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Study on impact process of AUV underwater docking with a cone-shaped dock
Ocean Engineering 130 (2017) 176–187
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Study on impact process of AUV underwater docking with a cone-shaped dock
MARK
⁎
Tao Zhang, Dejun Li , Canjun Yang The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Autonomous underwater vehicle Docking Impact ADAMS
This study investigates the impact issues associated with docking systems when autonomous underwater vehicles (AUVs) contact with a cone-shaped and unclosed dock, which has been proposed and realised by most AUV docking systems. The study aims to understand the impact process in AUV docking with the dock and derive a number of probable suggestions. To realise this objective, a dynamic model with impact is established in the commercial software ADAMS after identifying relevant forces especially obtaining hydrodynamic coefficients and completing impact configurations. Based on the proposed dynamic model, five interesting influence elements are discussed respectively. A pool trial was conducted, and experiment results are compared with the corresponding simulation data to validate the model. Several effective suggestions are proposed for the designs of the docking system and the docking control of the companion AUV.
1. Introduction Autonomous underwater vehicles (AUVs) are playing an increasing role in oceans in recent decades because of their vast scientific, commercial and military applications. However, poor endurance resulting from the battery's low capacity and the high-power draw of the instrumentation and poor real-time capacity of data transfers limit the wide use of AUVs in vast spaces and for long periods. Furthermore, underwater docking technology, which has the ability to recharge battery, transfer data and safely park AUVs, has been proposed to extend the use of AUVs in space and time. The development of cabled ocean observatory networks also makes the successful long-term operation of an underwater docking system possible. In addition, an underwater docking system is crucial in constructing a tri-dimensional ocean observatory system by combining dynamic and wide-range observation with static and long-term monitoring. Thus, a growing number of organisations have recently devoted significantly more attention to the research and manufacture of underwater docking systems. Underwater docking systems generally include the following classic types. Singh et al. (2001) attempted to use a passive latch on the AUV to grasp the pole on the dock and enable the AUV to accomplish the docking task omnidirectionally. Fukasawa et al. (2003) adopted the Marine Bird docking system, another docking type that operates like an aircraft landing on an aircraft carrier. As such, the vehicle catches the V-shaped guide on the base of the dock by running slowly over the base, using its catching arm, and joining the connecting device. Lambiotte et al. (2002) attempted the use of a pyramid-type docking ⁎
system with a guide above the intersection of each side to provide the vehicle with the option of docking from four directions. The structure of this pyramid-type docking system is comparatively simple but quite complex for the vehicle to lock, charge battery and transfer data. To the best of my knowledge, the most widely used type nowadays is the coneshaped docking system, which makes it comparatively convenient for the vehicle to navigate into the dock and lock in the protective housing, such as MBARI docking system for a 21″ AUV (McEwen et al., 2008), the REMUS docking system (Allen et al., 2006; Stokey et al., 2001), the flying plug docking system (Cowen, 1997) and the ISiMI docking system ( Park et al., 2007, 2009). Among the above docking systems, the cone-shaped type is quite a good compromise of structural complexity and functional reliability. This type of docking system can lower the AUV's navigation accuracy demand, which requires less modification or no extra mechanical accessories on the AUV for docking. It likewise offers a more reliable lock and protective housing, as well as makes it much more convenient and dependable to charge and transfer data. Although generally, considering the fixed-size cone and the definite direction an AUV should dock in on most situations, this type of docking system is only suitable for certain AUVs with specific sizes. The cone-shaped type is advantageous in its practicability and reliability compared with other types, making it the most widely used AUV underwater docking system today. Therefore, the coneshaped docking system is adopted in our project. Many of the developed cone-shaped docking systems have concentrated on AUV homing and docking control (McEwen et al., 2008), the method of transferring power and data (Shi et al., 2014) and the vision
Corresponding author.
http://dx.doi.org/10.1016/j.oceaneng.2016.12.002 Received 18 November 2015; Received in revised form 30 November 2016; Accepted 1 December 2016 0029-8018/ © 2016 Elsevier Ltd. All rights reserved.
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guided docking (Park et al., 2009). However, these characteristics are not sufficient for a docking system. When docking, the AUV may collide with the cone of the dock in most cases, which induces a number of necessary considerations on the docking system design and the companion AUV's docking control before docking. Considerations include how the shapes and material characteristics of a cone affect AUV docking, and how the deviation, velocity and propeller force of an AUV influence the complete docking mission of the vehicle with minimal damage and maximum docking success rate. This study expands what we have explored before (Shi et al., 2015). The paper is organised as follows. Section 1 introduces some AUV underwater docking systems, especially the cone-shaped docking system, and discusses some issues below. Section 2 briefly describes the AUV and the docking station in our project. Section 3 derives the dynamic model focusing on hydrodynamic characteristics and contact force, and builds the simulation model in ADAMS. Section 4 discusses the effects of different elements (i.e. cone angle, material characteristic, deviation, velocity and propeller force) on the impact process. Section 5 compares the experimental results with the preceding simulation data. Section 6 presents the conclusion.
Table 1 Main specifications of Dolphin II. Features
Unit
Description
Body length Body diameter Slenderness ratio of the body Surface area of the body Span length of the tail Chord length of the tail Aspect ratio of the tail Surface area of the tail Outer diameter of propeller Weight in air Operating depth
m m
m2 m kg m
2.47 0.20/0.29 0.084/0.123 1.499 0.340 0.110 3.091 0.0374 0.16 79.5 0–100
locking unit
tube
m2 m m
guidance accessories
cone
steering mechanism
housing
2. AUV and docking station 2.1. AUV − Dolphin II overview
base
The docking AUV in our project is a modified version of Dolphin II (Zhang et al., 2014), whose bow part was replaced with new sections. Furthermore, the sequence of some of its other sections was exchanged to conveniently accomplish the docking task and transfer power and data in the contactless method. Fig. 1 demonstrates that the modified AUV can be divided into five sections: Bow Section, Non-contact Section, Battery & Control Section, Navigation & Communications Section, and Tail Section. Apart from the bow section, which is a wet housing surrounded by engineering plastic shells, the modified AUV has an aluminium alloy and an air-filled pressure housing. After modification, it has an overall length of 2.47 m with a main body diameter of 0.2 m. However, the vehicle has a larger diameter of 0.29 m because the non-contact section requires extra space to install a secondary inductive coupling coil for contactless power transfer and a Wi-Fi antenna for a wireless network link. The entire mass of the AUV on the shelf weighs 79.5 kg in air, whereas the net weight is approximately close to zero in water because of appropriate buoyancy. According to its original design, the speed of the AUV can reach up to 5 knots, as verified in previous lake trials. The main specifications of the modified AUV are illustrated in Table 1. These details are helpful to the calculation of external forces and moments, especially to the hydrodynamic coefficients discussed in Section 3.2.
Bow Section
Non-contact Section
Fig. 2. Three-dimensional model of the docking station. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
2.2. Docking station The design approach of McEwen et al. (2008) is to keep the docking station as simple as possible; in contrast, our primary principle is to make the AUV's modification as simple as possible. Therefore, apart from some general equipment, such as tube, cone, base and housing, the docking station consists of the steering mechanism, guidance accessories (e.g. guidance light, transponder, acoustic doppler current profilers) and locking unit, as shown in Fig. 2. The dock body, consisting of the cone and the tube, is mounted on the base through the steering mechanism. The dock's entry, namely, the cone, is conically shaped and made up of some staves held in place by two stainless steel rings. The material of the staves and the taper angle of
Battery & Control Section
Navigation & Communications Section
Fig. 1. Configuration of the AUV Dolphin II.
