before the maintenance work of the waterway. For the towed and kite modes, the system is composed of the towed vehicle (it is an AUV), the mother ship, and the towing cable. The towing cable
Table 2 Specifications of the equipment in Table 1. Equipment (model or maker)
Specifications
Digital camera (Nikon COOLPIX 5400) Stroboscope (Nikon SPEEDLIGHT SB-800) Light DVL (RDI Workhorse Navigator DVL)
Resolution, 5.1 megapixels
2. The autonomous towed vehicle In this section, the autonomous towed vehicle that is the target of this study is overviewed and our previous works to realize the different navigation modes with an AUV are described, together with related issues.
winch
mother ship
cable
current
(a)
Accelerometer (TOKIMEC TA-25 D-02) Ceramic gyro (NEC-TOKIN CG-16D) SSBL transponder (ORE Model 4430B) SSBL transmitter/receiver (KDDI)a
vehicle
(b)
Depth sensor (Druck PTX 630-0) Magnetometer (PNI TCM2-50)
(c)
anchor
Fig. 2. Three different navigation modes. (a) Autonomous mode. (b) Towed mode. (c) Kite mode.
GPS receiver (JRC DGPS212)a a
Guide number, 38 (with zoom headset at 35 mm) DC 100 V halogen lamp (150 W) DC 24 V Configuration, 4-beam, convex Frequency, 300 kHz Temperature range,−5–45 °C Altitude range, 1–100 m Bottom velocity range, ±10 m/s Water velocity range, ± 10 m/s Depth range, 0–100 m Accuracy, ±0.05% FS (typical) DC 5 V Range (tilt information), ±50 ° Resolution, 0.3 ° Repeatability, ±30 ° DC, ± 15 V Range, ±35 m/s2 (± 90 °) Resolution, 1 × 10−6 m/s2 (0.02 °) Maximum detectable angular rate, ±90 °/s Sensitivity, 21 mV/°/s ± 25% Transmit frequency, 27 kHz Receive frequency, 19 kHz Beam angle, ± 40 ° AC 100 V, under 100 VA Beam angle, ± 60 ° Transmit frequency, 17 kHz–20 kHz Receive frequency, 22 kHz–31 kHz DC, 12 V Frequency, 1575.42 MHz ± 1 MHz (GPS) Frequency, 283.5 kHz–325 kHz (DGPS)
The equipment installed on the mother ship.
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is removed for the autonomous mode. The towed vehicle has two thrusters at the tail-wings for surge and yaw motions and two elevators at the forewings for pitch and roll motions. Table 1 shows the principal components of our system. The dimension of the towed vehicle was determined for easy handling by humans. Detailed specifications of the equipment in Table 1 are also presented in Table 2. In order to take still and moving images, a digital camera, two stroboscopes, and two underwater lighting devices kept in watertight containers are mounted on the towed vehicle. In the towed and kite modes, obtained photographs and moving images are displayed on the monitor placed on the mother ship and concurrently are recorded on hard disks on the mother ship and in the towed vehicle; however, those are recorded only on the hard disk installed in the towed vehicle for the autonomous mode. The hard disk in the towed vehicle is kept in the main watertight container with other electric and electronic devices. The position and orientation of the towed vehicle are mainly calculated with the data of a DVL (Doppler velocity log), a depth sensor, a magnetometer (for the yaw), and two accelerometers (for the pitch and roll). Their accumulated error, which is proportional to navigation time, is modified by incorporating with the data of the SSBL (super short base line) from the mother ship at every pre-defined time step. An SSBL transducer is installed on the towed vehicle and SSBL transmitter and receiver manufactured by the KDDI R&D Laboratories, Japan, are installed on the mother ship. The pose data are transferred to the mother ship or vice versa through the towing cable in the towed and kite modes and through an acoustic link in the autonomous mode. The pose of the mother ship is obtained by a GPS (global positioning system) receiver and a magnetometer (for heading) installed on the mother ship. Three ceramic gyros are installed on the towed vehicle for measuring angular velocities around the three axes of the moving frame attached at the towed vehicle. The roll and pitch angles are directly provided by two accelerometers, and the yaw angle is provided by a magnetometer. Based on mentioned sensors, the motion control of the towed vehicle can be achieved. In addition, an electric-powered winch is installed on the mother ship. It has an electric motor with a rotary encoder and a controller for remote control. 2.2. Issues and previous works There are two issues related with the development of the autonomous towed vehicle. One is how to get the three different navigation modes with a single vehicle. In general, the natures of AUVs and UTVs are mutually contradictory. For example, the underwater weight of AUVs is usually near zero, while UTVs are relatively heavy to obtain sufficient towing forces; the drag force of AUVs is small but that of UTVs is somewhat large for the same purpose.Although AUVs are, in general, intrinsically stable in surge and roll motions, they are commonly designed to be controlled easily in other motions, while UTVs are designed to be more stable for high speed surveying without motion control. Our towed vehicle was designed based on the AE-2 [9,10] developed by the KDDI R&D Laboratories, Japan, which has been successfully carried out on several missions to inspect underwater cables in real sea (note that it was used as an AUV, not as a towed vehicle). In order to add the capability of the towed vehicle to the AE-2, we first performed computer simulations to investigate the stability of the AE-2 in the towed mode. It was known from the simulations that each forewing needs to be longer than that of the AE-2 by 76 mm, both for increasing drag forces and stable navigation, and additional 10 kgf weights are required on the front side of the vehicle for submerging to 60 m depth (the maximum depth around the Tokyo bay). Instead of using the additional weights, the expansions of each forewing's chord and the cable length can also be considered; however, the excessive expansion of the chord is unsuitable for operation in steady state and the extension of the cable length results in a long distance between the
towed vehicle and the mother ship. These produce another demerit. Also, the simulation results suggested controlling the pitching and rolling motions for steady linear and turning motions, even though the AE-2 was designed to be stable in the rolling motion. We fabricated a half-sized test model based on the simulation study of which forewing is longer than that of the AE-2 by 38 mm (76 mm in the real-sized one). Then, towing tank tests for investigating the hydrodynamic properties were carried out with the test model, such as drag tests, oblique motion tests, elevator angle tests, pure heave, pure pitch, pure sway, and pure yaw motions tests. After that, we reexamined the stability in the towed mode through simulations using the parameters of the test model and also carried out tank tests with the real vehicle that has identical shape with the test model. In the tank tests, basic operations were tested and the control gains and the lower boundary of the towing speed for depth control were determined; it was clarified that the towing speed is needed to be over 1.5 knots for depth control. The first sea trial was conducted and the results showed that our autonomous towed vehicle can navigate stably in the towed mode as well as in the autonomous mode [6]. The other issue is the safety during operation. Since UTVs are always affected by the towed force, it is recommended to monitor and, if necessary, control the towed force for preventing cable breaks and making use of it more effectively. This paper focuses on this issue and discusses towed force monitoring and control for safer operation. 3. Towed force monitoring First, our towed force measuring and monitoring manners are introduced and an experimental methodology for obtaining the feasible range of the towed force is proposed. Towed force estimation only with vehicle dynamics is additionally presented for the case when the towed force sensor became useless. 3.1. Towed force sensor Strain gauges are attached at the connection part (the cable anchor shown in Fig. 1) between the towing cable and the towed vehicle for measuring the magnitude of the towed force. To measure the direction of the towed force, two accelerometers are installed at the same place; one is for the elevation and the other is for the azimuth. 3.2. Towed force monitoring Fig. 3 shows the user interface, with which the operator can monitor the motion of the towed vehicle and can control its depth by giving a reference value of depth. The magnitude and direction (elevation and azimuth) of the towed force are also displayed on the user interface in bar graph and/or in number as shown in Fig. 3. The bar graph has three colors according to the magnitude of the towed force. Green is for over-loosened case, yellow for normal, and red for over-tensioned case. When the towed force sensor is malfunctioned, estimated towed force information will be displayed. 3.3. Safety range of the towed force The information on the upper and lower bounds of the towed force and the range of controllable depth in accordance with the towing speed and cable length is important in knowing whether the present towed force is normal and the limitation of the depth control. In order to acquire such information, we propose the step-by-step depth control method shown in Fig. 4. The control process is as follows: Step 1 With given cable length and towing speed, the mother ship tows the towed vehicle until the depth of the towed vehicle approaches certain equilibrium. In this case, the towed vehicle does not carry out depth control.