177
Tail Section
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Fig. 3. Body-fixed and earth-fixed reference frames.
3.1. Reference frames and external forces
the cone are designated based on the analysis in Section 4. The tube is comprised of acrylonitrile butadiene styrene plastics and is analogously cylindraceous with inner diameters of 0.3 and 0.21 m, which are 0.01 m larger than the AUV's diameter, to match the shape of the modified vehicle. To avoid the vehicle touching the bottom and being disturbed by seafloor impurities, the base is a 3 m-high pyramid so that the vehicle can fly with a safe approach during docking. The original plan indicates that the docking station will be applied in a 100 m-deep ocean, such that, a reliable housing subjected to external pressure is necessary. Furthermore, the housing accommodates the electronics essential to control the steering mechanism, which can adjust the dock's orientation to be consistent with the AUV's heading, as well as support the power and data transfer between the AUV and the station. Guidance accessories are also considerably useful to guide an AUV into a docking station. After being guided into the station and locked by the locking unit, the AUV can tightly and securely park in the parking zone, which is represented by the red box in Fig. 2.
We define the body-fixed and earth-fixed reference frames indicated in Fig. 3 according to the definition of Fossen (1994). The origin O of the body-fixed reference frame is located at the centre of buoyancy and other axes, such as, X, Y and Z, which coincide with the principal axes of inertia. The earth-fixed reference frame, namely, the inertial coordinate system, is fixed in the docking station and denoted by the unit vectors ξ ,η and ζ . Furthermore, the origin is chosen to coincide with the centre of the cone's small face, ξ aligns with the axial direction of a stationary cone in the last docking phase, ζ points to the gravity and completes the right-handed triad. As mentioned in Timothy (2001), the general motion of the AUV in six degrees of freedom can be described by the following vectors: κ1 = [ x y z ]T ; κ2 = [ ϕ θ ψ ]T ; v1 = [ u v w ]T ; v2 = [ p q r ]T ; τ1 = [ X Y Z ]T ; τ2 = [ K M N ]T ; where κ describes the position and orientation of the AUV with respect to the earth-fixed reference frame; v shows the translational and rotational velocities of the AUV with respect to the earth-fixed reference frame, but expressed in the bodyfixed reference frame; and τ denotes the total external forces and moments acting on the AUV expressed in the body-fixed reference frame. Based on Thomasson and Woolsey (2013), the kinematic equations can be revealed as
3. Dynamic model The following are assumptions on the AUV and the docking station used as the basis for model development to simplify the challenge of building a dynamic model with impact (Chatterjee, 1997; Timothy, 2001).
• • •
• • •
The colliding bodies consisting of the AUV and the dock are rigid. Thus, both mass and mass distribution of the AUV and the dock do not change during operations without regard to the tiny deformations in the contact region. The AUV and docking station are deeply submerged in a homogeneous fluid 100 m far from the surface in reality. Environmental disturbances (e.g. waves, wind and ocean currents) are not considered during the docking process. Weight and buoyancy are approximately equal but are aligned in the opposite direction with the plumb line; however, their action points do not coincide with each other, which leads to a trimming moment for roll motion. For safety, most underwater vehicles like AUVs have a slightly negative net weight (i.e. the subtraction of weight and buoyancy) in reality. We simplify the situation here. The propulsion model used in the following is extremely simple; it treats the thruster as a source of constant thrust and torque under a constant propeller speed. The impact process, whose duration is fairly short, does not cause infinite interpenetration in the contact region. The dock is rigidly fixed to the base of docking station during impact in the last docking phase, although it can rotate under corresponding controls during the homing phase.
κ1̇ = RIB v1
(1)
̇ = RIB vˆ2 RIB
(2)
Where ˆ. denotes a 3×3 skew symmetric matrix satisfying aˆ b = a × b for vectors a and b, and RIB is the transition matrix from the body-fixed reference frame to the earth-fixed reference frame and can be expressed in conventional Euler angles (i.e. roll angle φ , pitch angle θ and heading angle ψ ) as
RIB = e eˆ3ψ e eˆ2θ e eˆ1φ where ei represents the standard basis vector for R3 , where i ∈ {1 2 3}, and e(.) denotes the matrix exponential. By applying Lagrangian mechanics, we can denote the dynamic equation in Lagrangian expressions as
d ⎛ ∂L ⎞ ∂L =Γ ⎜ ⎟− dt ⎝ ∂κ̇ ⎠ ∂κ
(3)
where L is the Lagrangian, namely the subtraction of the AUV's kinetic and potential energies, and Γ is the total external forces and moments acting on the AUV with respect to the earth-fixed reference frame; that T is Γ = [ τ1T τ2T ] . Eqs. (1–3) describe the dynamic model of the entire 178
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Fprop = CFρn 2D4 Mprop = CT ρn 2D 5
(5)
where CF indicates the coefficient of thrust force, CT shows the coefficient of propeller torque, n represents the propeller rotation speed andD denotes the outer diameter of the propeller. However, the appropriate balance weight and hydrostatic roll moment will counteract the propeller torque Mprop in practice. 3.2. Hydrodynamic characteristics Acquiring the hydrodynamic characteristics is necessary to accomplish the AUV dynamic model. According to the research by Wu et al. (2014), an unclosed dock has a minimal influence on the hydrodynamic characteristics of an AUV, which means we can typically deal with hydrodynamic forces and moments as usual. Generally, these characteristics include viscous and inviscid terms. Several methods, including analytical, computational and semi-empirical approaches, can be applied to predict the hydrodynamic characteristics of an AUV (De Barros et al., 2008). Considering our needs and the cost, we determined the viscous terms based on the computational fluid dynamics (CFD) software, and used an analytical approach to obtain the inviscid terms. Using the commercial software GAMBIT, we obtained the C-O type structured grids with the local grid refinement technology, shown in Fig. 4. We also adopted the CFD package FLUENT and followed the similar method described in Yang et al. (2014) to acquire the viscous hydrodynamic parameters. Fig. 5 shows the velocity pathline when the AUV model, as simulated in FLUENT, turns at the yawing rate of 0.3036 rad/s. Viscous forces fv and moments mv acting on the vehicle are part of external forces τ1 and moments τ2 , and can be expressed in the bodyfixed frame as follows:
Fig. 4. C-O type structured grids in GAMBIT.
Fig. 5. Velocity pathline in FLUENT.
vehicle system. In the forthcoming numerical analysis, the simulation software ADAMS is adopted. ADAMS can solve the kinematic and dynamic problems with impact processes according to the above modelling method. Afterwards, the crucial point of modelling the docking process is to search for the explicit expressions of the external forces and moments acted on the AUV. Total external forces and moments can be classified into hydrostatic terms (i.e. the weight and buoyancy of the AUV and their corresponding moments), propeller thrust and torque, hydrodynamic terms (i.e. added mass and hydrodynamic damping) and contact force during impact. We only discuss the hydrostatic terms, the propeller thrust and torque in this subsection owing to the relatively complex hydrodynamic terms and contact force. Hydrostatic terms, namely, restoring forces due to Archimedes, mainly consist of weight W and buoyancy B(both W and Bare threedimensional force vectors expressed in the earth-fixed reference frame), whose magnitude and direction almost remained unchanged in the submerged fluid. We know the hydrostatic force from a previous assumption as the resultant force of the weight and buoyancy that may vanish because of the approximate magnitude and opposite direction of the two component forces. However, in the case of the separate weight and buoyancy centres, the resultant moment causes a trimming torque useful for roll stability. In total, hydrostatic terms can be expressed in the body-fixed reference frame as
⎛ Xv ⎞ ⎜ ⎟ fv = ⎜Yv ⎟ ⎜ ⎟ ⎝ Zv ⎠ ⎛ Kv ⎞ ⎜ ⎟ mv = ⎜ Mv ⎟ ⎜ ⎟ ⎝ Nv ⎠
(6)
We choose 0.5ρV 2L2 and 0.5ρV 2L3 as the dimensionless factors to non-dimensionalise the viscous forces and moments as
Xv′ = Kv′ =
Xv 0.5ρV 2L2 Kv 0.5ρV 2L3
,
Yv′ =
,
Mv′ =
Yv 0.5ρV 2L2
Zv
,
Z v′
,
N ′v =
Mv 0.5ρV 2L3
0.5ρV 2L2 Nv 0.5ρV 2L3
The non-dimensional coefficients of these forces and moments can be obtained using linear derivative regression afterwards. According to the notational convention for aircraft (Nelson, 1998; Pamadi, 2004), the viscous coefficients with non-dimensional quantities can be provided as follows:
Xv′ = CX (α ) = CX0 + CXα1α + CXα 2α 2 + CXα3α 3 + CXα 4α 4
FHS ≈ 0
Kv′ = CK (β , p , r , δr ) = CKββ + CKp p + CKr r + CKδrδr T
MHS = rG × (RIB W )
Yv′ = CY (β , p , r , δr ) = CYββ + CYp p + CYr r + CYδrδr
(4)
Mv′ = CM (α , q , δe ) = CMα α + CMq q + CMδeδe
where FHS and MHS are the hydrostatic force and moment respectively, and rG is the vector from the centre of gravity to the origin of the bodyfixed reference frame (i.e. centre of buoyancy). The rotary propeller for marine vehicles not only generates the thrust for the surge motion but also the propeller torque, though it is generally counteracted. Afterwards, the directions of the thrust and the torque are aligned with the X axis in the body-fixed reference frame. According to a simple propulsion model (Kerwin and Hadler, 2010), the magnitudes of the thrust and the propeller torque can be shown as
Z v′ = CZ (α , q , δe ) = CZαα + CZq q + CZδeδe Nv′ = CN (β , p , r , δr ) = CNββ + CNp p + CNr r + CNδrδr where α , β are the attack and sideslip angles; p , q , r are the dimenpL qL rL sionless angular velocities defined as p = V , q = V , r = V ; and δr , δe are the rudder and elevator angles. The rest on the right side of the equal sign are the computed viscous coefficients of the AUV as listed in Table 2. 179
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Table 2 Viscous coefficients of the AUV. Notation
Value (×10−3)
Notation
Value (×10−3)
CX0
- 2.5933
CKβ
−0.2211
CXα1 CXα2 CXα3 CXα4 CYβ CYp CYr
2.7339
−0.0621
CYδr CZα CZq CZδe
−11.02
CKp CKr CKδr α CM q CM δe CM β CN CNp CNr CNδr
- 8.3656 - 91.791 165.11 −32.329 −1.2958 −7.4285 −26.228 6.23
0.0595 −0.001 −2.4682 4.0153 5.0858 −1.484 0.3554 4.3013 5.1003
10.975
Fig. 6. Difference between, and q0,q and d. (For interpretation of the references to color
Table 3 Inviscid coefficients of the AUV. Notation
Value (×10−3)
Notation
Value (×10−3)
X′u̇ Y′v̇ Z′ẇ
−0.1236 −6.9286 −6.8543
N′r ̇ Y′r ̇ Z′q̇
−0.3564 0.0890 −0.0612
K′ ṗ
−0.0181
M′ẇ
−0.0612
M′q̇
−0.3512
N′v̇
0.0890
According to the SNAME notation (Fossen, 1994), inviscid hydrodynamic parameters are the components of the generalised added inertia matrix. Owing to the vehicle symmetry and considering the mainly effective terms, the generalised added inertia matrix can be simplified as
⎛M f M f = ⎜⎜ C ⎝ f
⎛ Xu ̇ ⎜ ⎜0 T⎞ ⎜0 Cf ⎟=−⎜ ⎟ Jf ⎠ ⎜0 ⎜0 ⎜⎜ ⎝0
0 0 Yv ̇ 0 0 Z ẇ
0 0 0
0
0
K ṗ
0
Mẇ
0
Nv ̇
0
0
Fig. 7. Simulation model in ADAMS.
x-shaped configuration. Furthermore, the vehicle's hull is approximated as a spheroid, whereas the appendages, including antenna housing and control planes, are approximated as flat plates. Then the inviscid coefficients can be calculated as follows (Shi, 1995):
0 0⎞ ⎟ 0 Yr ̇ ⎟ Z q̇ 0 ⎟ ⎟ 0 0⎟ Mq ̇ 0 ⎟ ⎟⎟ 0 Nr ̇⎠
z ap π BH H π l b [1 + ( )2]K44 − ∑fv μ(λ ) ( )2( )2 60 L L 2 L L L L y ap π l b − ∑fh μ(λ ) ( )2( )2 2 L L L xap πBH π l b π BH H π l b Yv′ ̇ = − K − ∑fv μ(λ ) ( )2 Mq′ ̇ = − [1 + ( )2]K55 − ∑fh μ(λ ) ( )2( )2 3 L L 22 2 60 L L 2 L L L L L L x ap πBH π l b π BH B π l b Z w′ ̇ = − K − ∑fh μ(λ ) ( )2 Nr′̇ = − [1 + ( )2]K66 − ∑fv μ(λ ) ( )2( )2 3 L L 33 2 60 L L 2 L L L L L L π l b xap π l b xap Yr′̇ = Nv′ ̇ = ∑fv μ(λ ) ( )2 Z q′ ̇ = Mw′ ̇ = − ∑fh μ(λ ) ( )2 2 2 L L L L L L
Xu′ ̇ = −
πBH K 3 L L 11
K p′ ̇ = −
where Yr ̇ = Nv ,̇ Z q ̇ = Mẇ , and the component submatrices Mf , Jf and Cf represent added mass, added inertia and hydrodynamic coupling matrixes, respectively. The fluid inertia forces and moments, which are also part of external forces and moments, can be described as (Li, 2007)
where K11, K22, K33, K44, K55, K66 are the added mass coefficients, obtained by looking up the map of added mass in Shi (1995); and the rest on the right side are the geometrical parameters of AUV. Calculation results are presented in Table 3.