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towed force information
Fig. 3. Display of the towed force information on the user interface.
0 lower bound equilibrium upper bound
-10 -13.8
Depth (m)
Step 2 After reaching equilibrium, downward (toward the seabottom) stair-type depth control is performed until the depth control cannot be achieved anymore due to the shortage of lifting force for descending. At the ultimate depth, the magnitude of the towed force becomes largest (the upper bound) and the controllable depth also has the maximum value (the upper bound). Step 3 After Step 2, to obtain the lower bound, upward (toward the surface) stair-type control is performed until the depth control cannot be accomplished due to the shortage of lifting force for ascending.
-20.8
-20 -21.2 -27.2 -30
-27.2 -34
-40
-47.9
-49.6
-50
-60
-60 In our case, the step-by-step depth control was carried out with 2 knots towing speed and 30 m, 55 m, and 80 m cable lengths. A single step for the stair-type depth control is 5 m, 10 m, and 10 m for 30 m, 55 m, and 80 m cable lengths, respectively. Fig. 5 shows the experimental results and all the data were obtained by the mentioned towed force sensor. The figure shows that the equilibriums in depth are approximately center values between the upper and lower values,
cable
vehicle
lower bound of depth control
equilibrium step-by-step depth control step-by-step depth control
upper bound of depth control
Fig. 4. Step-by-step depth control for obtaining the upper and lower bounds of the towed force and the range of controllable depth.
-80 30
40
50
55
60
70
80
90
Cable length (m)
Magnitude of the towed force (kgf)
mother ship
-70
180 160
160 140
130 120
120 100 100
112 100
80 60
60 50
67
40 20 30
40
50
55
60
70
80
90
Cable length (m) Fig. 5. The ranges of the controllable depth and the magnitude of the towed force according to 30 m, 55 m, and 80 m cable lengths, when the towing speed is 2 knots. The equilibrium means that the steady state reached without depth control.
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but those in towed forces are more near the upper values. This implies that control sensitivity to the towed force is lower between the equilibriums and the upper bounds than at the counterpart; in other words, a larger change of elevation angle is needed for the same control purpose at the range. The data in Fig. 5 are very useful at the planning stage of field operation. For example, once the depth and the towing speed for an observation work are given, an efficient cable length can be determined based on the data. Surely, safer operation can be realized since the upper and lower bounds of controllable depth and the towed force are known. 3.4. Towed force estimation with vehicle dynamics Let fC ∈R2 be the towed force vector and x = (x, z, θ)T be the vector whose elements are the position in a vertical plane, (x, z), and the pitch angle, θ, of the towed vehicle. The coordinate system obeys the right-hand rule and the z-axis points to the downward (toward the sea-bed). In order to estimate the towed force, we consider the towed vehicle dynamics in a vertical plane (x–z plane) as: M x˙˙ + C x˙ + d + g = Bτ + H f C + f W T
ð1Þ
-10
-15
-20
lower bound upper bound
-25 -30
0
200
400
600
200
measured estimated
100 50 0
0
200
400
800
600
lower bound
when the mother ship is turning
-30
upper bound
-40 -50 -60
800
Time (sec) 150
Depth (m)
-10
-20
ð2Þ
where z = M x˙˙ + C x˙ + d + g−Bτ−f W is computed with the vehicle's parameters and the measurements of the motion sensors. For assuring the solution of Eq. (2), the matrix HHT should be nonsingular, i.e., its determinant should not be zero. As for our vehicle, the solution
Magnitude of the towed force (kgf)
Depth (m)
T −1 f C = HH Hz
(b) when the cable length is 55 m
(a) when the cable length is 30 m
Magnitude of the towed force (kgf)
where M = MRB + MA ∈R3×3 , MRB and MA are the rigid-body inertia matrix and the added inertia matrix, respectively; C = CRB + CA ∈ R3×3 , CRB and CA are the rigid-body Coriolis and centripetal matrix and the hydrodynamic Coriolis and centripetal matrix, respectively. In addition, d∈ R3 is drag terms; g∈R3 is gravity and buoyancy terms; B∈ R3×2 is the matrix mapping the forward thrust, tTH, exerted by the two thrusters and the synchronous elevator angle, eS, on the resultant forces and moment acting on the towed vehicle; H ∈ R2×3 is the geometry dependent matrix associated with the towed force; fW ∈ R3 is the vector having the forces and moment caused by additional weights; and τ = (tTH, eS)T∈R2 . The synchronous elevator angle is the averaged one of the left and right elevators' angles like eS = (eR + eL) /2. From Eq. (1), we can estimate the towed force by using the least squares estimation method as follows:
0
200
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800
1000
1200
Time (sec) 200
measured estimated
150 100 50 0
0
200
400
600
Time (sec)
800
1000
1200
Time (sec)
(c) when the cable length is 80 m
(d) when the cable length is 30 m and the operating depth is below the upper bound
Depth (m)
when the mother ship is turning
upper bound
-40
lower bound
-60
Depth (m)
-10 -20
-80 200
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Time (sec) 200
measured estimated
150 100 50 0
0
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Time (sec)
1000
1200
1400
-20 -25 -30 -35
1400
Magnitude of the towed force (kgf)
Magnitude of the towed force (kgf)
0
obstacle avoidance
-15
0
100
200
300
400
500
600
700
Time (sec) 200
measured estimated
150 100 50 0
0
100
200
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Time (sec)
Fig. 6. Measured and estimated values of the magnitude of the towed force when the towing speed is 2 knots.