⎡ f⎤ ⎡ v1̇ ⎤ ⎢ i ⎥ = − Mf⎢ ⎥ ⎣ mi ⎦ ⎣ v2̇ ⎦
3.3. Contact force
(7)
Given that 0.5ρL3, 0.5ρL 4 and 0.5ρL5 are selected the dimensionless factors, the inviscid hydrodynamic coefficients are as follows:
Xu′̇ = Yv′̇ = Z w′ ̇ =
Xu ̇
K p′ ̇ =
0.5ρL3 Yv ̇
Mq′̇ =
0.5ρL3 Z ẇ
Nr′̇ =
0.5ρL3
Yr′̇ = Nv′̇ =
Yr ̇ 0.5ρL 4
Contact force generally consists of impact and friction forces. Coulomb's law is frequently used to describe the friction phenomenon with static and dynamic friction coefficients for the impact problem. Describing the impact process is quite complicated. The most widely used approaches to complete this work are the impulse-momentum model and the contact force-indentation model (Gilardi and Sharf, 2002). We adopted the latter one here. Therefore, in its general form, impact force may appear as follows (Faik and Witteman, 2000):
K ṗ 0.5ρL5 Mq ̇ 0.5ρL5 Nr ̇ 0.5ρL5
Z q′̇ = Mw′ ̇ =
Zq̇
F = Fc(δ ) + Fv(δ, δ )̇ + Fp(δ, δ )̇
0.5ρL 4
Potential flow theory (Lewandowski, 2004) is widely adopted to calculate inviscid coefficients. According to the superposition principle, the total inviscid coefficients of the AUV are the sum contribution of the three subsections: hull, antenna housing and four control planes in the
(8)
where Fc is the elastic part of the impact force F , Fv is the viscous damping part, Fp is the dissipative part because of plastic deformation ̇ andδ andδ are the penetration and its rate respectively. Owing to the relatively low speed and rigidity of the colliding bodies (i.e. the AUV 180
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1 1 1 = + R R1 R2
Table 4 Model's initial configurations. Category
Notation (Unit)
Value
Cone Angle
ϑ(°)
75
Material Characteristics
k (N /mm1.5) *e *Cmax(N ⋅s /mm )
5700
Position Deviation
1 − μ12 1 − μ2 2 1 = + E1 E2 E* where R1 and R2 are the curvature radius of two rigid bodies at contact point; and E1 and E2 , μ1 and μ2 represent the material properties of the two contact bodies as the elastic modulus and the Poisson ratio respectively. Considering the complexity of the colliding detection and the contact zone recognition, we adopted the commercial software ADAMS to simulate the docking process. The simplified impact model (9) in ADAMS can be shown as
1.5
5 × 10−3
μs
0.08
μd
0.04 2
* ΔSξ(m )
⎧ 0 q > q0 F=⎨ e k ( q − q ) − c ( dq / dt ) step ( q , q − d , 1, q , 0) q ≤ q0 ⎩ 0 max 0 0 ⎪
Posture Deviation
ΔSη(m )
0.35
ΔSζ (m )
0
0
ψ (°)
0.8
u (m / s )
Angular Velocity
v (m / s )
0
w (m / s )
0 0 0 480
*q(°/s ) *r (°/s ) n(r /min)
Propeller Rotation Speed
and the dock), plastic deformation, which vanishes in the third part in (8), is negligible. Combined with the analogy of spring and damper, the above model can be simplified as the linear spring damper model as follows:
F = kδ e + cδ ̇
4. Numerical results and discussion
(9)
Note that the ADAMS model only contains the last section of the docking phase, where the distance of the two origins (i.e. O and E in Section 3) along theξ direction is less than 2 m. The entire discussion in this paper is based on the assumption that the dock is rigidly fixed on the ocean bottom mentioned at the beginning of Section 3. The ADAMS model is illustrated in Fig. 7 in accordance to the reference frame with the exerted total external forces and moments acquired in Section 3. A number of interesting terms, such as velocities, displacements and contact forces, have also been measured in the ADAMS model. The general configurations of the model are shown in Table 4, although part
where e and c are the force exponent and damping coefficient respectively, and k is the contact stiffness, which can be obtained as follows (Chatterjee, 1997):
k=
(10)
where q0 denotes the original distance of the two colliding bodies, whereas q corresponds to the actual distance; cmax indicates the maximum damping coefficient, d represents the penetration depth, k and e meet the previous definitions and step is a function in the ADAMS library. To show the difference between q0 and q, and d, Fig. 6 demonstrates the relevant variables. The dark spots in Fig. 6 indicate the mass centres of the impact bodies, and the dotted lines represent the line of impact. The left part where the bodies are represented with solid curves illustrates the state before impact, whereas the right part represents the state after the impact occurred. The red zone indicates the contact zone. Relevant variables are measured along the line of impact and marked in Fig. 6. ADAMS also adopts Coulomb's law to define the friction force usually determined by the static friction coefficient μs and the dynamic friction coefficient μd during impact simulation. The explicit expressions of the external forces and moments were recently obtained. They are shown in Eqs. (4–7) and (10) for further details.
0
θ(°)
Linear Velocity
⎪
4 1/2 * R E 3
where R and E * are the equivalent radius of the contact and equivalent elastic modulus calculated by 18
Resultant Impact Force (kN)
15
12
9
6
3
0
3
6
9
12
15
Time (s) Fig. 8. Resultant impact forces on the AUV in simulation. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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12
t
Fmax
c
10
21
19 8 17
Time Cost (s)
Maximum Impact Force (kN)
23
6 15
13 50
60
70
80
4 100
90
Cone Angle (deg) Fig. 9. Influence of different cone angles on the docking process.
of them are unmarked with an asterisk and would be modified to coincide with the various simulation situations discussed below. An appropriate thrust force Fprop , determined by the coefficient of thrust force CF and the propeller rotation speed n , have been exerted on the AUV to guarantee that the vehicle can reach the parking zone (indicated with a red box in Fig. 2) with a constant speed before contact. Five elements based on the ADAMS model, including cone angle, material characteristic, deviation, velocity and propeller force, will be discussed to verify the influence of impact on the docking process. The most considerable factor when docking is whether the AUV can
Table 5 Friction coefficients. μs
μd
0.05 0.08 0.13 0.15 0.25 0.30 0.50
0.03 0.04 0.09 0.10 0.20 0.25 0.43
18.5
t
9
c
18
8
17.5
7
17
Time Cost (s)
Maximum Impact Force (kN)
Fmax
6
16.5 0.05
0.1
0.15
0.2
5 0.3
0.25
Static Friction Coefficient
Fig. 10. Friction coefficient influences on the docking process.
Maximum Impact Force (kN)
Fmax
15
tc
27
13
22
11
17
9
12
7
7 2000
4000
6000
8000 Stiffness Coefficient (N/mm
10000 1.5
12000
)
Fig. 11. Influence of stiffness coefficient on the docking process.
182
14000
5
Time Cost (s)
32
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Fig. 12. Influence of position deviation on the docking process.
Fig. 13. Influence of posture deviation on the docking process.
Fig. 14. Influence of translational velocity in x direction on the docking process.
between two special moments (i.e. the first and last contact instances). We sampled the dynamic simulation by adopting the initial configurations in Table 4. Fig. 8 shows the resultant impact force in simulation during the last docking phase. From this figure, is 17.28 kN at the second contact moment stamped with red rectangle, and is about 9.3 s between the first and last contact moments marked with red circles. Following the same method, Fmax and can be obtained under various configurations.
complete the docking mission or not. Mission failure means that the AUV fails to reach the parking zone in the docking station. This phenomenon can occur in the case where relative configurations such as cone angle, material characteristic, deviation, velocity and propeller force are not reasonable, all of which were discussed in the following. The other two evaluation indexes are proposed to assess the docking process: maximum resultant impact forceFmax and time costtc .indicates the maximum of resultant impact force, and represents the duration 183
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Fig. 15. Influence of translational velocities in the y and z directions on the docking process.
Fig. 16. Influence of propeller force on the docking process.
the dock, the cone angle should not be as small as possible. 4.2. Material characteristic Two typical material characteristics, namely, friction coefficient and stiffness, are considered below. The typical friction coefficients are chosen based on general references and are shown in Table 5. The corresponding influence is depicted in Fig. 10, whose abscissa is selected as a static friction coefficient. Both the maximum resultant impact force and the time cost grew with an increasing friction coefficient, although the variation range of the maximum resultant impact force was minimal. However, the docking mission failed under the last friction coefficient set (i.e. μs = 0.50 and μd = 0.43), which indicates that the poor friction condition can challenge the docking process. Fortunately, the friction coefficient during docking is quite small in reality because of the surrounding fluid. Stiffness, the other material characteristic, greatly influences the docking process, as illustrated in Fig. 11. Similar to the simulation results under the friction coefficient configuration, the maximum resultant impact force and the time cost sharply increase, albeit with larger variation ranges as the stiffness coefficient rises. With a six-fold growth in static friction coefficient, the maximum resultant impact force and the time cost increased up to 1.08 and 1.7 times respectively, as displayed in Fig. 10. By contrast, the corresponding increase could reach 4 and 2.8 times given the same stiffness growth, as depicted in Fig. 11. These results illustrate that stiffness has a greater influence than friction coefficient. Once stiffness coefficient becomes larger than 14250N / mm1.5, the docking failure rate will significantly increase with
Fig. 17. Pool trial in Xixi Campus.
4.1. Cone angle In accordance with the AUV size and the control precision, the cone entry diameter is set as a constant at 1.2 m. Afterwards, the variable cone angles can make a difference on the docking process. Fig. 9 reveals the influence tendency under diverse cone angles by merely changing the cone angle. All the situations with different cone angles shown in this figure complete the docking mission. Considering the cone angle growth, both the maximum resultant impact force and the time cost increase with markedly large rates. Simulation results indicate that a relatively small cone angle is advantageous to optimise the docking process. However, considering the length of the cone and the balance of 184
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Fig. 18. Velocity comparison between the simulation results and the experimental data. The blue curve represents the simulation results, and the red curve indicates the experimental data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 19. Comparison of time-series pictures in the experiment and the simulation for one docking attempt. The red lines in the simulation pictures indicate the gravity and buoyancy exerted on the AUV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
is not much different under the η and ϛ direction deviations when the absolute value of abscissa is within 0.35 m. However, the maximum resultant impact force, especially under the η direction deviation, increases sharply when the abscissa falls outside that region. The increase rate of time cost under the η direction deviation is larger than that under the ϛ direction deviation within the entire process, and turned especially gradient when the absolute value of the position deviation is between 0.3 and 0.4 m. In comparison, it is much better to decrease the position deviation and thus improve the control requirements, better promoting the docking success rate and optimising the docking process. The perfect posture of a docking AUV is when the longitudinal axis can coincide with the central axis of the cone before the AUV makes contact with the dock. However, the appearance of some posture deviations during docking is inevitable. Fig. 13 depicts the changes in the maximum resultant impact force and the time cost under different posture deviations, which fail to consider the position deviation discussed above. The influence is also symmetric because of the structural characteristics already mentioned above. Apart from the
the rise of stiffness coefficient. Collectively, the above discussion shows it is better to use a material with small stiffness and friction coefficients to construct the dock, such as acrylic and nylon, instead of steel or aluminium, although the influence of the stiffness coefficient is more obvious than that of the friction coefficient. 4.3. Position and posture deviation Both position and posture deviations exert immense influence on the docking process, which will be discussed respectively. The entry radius of the cone has been set as 0.6 m and the main AUV diameter is 0.2 m. Afterwards, the position deviation is limited from −0.5 to 0.5 m to guarantee a successful docking. The detailed influence of the position deviation is illustrated in Fig. 12. The influence of the position deviation in the η direction and the ϛ direction is coincident and symmetric between the negative and positive position bias because of the characteristic symmetry of the AUV and the cone. The maximum resultant impact force and the time cost increase with the rise of absolute value. The change rate of the maximum resultant impact force 185
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absence of posture deviation, the maximum resultant impact force under pitch deviation is larger than that under yaw deviation. A sharp change of the force under pitch deviation occurs when the absolute value of pitch angle exceeds 12°. During the entire zone change, the time cost under yaw deviation is slightly greater than that under pitch deviation. Neither the pitch deviation nor the yaw deviation can actually reach 20° in most cases, which aids the docking process.
but the maximum resultant impact force and the failure rate of docking sharply increase until 900 r/min. The proper propeller force, just like the propeller rotation speed between 420 and 660r /min , is a good compromise between the time cost and the maximum resultant impact force.
4.4. Velocity
The preliminary docking experiment was conducted in a pool in the Xixi Campus of Zhejiang University (Fig. 17) to demonstrate the validity of the cone-shaped docking method. The pool is 50 m long, 30 m wide and nearly 1.7 m deep, dimensions which sufficiently and completely submerge the AUV. The weather was sunny with no wind in most cases during the study, leading to still water, which is the appropriate environment for docking. Based on upfront surveys, the cone angle was determined as 75°, and the stave materials in the cone and the fairing in the bow of the AUV were chosen as fibreglass and polycarbonate respectively. Owing to the limitations of the pool condition, only dock, housing and some necessary accessories were tested and submerged in water, and the dock was fixed in the temporary base without the steering mechanism. During the experiments, the AUV worked in orientation mode and constant speed mode followed by the expected orientation and velocity specified by the matched upper computer, while the specified velocity was much less than that in the wide area like in a lake. By adjusting the position, orientation and velocity of the AUV, we examined the docking processes under different situations. The maximum impact force and time cost are both difficult to measure in actuality. However, the velocities recorded by the AUV and photographs shot by an underwater camera were compared with the simulation results. Fig. 18 presents the comparison of the vehicle velocities in the body-fixed frame between the simulation results and the experiment data. Simulation results were acquired by configuring the initial velocity as 0.67m /s in the x direction, initial position deviation as 0.05 m in the η direction and −0.35 m in the ζ direction, with no posture deviation in ADAMS. The first contact time in simulation failed to coincide with that in the experiment because of the different initial moments selected in the two curves. After this first impact, the resultant velocity and velocity in the x direction vanished immediately in the simulation and experiment. In comparison, the corresponding velocities in the y and z directions increased in absolute values, although the increase rate in the simulation was much larger than that in the experiment. Owing to the positive deviation in the direction, the negative deviation in the direction and the velocity measurement at the centre of buoyancy, the velocities in the y and z directions coincided with the corresponding directions of the position deviation. In the simulation, two distinct acceleration processes with a similar acceleration occurred in the x direction before 4.3 and 8.7 s, namely the second and third contact moments respectively; several acceleration processes in the x direction were also found between 2.68 and 8.54 s in the experiment. With these three main contacts in the simulation, the vehicle completed the docking mission with a time cost of about 6.75 s, while the contact times before completing the docking mission were not intuitional in the experiment. Apart from the last impact at 10.42 s in the experiment, at which moment the vehicle actually entered the dock completely, the vehicle spent almost 6.14 s completing the docking mission. Finally, based on the above analyses, the simulation velocity tendencies coincided with the experimental velocity data as a whole, although some discrepancies, such as contact times and velocity magnitudes, occurred as a result of the differences in the model, initial configurations and circumstances, among others. Time-series pictures corresponding to the above velocities are compared to validate the posture changes during the docking process. These are shown in Fig. 19. The successes of the docking attempts in the experiment and the simulation are intuitionistic as well. A number of relevant postures in the simulation can coincide with those in the