500
600
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J.-K. Choi et al. / Automation in Construction 20 (2011) 1012–1019
always exists since det(HHT) = 1+a2 + b2 ≠ 0, where (a, b) is the position of the coupling point with the towing cable in the moving frame attached at the towed vehicle. Fig. 6 shows the estimated and measured values of the magnitude of the towed force during carrying out the step-by-step depth control to obtain the data shown in Fig. 5. Here, we did not take noise filtering in estimation for direct comparison with the data obtained by the towed force sensor. Figs. 6a–c are the values when towing speed is 2 knots and the cable lengths are 30 m, 55 m, and 80 m, respectively. From Fig. 6, we can observe the following: (1) The trends of the measured and estimated values are similar even though there is a difference between them. The difference is considered to be mainly caused by the modeling error. (2) The difference between the measured and estimated ones near the upper bound of the towed force is relatively large. (3) When the mother ship is turning (to acquire an area for the experiment), the difference becomes larger as shown in Fig. 6b and c. This is due to the break of static balance. (4) When the towed vehicle avoids an obstacle on the seabed, the difference grows larger as shown in Fig. 6d. This is also caused by the momentary break of static balance. These results give the following guidance in using the estimation method: there is a relatively large difference between the estimates and the measured ones when the towed vehicle approaches the upper bound and the static balance is broken and thus we need to use the estimation method while avoiding such situations. In addition, in order to ensure the safety during turning, we experimentally obtained the range of turning radius, in which the mother ship can turn without losing stability of the towed vehicle. Related experimental data will be presented in Section 4. 3.5. Implementation of the Kalman filter It is practical to utilize the towed force sensor measurements rather than the estimates because there are uncertainties in model parameters such as hydrodynamic coefficients that vary with operational conditions. However, it is worthy to provide the estimates in order to prepare for the case when the towed force sensor became useless and to detect the towed force sensor failure. To this end, we designed filter such as below. theKalman −1 ˜ Let HHT H = N + Nδθ, z = z + z˜ δs, and U be the towing speed, whereN and z denote the mean values of N and z, respectively; Ñ and z˜ are the error coupling matrices; and δθ and δs are the errors caused by sensor noises. Then, Eq. (2) can be rewritten into: h i ˜ O2×2 δs f C = Nz + N z˜ + O2×3 O2×3 Nz
cosα f + −sinα S
ð
−fS sinα cosα −fS cosα −sin α
0
0
1
I2×2
B B O3×2 B B Φk = B O3×2 B BO @ 3×2 O2×2 T
B A1 = @
T
I3×3
C C C C C; C C A
O
A1
I3×3
A2
A3
I3×3
O2×3 O2×3 O2×3 I2×2 0 1 1 0 O 0 0 0 T2 = 2 B C C B B C A; A2 = @ 0 0 0 A; A3 = @ 0
O T 0 0 0 Γ k O2×2 O2×9 Ωk Γ ′k = ; Λ k = I13×13 ; Ω′k = ; I11×11 I11×11 h i ˜ zk O2×2 δsk ; Γ k = N k z˜k + O2×3 O2×3 N k ! cosα k −fSk sinα k Ωk = ; −fSk cosα k −sinα k T T X k = f C ; x˙˙; z˙˙; θ˙˙; x; ˙ z; ˙ θ˙ ; θ; U; eS ; α; fS ; T ˙ δθ; δU; δeS ; δα; δfS ; wk = δx˙˙; δz˙˙; δθ˙˙; δ x; ˙ δ z; ˙ δ θ;
0
1
0
T
0
C 0 A;
0
0
vk = wk;T is the sampling period;Ii × j is a i × j identity matrix of which diagonal components are all 1;O denotes zeros; and wk, w ′k, and vk are assumed to be zero-mean white Gaussian noises whose covariance matrices are Q k, Q ′k, and Rk, respectively. Fig. 7 shows the estimates obtained by the implemented Kalman filter for the case in Fig. 6d, where T = 1 s, Q k = 0.01I11 × 11, Q ′k = 0.001I13 × 13, and Rk = 0.01I11 × 11. In addition, the sensor failure can be checked by examining the magnitude of the residual (also called the measurement innovation) in the Kalman filter equations [11–13]. 4. Discussion on towed force control Letting TFmax and TFmin be the upper and lower limits of the towed force, respectively, the magnitude of the towed force can be classified into the following three cases: jj f C jjbTFmin : Over loosened;
ð7Þ
TFmin ≤jj f C jj≤TFmax : Feasible;
ð8Þ
jj f C jj N TFmax : Over tensioned:
ð9Þ
Þð
Þ
δα δfS
ð4Þ
where α and fS are the sensor data obtained from the accelerometer for the elevation of the towed force and the strain gauge for the magnitude, respectively. From Eqs. (3) and (4), we can formulate the process model and the measurements model for Kalman filter implementation as follows: ′ wk−1 + wk−1 ′ X k = Φk−1 X k−1 + Γ k−1
ð5Þ
Z k = Λ k X k + Ωk′ vk
ð6Þ
200
Magnitude of the towed force (kgf)
T ˙ δθ; δU; δeS and Oi × j is a i × j zero ˙ δ z;˙ δ θ; where δs = δx˙˙; δz˙˙; δθ˙˙; δ x; matrix of which elements are all zero. Also, the model for the towed force sensor can be formulated as:
where
ð3Þ
f CM =
1017
measured estimated 150
100
50
0
0
100
200
300
400
500
600
700
Time (sec) Fig. 7. Estimated values of the case in Fig. 6d, obtained by the Kalman filter.
J.-K. Choi et al. / Automation in Construction 20 (2011) 1012–1019
f C = −ΨBτ + Ψz′
ð10Þ
where z′ = M x˙˙ + C x˙ + d + g−f W and Ψ = (HHT)− 1H. Ψ and B are geometry dependent terms and z′ depends on the towing speed, the pitch angle of the towed vehicle, and the cable length. This equation shows that the towed force, fC, can be actively controlled by changing the input τ = (tTH, eS)T, the towing speed, and the cable length. Thus, the following four towed force control methods can be considered. The first one is by changing the cable length through winch motion using the winch on the mother ship; the second is by changing the speed of the mother ship, i.e., changing the towing speed; the third is by the thrusters input, tTH; and the fourth is by the synchronous elevator input, eS. In what follows, we shall discuss each method in detail. 1) By the winch. The length of the towing cable can be adjusted by the electric winch installed on the mother ship and, accordingly, the towed force can also be controlled. Figs. 5 and 6 give the example. We can confirm that the towed force increases in accordance with the increase of the cable length. Letting || f Cd || be the magnitude of a desired towed force, the winch torque for controlling the towed force can be given by: τwinch = τwinch
r
+ k winch ðjj f Cd jj−jj f C jjÞ
ð11Þ
where τwinch_r is a reference value of winch torque and kwinch is a positive control gain. The winch control conducts until | || fCd || − || fC || | ≤ ε is satisfied, where ε is a positive real number. There are some points to be considered carefully for this control method. In normal operation, the drags to the towed vehicle are applied to mainly the front side and the towing cable, and hence, the magnitude of the towed force varies in proportion to the towing speed and the cable length. However, during the winch and release motions by the winch, different trends appear. For example, during the winch motion, additional drags occur around the upside of the towed vehicle although the cable length is lessened gradually. In this case, the towed force strongly depends on the winch speed. Similarly, the towed force during the release motion also depends on the release speed of the winch and the entire drags including the additional drags around the downside reduce the speed of the towed vehicle. This consequently decreases the towed force even though the cable length becomes longer. In addition, the winch and release motions need to be executed while maintaining the static balance for the steady motion of the towed vehicle. 2) By the mother ship. The drags on the towed vehicle and the towing cable increase with the towing speed and thus the towed force can be controlled by changing the speed of the mother ship. Fig. 8 shows the magnitude of the towed force according to the synchronous elevator angle (from −30° to 15°), the towing speed (1.5 knots, 2 knots, and 2.5 knots), and the pitch angle (0° and − 5°). This result was obtained through numerical simulations on the assumption that the towed system is in a static balance. As shown, the magnitude of the towed force varies responding to the change of the towing speed. This towed force control method can be effectively used for emergency situation, e.g., when the magnitude of the towed force became abnormally large. However, it is to be noted that frequent change in speed of the mother ship
can cause an unstable motion of the towed vehicle because it takes time to go into the static balance after the towing speed is changed. 3) By the thrusters. As shown in Eq. (10), the towed force fC can be controlled by the thrusters input tTH. In a vertical plane, the forward and backward thrusts of the towed vehicle can respectively reduce and increase the magnitude of the towed force. Specifically, the forward motion results in increase in speed of the towed vehicle and this weakens the pulling force exerted by the mother ship. Conversely, the decrease in speed of the towed vehicle caused by the backward motion strengthens the towed force. In addition, this method will be useful when the operator wants to rapidly stop the towed vehicle for avoiding an unexpected collision after the mother ship is stopped; however, this method requires a great deal of thrust and accordingly results in large consumption of energy. 4) By the elevators. The depth control using the synchronous elevator input is effective to change the magnitude of the towed force as shown in Figs. 5 and 6. Moreover, Fig. 8 shows that the magnitude of the towed force varies linearly with respect to the synchronous elevator angle. Usually, the towed vehicle carries out a given mission while changing its depth using the elevators. Therefore, this method is considered to be most natural comparing with mentioned other three methods. For our towed system, this method is mainly used to control the towed force for normal operation. In addition, it was stated in Section 3 that the towed force estimation method needs to be used while avoiding the situation like the static balance of the towed system is broken; this situation
(a) when the pitch angle is 0o Magnitude of the towed force (kgf)
If the towed vehicle meets the cases of Eqs. (7) and (9), it/the operator needs to control the towed force in order to move into the feasible region defined in Eq. (8); this can avoid undesirable situations, e.g., cable breaks due to excessive tension and a collision with an obstacle due to uncontrolled motion caused by excessively loosened cable. The feasible region is determined based on the data shown in Fig. 5. For explanatory convenience, Eq. (2) is rewritten into:
400 300 2.5 knots 200 2 knots 100 0 -30
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-20
-10
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10
20
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(b) when the pitch angle is -5o Magnitude of the towed force (kgf)
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300 2 knots 200 1.5 knots 100
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20
Synchronous elevator angle (deg) Fig. 8. The magnitude of the towed force according to the elevator angle (from −30° to 15°), the towing speed (1.5 knots, 2 knots, and 2.5 knots), and the pitch angle (0° and −5°).