5. Experiment validation
The initial translational velocity also exerts an important effect on the docking process; it has been evaluated in the body-fixed frame as a component velocity as well. Fig. 14 depicts the influence of the translational velocity in the x direction. The maximum resultant impact force increases almost linearly with the x-component velocity growth, whereas the time cost decreases without a distinct linear relation. However, when the x-component velocity is larger than 1.7m / s , the time cost nearly remains constant, though the maximum resultant impact force continues to increase rapidly. Moreover, if the translational velocity continues growing, the failure rate of docking and the possibility of damage will increase. The actual cruising speed of the AUV is approximately 3 knots (Zhang et al., 2014), which is almost the middle abscissa value in Fig. 14. Combined with the minimum speed for buoyancy balance required, the speed for docking can be selected between 0.8 and 1.5 m/s. The lateral and vertical velocities also affect the docking process. Fig. 15 synthesises the evaluation indexes in the y and z directions. The maximum resultant impact force and the time cost increase in quite a small rate from negative to positive velocity in the y direction. The docking process can benefit from the negative velocity in the y direction as the corresponding positive velocity becomes the obstacle because of the position deviation under the positive η direction. Owing to the approximate symmetry in the x−y plane of the AUV and the absence of the position deviation in the ϛ direction, the influence of translational velocity in the z direction is almost symmetrical between the positive and negative velocity configurations. The two evaluation indexes increase and the time cost augments with a large rate with the growth of the absolute velocity value in the z direction. The velocity variations in the y and z directions exert much more obvious influences on the time cost than on the maximum resultant impact force. The influence of time cost in the z direction is much worse than in the y direction because of the position deviation in the positive y direction. Although the negative velocity in the y direction has the beneficial influence on the docking process, eliminating the lateral and vertical velocities by reducing the sideslip angle and angle of attack for instance is better considering the difficulty of controllability. 4.5. Propeller force The propeller rotation speed is deliberately set in the above configurations to ascertain that the AUV can go ahead at constant speed before contact so that the propeller force can balance the viscous drag. In this subsection, the propeller rotation speed is changed under the same initial velocity 0.8m / s to evaluate the influence of different propeller forces. Moreover, if the uniform velocity before contact is necessary, the propeller rotation speed 480r /min is configured. Fig. 16 depicts the influence of the propeller force as delegated by diverse propeller rotation speeds. The time cost is negatively related to the propeller rotation speed, whereas the maximum resultant impact force indicates a positive relation. With regard to the time cost, the propeller rotation speed is a demarcation point, and the rate of descent before this point is four times as large as that after this point. When the propeller rotation speed is larger than 680r /min , the growth rate of the maximum resultant impact force can be up to 20.01kN /(r /min), which is nearly two times larger than that of the previous segment. However, if the propeller rotation speed continues to grow, time cost varies weakly 186
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Cowen, S., 1997. Flying plug: a small uuv designed for submarine data connectivity (Report documentation). Space and Naval Warfare Systems Center, San Diego, CA. Chatterjee, A., 1997. Rigid body collisions: some general considerations, new collision laws, and some experimental data. Cornell University, New York. De Barros, E., Dantas, J.L., Pascoal, A.M., De Sá, E., 2008. Investigation of normal force and moment coefficients for an AUV at nonlinear angle of attack and sideslip range. IEEE J. Ocean. Eng. 33 (4), 538–549. Li, D., 2007. Ship Motion and Modelling second edition. National defense industry press, Beijing. Faik S., Witteman H., 2000. Modeling of impact dynamics: a literature survey. In: International ADAMS User Conference. Orlando, FL, pp. 1–11 Fossen, T.I., 1994. Guidance and Control of Ocean Vehicles. John Wiley & Sons Inc, New York. Fukasawa, T., Noguchi, T., Kawasaki, T., Baino, M., 2003. "MARINE BIRD", a new experimental AUV with underwater docking and recharging system. MTS/IEEE Oceans. IEEE, San. Diego, CA, 2195–2200. Gilardi, G., Sharf, I., 2002. Literature survey of contact dynamics modelling. Mech. Mach. Theory 37 (10), 1213–1239. Kerwin, J.E., Hadler, J.B., 2010. Principles of Naval Architecture Series: Propulsion. The Society of Naval Architects and Marine Engineers (SNAME), Alexandria, VA. Lambiotte, J.C., Coulson, R., Smith, S.M., An, A., 2002. Results from mechanical docking tests of a Morpheus class AUV with a dock designed for an OEX class AUV. MTS/ IEEE Oceans. IEEE, Biloxi, MS, 260–265. Lewandowski, E.M., 2004. The dynamics of marine craft: maneuvering and seakeeping. World Scientific, River Edge, NJ. McEwen, R.S., Hobson, B.W., McBride, L., Bellingham, J.G., 2008. Docking control system for a 54-cm-diameter (21-in) AUV. IEEE J. Ocean. Eng. 33 (4), 550–562. Nelson, R.C., 1998. Flight Stability and Automatic Control. WCB/McGraw-Hill, New York. Pamadi, B.N., 2004. Performance, stability dynamics, and Control of Airplanes. AIAA, Reston, VA, 780. Park, J.Y., Jun, B.H., Lee, P.M., Lee, F.Y., Oh, J., 2007. Experiment on Underwater docking of an autonomous underwater vehicle 'ISiMI' using optical terminal guidance. MTS/IEEE Oceans. IEEE, Aberd., 1–6. Park, J.Y., Jun, B.H., Lee, P.M., Oh, J., 2009. Experiments on vision guided docking of an autonomous underwater vehicle using one camera. Ocean Eng. 36 (1), 48–61. Shi, S., 1995. Submarine Maneuverability. National Defense Industry Press, Beijing. Shi, J., Li, D., Yang, C., 2014. Design and analysis of an underwater inductive coupling power transfer system for autonomous underwater vehicle docking applications. J. Zhejiang Univ. -Sci. C. (Comput. Electron. ) 15 (1), 51–62. Shi, J., Li, D., Yang, C., Cai, Y., 2015. Impact analysis during docking process of autonomous underwater vehicle. J. Zhejiang Univ. (Eng. Sci. ) 49 (3), 497–504. Singh, H., Bellingham, J.G., Hover, F., Lerner, S., Moran, B.A., von der Heydt, K., Yoerger, D., 2001. Docking for an autonomous ocean sampling network. IEEE J. Ocean. Eng. 26 (4), 498–514. Stokey, R., Allen, B., Austin, T., Goldsborough, R., Forrester, N., Purcell, M., von Alt, C., 2001. Enabling technologies for REMUS docking: an integral component of an autonomous ocean-sampling network. IEEE J. Ocean. Eng. 26 (4), 487–497. Thomasson, P.G., Woolsey, C.A., 2013. Vehicle motion in currents. IEEE J. Ocean. Eng. 38 (2), 226–242. Timothy, P., 2001. Verification of a six-degree of freedom simulation model for the REMUS autonomous underwater vehicle (Master thesis). Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, Cambridge, MA. Wu, L., Li, Y., Su, S., Yan, P., Qin, Y., 2014. Hydrodynamic analysis of AUV underwater docking with a cone-shaped dock under ocean currents. Ocean Eng. 85, 110–126. Yang, C., Peng, S., Fan, S., 2014. Performance and stability analysis for ZJU Glider. Mar. Technol. Soc. J. 48 (3), 88–103. Zhang, M., Xu, Y., Li, B., Wang, D., Xu, W., 2014. A modular autonomous underwater vehicle for environmental sampling: system design and preliminary experimental results. MTS/IEEE Oceans. IEEE, Taipei, 1–5.
experiment, although with attitude deviations and at different moments because of the previously mentioned discrepancies between the simulation and the experiment. 6. Conclusions Considering the influence of impact on a docking AUV, an underwater impact model in ADAMS was proposed after the hydrodynamic coefficients were identified. Five interesting influence elements, including cone angle, material characteristic, deviation, velocity and propeller force, were discussed. A pool trial was conducted to validate the proposed simulation model. Results of this study can provide some insights into the design of the docking system and the docking control of the companion AUV, including the following: 1) The cone-shaped dock, especially one with a proper cone angle, is a good choice for underwater docking. 2) Docking materials with small friction and stiffness coefficients are suggested. 3) Large deviations in both position and posture serve as obstacles for docking, meaning the remarkable significance of high control accuracy. 4) Lateral and vertical velocities negatively affect docking, whereas an appropriate forward speed can optimise the impact process. 5) A propeller force slightly larger than the need of constant forward speed is beneficial to the impact process. 6) The maximum impact force between the AUV and the docking station can provide some reference to optimise the structure of the docking station to make this station satisfy the use in ocean bottom during the whole docking mission. Our ongoing work is focused on the entire docking system trials in the lake and the shallow sea to realise docking missions with high success rates in water 100 m deep. Acknowledgment This project was supported by the National High-Tech Research and Development Program of China (Grant No. 2013AA09A414) and the Science Fund for Creative Research Groups of National Natural Science Foundation of China (No. 51221004). References Allen, B., Austin, T., Forrester, N., Goldsborough, R., Kukulya, A., 2006. Autonomous docking demonstrations with enhanced REMUS technology. MTS/IEEE Oceans. IEEE, Boston, MA, 1539–1544.
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Study on impact process of AUV underwater docking with a cone-shaped dock
MARK
⁎
Tao Zhang, Dejun Li , Canjun Yang The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Autonomous underwater vehicle Docking Impact ADAMS
This study investigates the impact issues associated with docking systems when autonomous underwater vehicles (AUVs) contact with a cone-shaped and unclosed dock, which has been proposed and realised by most AUV docking systems. The study aims to understand the impact process in AUV docking with the dock and derive a number of probable suggestions. To realise this objective, a dynamic model with impact is established in the commercial software ADAMS after identifying relevant forces especially obtaining hydrodynamic coefficients and completing impact configurations. Based on the proposed dynamic model, five interesting influence elements are discussed respectively. A pool trial was conducted, and experiment results are compared with the corresponding simulation data to validate the model. Several effective suggestions are proposed for the designs of the docking system and the docking control of the companion AUV.
1. Introduction Autonomous underwater vehicles (AUVs) are playing an increasing role in oceans in recent decades because of their vast scientific, commercial and military applications. However, poor endurance resulting from the battery's low capacity and the high-power draw of the instrumentation and poor real-time capacity of data transfers limit the wide use of AUVs in vast spaces and for long periods. Furthermore, underwater docking technology, which has the ability to recharge battery, transfer data and safely park AUVs, has been proposed to extend the use of AUVs in space and time. The development of cabled ocean observatory networks also makes the successful long-term operation of an underwater docking system possible. In addition, an underwater docking system is crucial in constructing a tri-dimensional ocean observatory system by combining dynamic and wide-range observation with static and long-term monitoring. Thus, a growing number of organisations have recently devoted significantly more attention to the research and manufacture of underwater docking systems. Underwater docking systems generally include the following classic types. Singh et al. (2001) attempted to use a passive latch on the AUV to grasp the pole on the dock and enable the AUV to accomplish the docking task omnidirectionally. Fukasawa et al. (2003) adopted the Marine Bird docking system, another docking type that operates like an aircraft landing on an aircraft carrier. As such, the vehicle catches the V-shaped guide on the base of the dock by running slowly over the base, using its catching arm, and joining the connecting device. Lambiotte et al. (2002) attempted the use of a pyramid-type docking ⁎
system with a guide above the intersection of each side to provide the vehicle with the option of docking from four directions. The structure of this pyramid-type docking system is comparatively simple but quite complex for the vehicle to lock, charge battery and transfer data. To the best of my knowledge, the most widely used type nowadays is the coneshaped docking system, which makes it comparatively convenient for the vehicle to navigate into the dock and lock in the protective housing, such as MBARI docking system for a 21″ AUV (McEwen et al., 2008), the REMUS docking system (Allen et al., 2006; Stokey et al., 2001), the flying plug docking system (Cowen, 1997) and the ISiMI docking system ( Park et al., 2007, 2009). Among the above docking systems, the cone-shaped type is quite a good compromise of structural complexity and functional reliability. This type of docking system can lower the AUV's navigation accuracy demand, which requires less modification or no extra mechanical accessories on the AUV for docking. It likewise offers a more reliable lock and protective housing, as well as makes it much more convenient and dependable to charge and transfer data. Although generally, considering the fixed-size cone and the definite direction an AUV should dock in on most situations, this type of docking system is only suitable for certain AUVs with specific sizes. The cone-shaped type is advantageous in its practicability and reliability compared with other types, making it the most widely used AUV underwater docking system today. Therefore, the coneshaped docking system is adopted in our project. Many of the developed cone-shaped docking systems have concentrated on AUV homing and docking control (McEwen et al., 2008), the method of transferring power and data (Shi et al., 2014) and the vision
Corresponding author.
http://dx.doi.org/10.1016/j.oceaneng.2016.12.002 Received 18 November 2015; Received in revised form 30 November 2016; Accepted 1 December 2016 0029-8018/ © 2016 Elsevier Ltd. All rights reserved.
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guided docking (Park et al., 2009). However, these characteristics are not sufficient for a docking system. When docking, the AUV may collide with the cone of the dock in most cases, which induces a number of necessary considerations on the docking system design and the companion AUV's docking control before docking. Considerations include how the shapes and material characteristics of a cone affect AUV docking, and how the deviation, velocity and propeller force of an AUV influence the complete docking mission of the vehicle with minimal damage and maximum docking success rate. This study expands what we have explored before (Shi et al., 2015). The paper is organised as follows. Section 1 introduces some AUV underwater docking systems, especially the cone-shaped docking system, and discusses some issues below. Section 2 briefly describes the AUV and the docking station in our project. Section 3 derives the dynamic model focusing on hydrodynamic characteristics and contact force, and builds the simulation model in ADAMS. Section 4 discusses the effects of different elements (i.e. cone angle, material characteristic, deviation, velocity and propeller force) on the impact process. Section 5 compares the experimental results with the preceding simulation data. Section 6 presents the conclusion.