J.-K. Choi et al. / Automation in Construction 20 (2011) 1012–1019
(a)
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towed vehicle and the magnitude of the towed force are stable when the mother ship turns with 100 m turning radius; however, there are small variations such as ± 1 m in the depth and ±10 kgf in the towed force when the turning radius is 50 m. From this result, we arrive at the conclusion that the safety of the towed vehicle can be ensured if the mother ship turns with the turning radius between 50 m and 100 m.
-1150 start -1200 turning radius: 100 m
y (m)
-1250
5. Conclusion
-1300
-1350
This paper has discussed towed force monitoring and control for safe operation of our autonomous towed vehicle. We first overviewed the autonomous towed vehicle and described our related previous works. We then presented our approach to the towed force measurement and monitoring, as well as our experimental methodology for obtaining the safety range of the towed force. We showed that the towed force sensor attached near the towed vehicle provides understandable measurements and the obtained safety range of the towed force is useful when determining the cable length for a given observation work and judging whether the present towed force is normal. In addition, we presented a towed force estimation method based only on vehicle dynamics to prepare for the case when the towed force sensor is malfunctioned. It was illustrated that the estimator supplies close values to the sensor measurements. Finally, four towed force control methods for keeping the towed force inside the safety range were discussed.
turning radius: 50 m
-1400
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(b) Depth (m)
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References
200 150 100 50 0
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Fig. 9. The results of the experiment to obtain the range of turning radius in which the mother ship can turn without losing stability of the towed vehicle. (a) The position of the towed vehicle. (b) The depth and the magnitude of the towed force. In this experiment, the towing speed was 2 knots and the cable length was 55 m.
frequently occurs when the mother ship is turning. To ensure the safety of the towed vehicle for this case, we experimentally obtained the safety range of turning radius, in which the mother ship can turn without losing stability of the towed vehicle. In the experiment, the mother ship first turned with 100 m turning radius and then turned with 50 m turning radius after confirming the stability of the towed vehicle, under the towing speed of 2 knots and the cable length of 55 m. Fig. 9 shows the results. It is observed that the depth of the
[1] J.W. Schram, S.P. Reyle, A three-dimensional dynamic analysis of a towed system, J. Hydronautics 2 (4) (1968) 214–220. [2] J.D. Burroughs, R.C. Benz, Computer support in the design and testing of undersea towed systems, Mar. Tech. 10 (4) (1974) 159–172. [3] N. Kato, S. Kouda, T. Takahashi, Motions of underwater towed system, Proc. 5th OMAE, Tokyo, vol. 3, 1986, pp. 426–433. [4] N. Kato, Vibration analysis of underwater towed system, J. Soc. Nav. Arch. Japan 162 (1987) 363–373. [5] J. Yuh, Underwater robotics, Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, 2000, pp. 932–937. [6] J.-K. Choi, T. Shiraishi, T. Tanaka, H. Sakai, A practical and useful autonomous towed vehicle for port area inspection, Adv. Robot. 21 (3–4) (2007) 351–370. [7] J.-K. Choi, T. Shiraishi, T. Tanaka, Safe breakwater-following control of an autonomous underwater vehicle with non-zero forward velocity, Automation in Construction 16 (2007) 778–786. [8] J. Yuh, Design and control of autonomous underwater robots: A survey, Autonomous Robots 8 (2000) 7–24. [9] N. Kato, J. Kojima, Y. Kato, S. Matumoto, K. Asakawa, Optimization of autonomous underwater vehicle for inspection of underwater cables, Proc. IEEE Int. Conf. on Robotics and Automation, Leuven, 1998, pp. 1045–1050. [10] K. Asakawa, J. Kojima, Y. Kato, S. Matsumoto, N. Kato, T. Asai, T. Iso, Design concept and experimental results of the autonomous underwater vehicle AQUA EXPLORER 2 for the inspection of underwater cables, Adv. Robot. 16 (1) (2002) 27–42. [11] Y. Bar-Shalom, X.-R. Li, Estimation and Tracking: Principles, Techniques, and Software, Artech House, Inc., 1993 [12] R.E. Kalman, A new approach to linear filtering and prediction problems, Trans. ASME J. Basic Eng. 82D (1960) 35–45. [13] M.S. Grewal, A.P. Andrews, Kalman Filtering: Theory and Practice, Prentice Hall, Inc, 1993.
Contents lists available at ScienceDirect
Automation in Construction j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a u t c o n
Safe operation of an autonomous underwater towed vehicle: Towed force monitoring and control Jin-Kyu Choi a,b,⁎, Tetsuya Shiraishi a, Toshinari Tanaka a, Hayato Kondo b a b
Port and Airport Research Institute, 3-1-1 Nagase, Yokosuka, Kanagawa 239–0826, Japan Tokyo University of Marine Science and Technology, 2-1-6 Etchujima, Koto-ku, Tokyo 135–8533, Japan
a r t i c l e
i n f o
Article history: Accepted 5 April 2011 Available online 8 May 2011 Keywords: Towed vehicle AUV Safe operation Towed force monitoring Towed force control
a b s t r a c t On underwater towed systems, the towing cable plays an important role in transmitting electric signals and towing forces. Hence, it is strongly recommended to monitor the towed force for preventing cable breaks and making use of it more efficiently; however, most existing underwater towed systems do not have such a capability. This paper discusses towed force monitoring and control for safe operation of an autonomous towed vehicle that is a kind of autonomous underwater vehicle (AUV). We first overview the autonomous towed vehicle and describe our related previous works. We then present our towed force measuring and monitoring manners and an experimental methodology for obtaining the feasible range of the towed force. In addition, towed force estimation only with vehicle dynamics is presented for the case when the towed force sensor became useless. Finally, we discuss towed force control to keep the towed force inside its feasible region. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Underwater towed vehicles (UTVs) [1–4] make use of a towing cable for transmitting towing forces and electric signals and have been frequently used for high-speed exploration and online monitoring of the sea-bottom or underwater resources. Generally, UTVs have less risk of being lost than autonomous underwater vehicles (AUVs) by virtue of the connection with the mother ship through the towing cable; however, it was reported in the literature [5] that “about ten percent of remotely operated vehicles (ROVs) are lost because of broken tethers.” Thus, it is strongly recommended to monitor the towed force information for preventing cable breaks and making use of it more efficiently. Meanwhile, we have developed an autonomous towed vehicle (see Fig. 1) that has three different navigation modes (autonomous, towed, and kite modes) to accomplish a given observation work regardless of the speed of sea currents [6,7]. Specifically, as shown in Fig. 2, when the current speed is below 2 knots, the vehicle can carry out a given work without the cable constraint (autonomous mode), and when the current speed is greater than 2 knots and less than 3 knots, it can do the work using the towing force exerted by the mother ship (towed mode). When the current speed is over 3 knots, the winch mounted on the moored mother ship can be used for generating kite-like motion (kite mode). Like this, the autonomous ⁎ Corresponding author at: Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Yokosuka, Kanagawa 237-0061, Japan. Tel: +81 46 867 9354; fax: +81 46 867 9343. E-mail address: [email protected] (J.-K. Choi). 0926-5805/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2011.04.002
towed vehicle makes use of towing forces in two navigation modes (towed and kite modes), and therefore, towed force monitoring is essential to raise the safety level during operation. Section 2 of this paper first overviews our autonomous towed vehicle and describes previous works to realize the three navigation modes with an AUV. Then, we will deal with towed force monitoring and control for safe operation in the remaining sections. Two towed force monitoring methods are considered in this paper: one is by direct measuring using a sensor(s) and the other is by estimation based on math models. Many oceanic engineers commonly point out that it is difficult to attach a towed force sensor to a part of the towing cable (or towing device) and to understand a sensed data due to external disturbances, e.g., waves and air friction, etc., even though it was installed (the sensor is usually attached near the mother ship). In Section 3, we describe our towed force measuring manner, for which a towed force sensor is attached near the underwater towed vehicle. We then present an experimental methodology called “stepby-step depth control” in order to define the feasible range of depth control and the safety range of the towed force in relation to the cable length and towing speed. The obtained ranges play a role as indexes when determining the cable length for a given task and judging whether the present towed force is normal. The direct measuring method using a physical sensor is obviously simple and practical; however, it is desirable to prepare for the case when the towed force sensor became useless because underwater environment is severe and unexpected. To this end, towed force estimation based only on vehicle dynamics is also presented in Section 3. State estimation is generally carried out with the input– output relationship, and if such a relationship of the towed system is
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Table 1 Principal components of the autonomous towed vehicle.
cable anchor
Dimension (L × W × H) Weight Actuators OS Communications
towing cable
Equipment
Batteries Duration Maximum depth Towing cable Fig. 1. Autonomous towed vehicle. It is an autonomous underwater vehicle (AUV) with two thrusters at the tail-wings for surge and yaw motions, two elevators at the forewings for pitch and roll motions, and sensors for its motion control.
well defined, the towed force can be estimated. However, this method is difficult to be implemented for the existing UTVs because they commonly have no sensors to identify their motions (the outputs). Moreover, the cable model is very complex and its parameters vary with operational conditions for the estimation using the vehicle-cable dynamics,whereas our autonomous towed vehicle has motion sensors (see Tables 1 and 2) as other AUVs have [8] and this property makes the towed force estimation only with vehicle dynamics possible. After obtaining the towed force information, the operator and/or the towed vehicle can take an appropriate action against an abnormal situation, e.g., over-loosened or over-tensioned case. Section 4 discusses towed force control for maintaining a steady towed force to be remained in the safety region. Four control methods are considered. The first one is to control it by changing the cable length instantaneously using the winch mounted on the mother ship, the second is by changing the towing speed (the speed of the mother ship), the third is by changing the thrusts of the towed vehicle (the speed of the towed vehicle), and the fourth is by changing the elevator angles of the towed vehicle (depth control). Note that the third and fourth methods are another merits produced from the employment of an AUV as a towed vehicle.
3.187 m × 1.469 m × 1.357 m 300 kgf (approximately) Thruster, ×2;elevator ×2 V × Works Acoustic links (autonomous mode) Optical fiber cable (towed mode) Digital camera, ×1;stroboscope, ×2;light, ×2; DVL, ×1; depth sensor, ×1;magnetometer, ×2 (one is for the mother ship); accelerometer, ×2;ceramic gyro, ×3; SSBL transponder, ×1; SSBL transmitter/receiver, ×1; GPS, ×1 Lithium-ion batteries 12 h (autonomous mode) 3.4–8.5 h (towed mode ) 100 m Optical fiber (single mode) Outside diameter, 7 mm Weight, 36 kg/km (in the air) Weight, −3 kg/km (underwater) Working load, 180 kgf Margin load, 450 kgf Rupture strength, 500 kgf
2.1. Overview [6] The autonomous towed vehicle has been developed for underwater observation in the Tokyo bay. The given mission is to take still and moving images to understand the underwater situation around the Tokyo bay before the maintenance work of the waterway. For the towed and kite modes, the system is composed of the towed vehicle (it is an AUV), the mother ship, and the towing cable. The towing cable
Table 2 Specifications of the equipment in Table 1. Equipment (model or maker)
Specifications
Digital camera (Nikon COOLPIX 5400) Stroboscope (Nikon SPEEDLIGHT SB-800) Light DVL (RDI Workhorse Navigator DVL)
Resolution, 5.1 megapixels
2. The autonomous towed vehicle In this section, the autonomous towed vehicle that is the target of this study is overviewed and our previous works to realize the different navigation modes with an AUV are described, together with related issues.
winch
mother ship
cable
current
(a)
Accelerometer (TOKIMEC TA-25 D-02) Ceramic gyro (NEC-TOKIN CG-16D) SSBL transponder (ORE Model 4430B) SSBL transmitter/receiver (KDDI)a
vehicle
(b)
Depth sensor (Druck PTX 630-0) Magnetometer (PNI TCM2-50)
(c)
anchor
Fig. 2. Three different navigation modes. (a) Autonomous mode. (b) Towed mode. (c) Kite mode.
GPS receiver (JRC DGPS212)a a
Guide number, 38 (with zoom headset at 35 mm) DC 100 V halogen lamp (150 W) DC 24 V Configuration, 4-beam, convex Frequency, 300 kHz Temperature range,−5–45 °C Altitude range, 1–100 m Bottom velocity range, ±10 m/s Water velocity range, ± 10 m/s Depth range, 0–100 m Accuracy, ±0.05% FS (typical) DC 5 V Range (tilt information), ±50 ° Resolution, 0.3 ° Repeatability, ±30 ° DC, ± 15 V Range, ±35 m/s2 (± 90 °) Resolution, 1 × 10−6 m/s2 (0.02 °) Maximum detectable angular rate, ±90 °/s Sensitivity, 21 mV/°/s ± 25% Transmit frequency, 27 kHz Receive frequency, 19 kHz Beam angle, ± 40 ° AC 100 V, under 100 VA Beam angle, ± 60 ° Transmit frequency, 17 kHz–20 kHz Receive frequency, 22 kHz–31 kHz DC, 12 V Frequency, 1575.42 MHz ± 1 MHz (GPS) Frequency, 283.5 kHz–325 kHz (DGPS)
The equipment installed on the mother ship.
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is removed for the autonomous mode. The towed vehicle has two thrusters at the tail-wings for surge and yaw motions and two elevators at the forewings for pitch and roll motions. Table 1 shows the principal components of our system. The dimension of the towed vehicle was determined for easy handling by humans. Detailed specifications of the equipment in Table 1 are also presented in Table 2. In order to take still and moving images, a digital camera, two stroboscopes, and two underwater lighting devices kept in watertight containers are mounted on the towed vehicle. In the towed and kite modes, obtained photographs and moving images are displayed on the monitor placed on the mother ship and concurrently are recorded on hard disks on the mother ship and in the towed vehicle; however, those are recorded only on the hard disk installed in the towed vehicle for the autonomous mode. The hard disk in the towed vehicle is kept in the main watertight container with other electric and electronic devices. The position and orientation of the towed vehicle are mainly calculated with the data of a DVL (Doppler velocity log), a depth sensor, a magnetometer (for the yaw), and two accelerometers (for the pitch and roll). Their accumulated error, which is proportional to navigation time, is modified by incorporating with the data of the SSBL (super short base line) from the mother ship at every pre-defined time step. An SSBL transducer is installed on the towed vehicle and SSBL transmitter and receiver manufactured by the KDDI R&D Laboratories, Japan, are installed on the mother ship. The pose data are transferred to the mother ship or vice versa through the towing cable in the towed and kite modes and through an acoustic link in the autonomous mode. The pose of the mother ship is obtained by a GPS (global positioning system) receiver and a magnetometer (for heading) installed on the mother ship. Three ceramic gyros are installed on the towed vehicle for measuring angular velocities around the three axes of the moving frame attached at the towed vehicle. The roll and pitch angles are directly provided by two accelerometers, and the yaw angle is provided by a magnetometer. Based on mentioned sensors, the motion control of the towed vehicle can be achieved. In addition, an electric-powered winch is installed on the mother ship. It has an electric motor with a rotary encoder and a controller for remote control. 2.2. Issues and previous works There are two issues related with the development of the autonomous towed vehicle. One is how to get the three different navigation modes with a single vehicle. In general, the natures of AUVs and UTVs are mutually contradictory. For example, the underwater weight of AUVs is usually near zero, while UTVs are relatively heavy to obtain sufficient towing forces; the drag force of AUVs is small but that of UTVs is somewhat large for the same purpose.Although AUVs are, in general, intrinsically stable in surge and roll motions, they are commonly designed to be controlled easily in other motions, while UTVs are designed to be more stable for high speed surveying without motion control. Our towed vehicle was designed based on the AE-2 [9,10] developed by the KDDI R&D Laboratories, Japan, which has been successfully carried out on several missions to inspect underwater cables in real sea (note that it was used as an AUV, not as a towed vehicle). In order to add the capability of the towed vehicle to the AE-2, we first performed computer simulations to investigate the stability of the AE-2 in the towed mode. It was known from the simulations that each forewing needs to be longer than that of the AE-2 by 76 mm, both for increasing drag forces and stable navigation, and additional 10 kgf weights are required on the front side of the vehicle for submerging to 60 m depth (the maximum depth around the Tokyo bay). Instead of using the additional weights, the expansions of each forewing's chord and the cable length can also be considered; however, the excessive expansion of the chord is unsuitable for operation in steady state and the extension of the cable length results in a long distance between the
towed vehicle and the mother ship. These produce another demerit. Also, the simulation results suggested controlling the pitching and rolling motions for steady linear and turning motions, even though the AE-2 was designed to be stable in the rolling motion. We fabricated a half-sized test model based on the simulation study of which forewing is longer than that of the AE-2 by 38 mm (76 mm in the real-sized one). Then, towing tank tests for investigating the hydrodynamic properties were carried out with the test model, such as drag tests, oblique motion tests, elevator angle tests, pure heave, pure pitch, pure sway, and pure yaw motions tests. After that, we reexamined the stability in the towed mode through simulations using the parameters of the test model and also carried out tank tests with the real vehicle that has identical shape with the test model. In the tank tests, basic operations were tested and the control gains and the lower boundary of the towing speed for depth control were determined; it was clarified that the towing speed is needed to be over 1.5 knots for depth control. The first sea trial was conducted and the results showed that our autonomous towed vehicle can navigate stably in the towed mode as well as in the autonomous mode [6]. The other issue is the safety during operation. Since UTVs are always affected by the towed force, it is recommended to monitor and, if necessary, control the towed force for preventing cable breaks and making use of it more effectively. This paper focuses on this issue and discusses towed force monitoring and control for safer operation. 3. Towed force monitoring First, our towed force measuring and monitoring manners are introduced and an experimental methodology for obtaining the feasible range of the towed force is proposed. Towed force estimation only with vehicle dynamics is additionally presented for the case when the towed force sensor became useless. 3.1. Towed force sensor Strain gauges are attached at the connection part (the cable anchor shown in Fig. 1) between the towing cable and the towed vehicle for measuring the magnitude of the towed force. To measure the direction of the towed force, two accelerometers are installed at the same place; one is for the elevation and the other is for the azimuth. 3.2. Towed force monitoring Fig. 3 shows the user interface, with which the operator can monitor the motion of the towed vehicle and can control its depth by giving a reference value of depth. The magnitude and direction (elevation and azimuth) of the towed force are also displayed on the user interface in bar graph and/or in number as shown in Fig. 3. The bar graph has three colors according to the magnitude of the towed force. Green is for over-loosened case, yellow for normal, and red for over-tensioned case. When the towed force sensor is malfunctioned, estimated towed force information will be displayed. 3.3. Safety range of the towed force The information on the upper and lower bounds of the towed force and the range of controllable depth in accordance with the towing speed and cable length is important in knowing whether the present towed force is normal and the limitation of the depth control. In order to acquire such information, we propose the step-by-step depth control method shown in Fig. 4. The control process is as follows: Step 1 With given cable length and towing speed, the mother ship tows the towed vehicle until the depth of the towed vehicle approaches certain equilibrium. In this case, the towed vehicle does not carry out depth control.
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towed force information
Fig. 3. Display of the towed force information on the user interface.
0 lower bound equilibrium upper bound
-10 -13.8
Depth (m)
Step 2 After reaching equilibrium, downward (toward the seabottom) stair-type depth control is performed until the depth control cannot be achieved anymore due to the shortage of lifting force for descending. At the ultimate depth, the magnitude of the towed force becomes largest (the upper bound) and the controllable depth also has the maximum value (the upper bound). Step 3 After Step 2, to obtain the lower bound, upward (toward the surface) stair-type control is performed until the depth control cannot be accomplished due to the shortage of lifting force for ascending.
-20.8
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-60 In our case, the step-by-step depth control was carried out with 2 knots towing speed and 30 m, 55 m, and 80 m cable lengths. A single step for the stair-type depth control is 5 m, 10 m, and 10 m for 30 m, 55 m, and 80 m cable lengths, respectively. Fig. 5 shows the experimental results and all the data were obtained by the mentioned towed force sensor. The figure shows that the equilibriums in depth are approximately center values between the upper and lower values,
cable
vehicle
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equilibrium step-by-step depth control step-by-step depth control
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Fig. 4. Step-by-step depth control for obtaining the upper and lower bounds of the towed force and the range of controllable depth.
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Cable length (m) Fig. 5. The ranges of the controllable depth and the magnitude of the towed force according to 30 m, 55 m, and 80 m cable lengths, when the towing speed is 2 knots. The equilibrium means that the steady state reached without depth control.
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but those in towed forces are more near the upper values. This implies that control sensitivity to the towed force is lower between the equilibriums and the upper bounds than at the counterpart; in other words, a larger change of elevation angle is needed for the same control purpose at the range. The data in Fig. 5 are very useful at the planning stage of field operation. For example, once the depth and the towing speed for an observation work are given, an efficient cable length can be determined based on the data. Surely, safer operation can be realized since the upper and lower bounds of controllable depth and the towed force are known. 3.4. Towed force estimation with vehicle dynamics Let fC ∈R2 be the towed force vector and x = (x, z, θ)T be the vector whose elements are the position in a vertical plane, (x, z), and the pitch angle, θ, of the towed vehicle. The coordinate system obeys the right-hand rule and the z-axis points to the downward (toward the sea-bed). In order to estimate the towed force, we consider the towed vehicle dynamics in a vertical plane (x–z plane) as: M x˙˙ + C x˙ + d + g = Bτ + H f C + f W T
ð1Þ
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200
400
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400
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when the mother ship is turning
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800
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ð2Þ
where z = M x˙˙ + C x˙ + d + g−Bτ−f W is computed with the vehicle's parameters and the measurements of the motion sensors. For assuring the solution of Eq. (2), the matrix HHT should be nonsingular, i.e., its determinant should not be zero. As for our vehicle, the solution
Magnitude of the towed force (kgf)
Depth (m)
T −1 f C = HH Hz
(b) when the cable length is 55 m
(a) when the cable length is 30 m
Magnitude of the towed force (kgf)
where M = MRB + MA ∈R3×3 , MRB and MA are the rigid-body inertia matrix and the added inertia matrix, respectively; C = CRB + CA ∈ R3×3 , CRB and CA are the rigid-body Coriolis and centripetal matrix and the hydrodynamic Coriolis and centripetal matrix, respectively. In addition, d∈ R3 is drag terms; g∈R3 is gravity and buoyancy terms; B∈ R3×2 is the matrix mapping the forward thrust, tTH, exerted by the two thrusters and the synchronous elevator angle, eS, on the resultant forces and moment acting on the towed vehicle; H ∈ R2×3 is the geometry dependent matrix associated with the towed force; fW ∈ R3 is the vector having the forces and moment caused by additional weights; and τ = (tTH, eS)T∈R2 . The synchronous elevator angle is the averaged one of the left and right elevators' angles like eS = (eR + eL) /2. From Eq. (1), we can estimate the towed force by using the least squares estimation method as follows:
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800
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(c) when the cable length is 80 m
(d) when the cable length is 30 m and the operating depth is below the upper bound
Depth (m)
when the mother ship is turning
upper bound
-40
lower bound
-60
Depth (m)
-10 -20
-80 200
400
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800
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1200
Time (sec) 200
measured estimated
150 100 50 0
0
200
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800
Time (sec)
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1400
-20 -25 -30 -35
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Magnitude of the towed force (kgf)
Magnitude of the towed force (kgf)
0
obstacle avoidance
-15
0
100
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500
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700
Time (sec) 200
measured estimated
150 100 50 0
0
100
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400
Time (sec)
Fig. 6. Measured and estimated values of the magnitude of the towed force when the towing speed is 2 knots.
500
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700
J.-K. Choi et al. / Automation in Construction 20 (2011) 1012–1019
always exists since det(HHT) = 1+a2 + b2 ≠ 0, where (a, b) is the position of the coupling point with the towing cable in the moving frame attached at the towed vehicle. Fig. 6 shows the estimated and measured values of the magnitude of the towed force during carrying out the step-by-step depth control to obtain the data shown in Fig. 5. Here, we did not take noise filtering in estimation for direct comparison with the data obtained by the towed force sensor. Figs. 6a–c are the values when towing speed is 2 knots and the cable lengths are 30 m, 55 m, and 80 m, respectively. From Fig. 6, we can observe the following: (1) The trends of the measured and estimated values are similar even though there is a difference between them. The difference is considered to be mainly caused by the modeling error. (2) The difference between the measured and estimated ones near the upper bound of the towed force is relatively large. (3) When the mother ship is turning (to acquire an area for the experiment), the difference becomes larger as shown in Fig. 6b and c. This is due to the break of static balance. (4) When the towed vehicle avoids an obstacle on the seabed, the difference grows larger as shown in Fig. 6d. This is also caused by the momentary break of static balance. These results give the following guidance in using the estimation method: there is a relatively large difference between the estimates and the measured ones when the towed vehicle approaches the upper bound and the static balance is broken and thus we need to use the estimation method while avoiding such situations. In addition, in order to ensure the safety during turning, we experimentally obtained the range of turning radius, in which the mother ship can turn without losing stability of the towed vehicle. Related experimental data will be presented in Section 4. 3.5. Implementation of the Kalman filter It is practical to utilize the towed force sensor measurements rather than the estimates because there are uncertainties in model parameters such as hydrodynamic coefficients that vary with operational conditions. However, it is worthy to provide the estimates in order to prepare for the case when the towed force sensor became useless and to detect the towed force sensor failure. To this end, we designed filter such as below. theKalman −1 ˜ Let HHT H = N + Nδθ, z = z + z˜ δs, and U be the towing speed, whereN and z denote the mean values of N and z, respectively; Ñ and z˜ are the error coupling matrices; and δθ and δs are the errors caused by sensor noises. Then, Eq. (2) can be rewritten into: h i ˜ O2×2 δs f C = Nz + N z˜ + O2×3 O2×3 Nz
cosα f + −sinα S
ð
−fS sinα cosα −fS cosα −sin α
0
0
1
I2×2
B B O3×2 B B Φk = B O3×2 B BO @ 3×2 O2×2 T
B A1 = @
T
I3×3
C C C C C; C C A
O
A1
I3×3
A2
A3
I3×3
O2×3 O2×3 O2×3 I2×2 0 1 1 0 O 0 0 0 T2 = 2 B C C B B C A; A2 = @ 0 0 0 A; A3 = @ 0
O T 0 0 0 Γ k O2×2 O2×9 Ωk Γ ′k = ; Λ k = I13×13 ; Ω′k = ; I11×11 I11×11 h i ˜ zk O2×2 δsk ; Γ k = N k z˜k + O2×3 O2×3 N k ! cosα k −fSk sinα k Ωk = ; −fSk cosα k −sinα k T T X k = f C ; x˙˙; z˙˙; θ˙˙; x; ˙ z; ˙ θ˙ ; θ; U; eS ; α; fS ; T ˙ δθ; δU; δeS ; δα; δfS ; wk = δx˙˙; δz˙˙; δθ˙˙; δ x; ˙ δ z; ˙ δ θ;
0
1
0
T
0
C 0 A;
0
0
vk = wk;T is the sampling period;Ii × j is a i × j identity matrix of which diagonal components are all 1;O denotes zeros; and wk, w ′k, and vk are assumed to be zero-mean white Gaussian noises whose covariance matrices are Q k, Q ′k, and Rk, respectively. Fig. 7 shows the estimates obtained by the implemented Kalman filter for the case in Fig. 6d, where T = 1 s, Q k = 0.01I11 × 11, Q ′k = 0.001I13 × 13, and Rk = 0.01I11 × 11. In addition, the sensor failure can be checked by examining the magnitude of the residual (also called the measurement innovation) in the Kalman filter equations [11–13]. 4. Discussion on towed force control Letting TFmax and TFmin be the upper and lower limits of the towed force, respectively, the magnitude of the towed force can be classified into the following three cases: jj f C jjbTFmin : Over loosened;
ð7Þ
TFmin ≤jj f C jj≤TFmax : Feasible;
ð8Þ
jj f C jj N TFmax : Over tensioned:
ð9Þ
Þð
Þ
δα δfS
ð4Þ
where α and fS are the sensor data obtained from the accelerometer for the elevation of the towed force and the strain gauge for the magnitude, respectively. From Eqs. (3) and (4), we can formulate the process model and the measurements model for Kalman filter implementation as follows: ′ wk−1 + wk−1 ′ X k = Φk−1 X k−1 + Γ k−1
ð5Þ
Z k = Λ k X k + Ωk′ vk
ð6Þ
200
Magnitude of the towed force (kgf)
T ˙ δθ; δU; δeS and Oi × j is a i × j zero ˙ δ z;˙ δ θ; where δs = δx˙˙; δz˙˙; δθ˙˙; δ x; matrix of which elements are all zero. Also, the model for the towed force sensor can be formulated as:
where
ð3Þ
f CM =
1017
measured estimated 150
100
50
0
0
100
200
300
400
500
600
700
Time (sec) Fig. 7. Estimated values of the case in Fig. 6d, obtained by the Kalman filter.
J.-K. Choi et al. / Automation in Construction 20 (2011) 1012–1019
f C = −ΨBτ + Ψz′
ð10Þ
where z′ = M x˙˙ + C x˙ + d + g−f W and Ψ = (HHT)− 1H. Ψ and B are geometry dependent terms and z′ depends on the towing speed, the pitch angle of the towed vehicle, and the cable length. This equation shows that the towed force, fC, can be actively controlled by changing the input τ = (tTH, eS)T, the towing speed, and the cable length. Thus, the following four towed force control methods can be considered. The first one is by changing the cable length through winch motion using the winch on the mother ship; the second is by changing the speed of the mother ship, i.e., changing the towing speed; the third is by the thrusters input, tTH; and the fourth is by the synchronous elevator input, eS. In what follows, we shall discuss each method in detail. 1) By the winch. The length of the towing cable can be adjusted by the electric winch installed on the mother ship and, accordingly, the towed force can also be controlled. Figs. 5 and 6 give the example. We can confirm that the towed force increases in accordance with the increase of the cable length. Letting || f Cd || be the magnitude of a desired towed force, the winch torque for controlling the towed force can be given by: τwinch = τwinch
r
+ k winch ðjj f Cd jj−jj f C jjÞ
ð11Þ
where τwinch_r is a reference value of winch torque and kwinch is a positive control gain. The winch control conducts until | || fCd || − || fC || | ≤ ε is satisfied, where ε is a positive real number. There are some points to be considered carefully for this control method. In normal operation, the drags to the towed vehicle are applied to mainly the front side and the towing cable, and hence, the magnitude of the towed force varies in proportion to the towing speed and the cable length. However, during the winch and release motions by the winch, different trends appear. For example, during the winch motion, additional drags occur around the upside of the towed vehicle although the cable length is lessened gradually. In this case, the towed force strongly depends on the winch speed. Similarly, the towed force during the release motion also depends on the release speed of the winch and the entire drags including the additional drags around the downside reduce the speed of the towed vehicle. This consequently decreases the towed force even though the cable length becomes longer. In addition, the winch and release motions need to be executed while maintaining the static balance for the steady motion of the towed vehicle. 2) By the mother ship. The drags on the towed vehicle and the towing cable increase with the towing speed and thus the towed force can be controlled by changing the speed of the mother ship. Fig. 8 shows the magnitude of the towed force according to the synchronous elevator angle (from −30° to 15°), the towing speed (1.5 knots, 2 knots, and 2.5 knots), and the pitch angle (0° and − 5°). This result was obtained through numerical simulations on the assumption that the towed system is in a static balance. As shown, the magnitude of the towed force varies responding to the change of the towing speed. This towed force control method can be effectively used for emergency situation, e.g., when the magnitude of the towed force became abnormally large. However, it is to be noted that frequent change in speed of the mother ship
can cause an unstable motion of the towed vehicle because it takes time to go into the static balance after the towing speed is changed. 3) By the thrusters. As shown in Eq. (10), the towed force fC can be controlled by the thrusters input tTH. In a vertical plane, the forward and backward thrusts of the towed vehicle can respectively reduce and increase the magnitude of the towed force. Specifically, the forward motion results in increase in speed of the towed vehicle and this weakens the pulling force exerted by the mother ship. Conversely, the decrease in speed of the towed vehicle caused by the backward motion strengthens the towed force. In addition, this method will be useful when the operator wants to rapidly stop the towed vehicle for avoiding an unexpected collision after the mother ship is stopped; however, this method requires a great deal of thrust and accordingly results in large consumption of energy. 4) By the elevators. The depth control using the synchronous elevator input is effective to change the magnitude of the towed force as shown in Figs. 5 and 6. Moreover, Fig. 8 shows that the magnitude of the towed force varies linearly with respect to the synchronous elevator angle. Usually, the towed vehicle carries out a given mission while changing its depth using the elevators. Therefore, this method is considered to be most natural comparing with mentioned other three methods. For our towed system, this method is mainly used to control the towed force for normal operation. In addition, it was stated in Section 3 that the towed force estimation method needs to be used while avoiding the situation like the static balance of the towed system is broken; this situation
(a) when the pitch angle is 0o Magnitude of the towed force (kgf)
If the towed vehicle meets the cases of Eqs. (7) and (9), it/the operator needs to control the towed force in order to move into the feasible region defined in Eq. (8); this can avoid undesirable situations, e.g., cable breaks due to excessive tension and a collision with an obstacle due to uncontrolled motion caused by excessively loosened cable. The feasible region is determined based on the data shown in Fig. 5. For explanatory convenience, Eq. (2) is rewritten into:
400 300 2.5 knots 200 2 knots 100 0 -30
1.5 knots
-20
-10
0
10
20
Synchronous elevator angle (deg)
(b) when the pitch angle is -5o Magnitude of the towed force (kgf)
1018
400
2.5 knots
300 2 knots 200 1.5 knots 100
0 -30
-20
-10
0
10
20
Synchronous elevator angle (deg) Fig. 8. The magnitude of the towed force according to the elevator angle (from −30° to 15°), the towing speed (1.5 knots, 2 knots, and 2.5 knots), and the pitch angle (0° and −5°).
J.-K. Choi et al. / Automation in Construction 20 (2011) 1012–1019
(a)
1019
towed vehicle and the magnitude of the towed force are stable when the mother ship turns with 100 m turning radius; however, there are small variations such as ± 1 m in the depth and ±10 kgf in the towed force when the turning radius is 50 m. From this result, we arrive at the conclusion that the safety of the towed vehicle can be ensured if the mother ship turns with the turning radius between 50 m and 100 m.
-1150 start -1200 turning radius: 100 m
y (m)
-1250
5. Conclusion
-1300
-1350
This paper has discussed towed force monitoring and control for safe operation of our autonomous towed vehicle. We first overviewed the autonomous towed vehicle and described our related previous works. We then presented our approach to the towed force measurement and monitoring, as well as our experimental methodology for obtaining the safety range of the towed force. We showed that the towed force sensor attached near the towed vehicle provides understandable measurements and the obtained safety range of the towed force is useful when determining the cable length for a given observation work and judging whether the present towed force is normal. In addition, we presented a towed force estimation method based only on vehicle dynamics to prepare for the case when the towed force sensor is malfunctioned. It was illustrated that the estimator supplies close values to the sensor measurements. Finally, four towed force control methods for keeping the towed force inside the safety range were discussed.
turning radius: 50 m
-1400
1900
1950
2000
2050
2100
x (m)
(b) Depth (m)
-10 -20 -30 -40 -50
Magnitude of the towed force (kgf)
-60
0
50
100
150
200
250
300
350
Time (sec)
References
200 150 100 50 0
0
50
100
150
200
250
300
350
Time (sec)
Fig. 9. The results of the experiment to obtain the range of turning radius in which the mother ship can turn without losing stability of the towed vehicle. (a) The position of the towed vehicle. (b) The depth and the magnitude of the towed force. In this experiment, the towing speed was 2 knots and the cable length was 55 m.
frequently occurs when the mother ship is turning. To ensure the safety of the towed vehicle for this case, we experimentally obtained the safety range of turning radius, in which the mother ship can turn without losing stability of the towed vehicle. In the experiment, the mother ship first turned with 100 m turning radius and then turned with 50 m turning radius after confirming the stability of the towed vehicle, under the towing speed of 2 knots and the cable length of 55 m. Fig. 9 shows the results. It is observed that the depth of the
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