Table 1 Main specifications of Dolphin II. Features
Unit
Description
Body length Body diameter Slenderness ratio of the body Surface area of the body Span length of the tail Chord length of the tail Aspect ratio of the tail Surface area of the tail Outer diameter of propeller Weight in air Operating depth
m m
m2 m kg m
2.47 0.20/0.29 0.084/0.123 1.499 0.340 0.110 3.091 0.0374 0.16 79.5 0–100
locking unit
tube
m2 m m
guidance accessories
cone
steering mechanism
housing
2. AUV and docking station 2.1. AUV − Dolphin II overview
base
The docking AUV in our project is a modified version of Dolphin II (Zhang et al., 2014), whose bow part was replaced with new sections. Furthermore, the sequence of some of its other sections was exchanged to conveniently accomplish the docking task and transfer power and data in the contactless method. Fig. 1 demonstrates that the modified AUV can be divided into five sections: Bow Section, Non-contact Section, Battery & Control Section, Navigation & Communications Section, and Tail Section. Apart from the bow section, which is a wet housing surrounded by engineering plastic shells, the modified AUV has an aluminium alloy and an air-filled pressure housing. After modification, it has an overall length of 2.47 m with a main body diameter of 0.2 m. However, the vehicle has a larger diameter of 0.29 m because the non-contact section requires extra space to install a secondary inductive coupling coil for contactless power transfer and a Wi-Fi antenna for a wireless network link. The entire mass of the AUV on the shelf weighs 79.5 kg in air, whereas the net weight is approximately close to zero in water because of appropriate buoyancy. According to its original design, the speed of the AUV can reach up to 5 knots, as verified in previous lake trials. The main specifications of the modified AUV are illustrated in Table 1. These details are helpful to the calculation of external forces and moments, especially to the hydrodynamic coefficients discussed in Section 3.2.
Bow Section
Non-contact Section
Fig. 2. Three-dimensional model of the docking station. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
2.2. Docking station The design approach of McEwen et al. (2008) is to keep the docking station as simple as possible; in contrast, our primary principle is to make the AUV's modification as simple as possible. Therefore, apart from some general equipment, such as tube, cone, base and housing, the docking station consists of the steering mechanism, guidance accessories (e.g. guidance light, transponder, acoustic doppler current profilers) and locking unit, as shown in Fig. 2. The dock body, consisting of the cone and the tube, is mounted on the base through the steering mechanism. The dock's entry, namely, the cone, is conically shaped and made up of some staves held in place by two stainless steel rings. The material of the staves and the taper angle of
Battery & Control Section
Navigation & Communications Section
Fig. 1. Configuration of the AUV Dolphin II.
177
Tail Section
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Fig. 3. Body-fixed and earth-fixed reference frames.
3.1. Reference frames and external forces
the cone are designated based on the analysis in Section 4. The tube is comprised of acrylonitrile butadiene styrene plastics and is analogously cylindraceous with inner diameters of 0.3 and 0.21 m, which are 0.01 m larger than the AUV's diameter, to match the shape of the modified vehicle. To avoid the vehicle touching the bottom and being disturbed by seafloor impurities, the base is a 3 m-high pyramid so that the vehicle can fly with a safe approach during docking. The original plan indicates that the docking station will be applied in a 100 m-deep ocean, such that, a reliable housing subjected to external pressure is necessary. Furthermore, the housing accommodates the electronics essential to control the steering mechanism, which can adjust the dock's orientation to be consistent with the AUV's heading, as well as support the power and data transfer between the AUV and the station. Guidance accessories are also considerably useful to guide an AUV into a docking station. After being guided into the station and locked by the locking unit, the AUV can tightly and securely park in the parking zone, which is represented by the red box in Fig. 2.
We define the body-fixed and earth-fixed reference frames indicated in Fig. 3 according to the definition of Fossen (1994). The origin O of the body-fixed reference frame is located at the centre of buoyancy and other axes, such as, X, Y and Z, which coincide with the principal axes of inertia. The earth-fixed reference frame, namely, the inertial coordinate system, is fixed in the docking station and denoted by the unit vectors ξ ,η and ζ . Furthermore, the origin is chosen to coincide with the centre of the cone's small face, ξ aligns with the axial direction of a stationary cone in the last docking phase, ζ points to the gravity and completes the right-handed triad. As mentioned in Timothy (2001), the general motion of the AUV in six degrees of freedom can be described by the following vectors: κ1 = [ x y z ]T ; κ2 = [ ϕ θ ψ ]T ; v1 = [ u v w ]T ; v2 = [ p q r ]T ; τ1 = [ X Y Z ]T ; τ2 = [ K M N ]T ; where κ describes the position and orientation of the AUV with respect to the earth-fixed reference frame; v shows the translational and rotational velocities of the AUV with respect to the earth-fixed reference frame, but expressed in the bodyfixed reference frame; and τ denotes the total external forces and moments acting on the AUV expressed in the body-fixed reference frame. Based on Thomasson and Woolsey (2013), the kinematic equations can be revealed as
3. Dynamic model The following are assumptions on the AUV and the docking station used as the basis for model development to simplify the challenge of building a dynamic model with impact (Chatterjee, 1997; Timothy, 2001).
• • •
• • •
The colliding bodies consisting of the AUV and the dock are rigid. Thus, both mass and mass distribution of the AUV and the dock do not change during operations without regard to the tiny deformations in the contact region. The AUV and docking station are deeply submerged in a homogeneous fluid 100 m far from the surface in reality. Environmental disturbances (e.g. waves, wind and ocean currents) are not considered during the docking process. Weight and buoyancy are approximately equal but are aligned in the opposite direction with the plumb line; however, their action points do not coincide with each other, which leads to a trimming moment for roll motion. For safety, most underwater vehicles like AUVs have a slightly negative net weight (i.e. the subtraction of weight and buoyancy) in reality. We simplify the situation here. The propulsion model used in the following is extremely simple; it treats the thruster as a source of constant thrust and torque under a constant propeller speed. The impact process, whose duration is fairly short, does not cause infinite interpenetration in the contact region. The dock is rigidly fixed to the base of docking station during impact in the last docking phase, although it can rotate under corresponding controls during the homing phase.
κ1̇ = RIB v1
(1)
̇ = RIB vˆ2 RIB
(2)
Where ˆ. denotes a 3×3 skew symmetric matrix satisfying aˆ b = a × b for vectors a and b, and RIB is the transition matrix from the body-fixed reference frame to the earth-fixed reference frame and can be expressed in conventional Euler angles (i.e. roll angle φ , pitch angle θ and heading angle ψ ) as
RIB = e eˆ3ψ e eˆ2θ e eˆ1φ where ei represents the standard basis vector for R3 , where i ∈ {1 2 3}, and e(.) denotes the matrix exponential. By applying Lagrangian mechanics, we can denote the dynamic equation in Lagrangian expressions as
d ⎛ ∂L ⎞ ∂L =Γ ⎜ ⎟− dt ⎝ ∂κ̇ ⎠ ∂κ
(3)
where L is the Lagrangian, namely the subtraction of the AUV's kinetic and potential energies, and Γ is the total external forces and moments acting on the AUV with respect to the earth-fixed reference frame; that T is Γ = [ τ1T τ2T ] . Eqs. (1–3) describe the dynamic model of the entire 178
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Fprop = CFρn 2D4 Mprop = CT ρn 2D 5
(5)
where CF indicates the coefficient of thrust force, CT shows the coefficient of propeller torque, n represents the propeller rotation speed andD denotes the outer diameter of the propeller. However, the appropriate balance weight and hydrostatic roll moment will counteract the propeller torque Mprop in practice. 3.2. Hydrodynamic characteristics Acquiring the hydrodynamic characteristics is necessary to accomplish the AUV dynamic model. According to the research by Wu et al. (2014), an unclosed dock has a minimal influence on the hydrodynamic characteristics of an AUV, which means we can typically deal with hydrodynamic forces and moments as usual. Generally, these characteristics include viscous and inviscid terms. Several methods, including analytical, computational and semi-empirical approaches, can be applied to predict the hydrodynamic characteristics of an AUV (De Barros et al., 2008). Considering our needs and the cost, we determined the viscous terms based on the computational fluid dynamics (CFD) software, and used an analytical approach to obtain the inviscid terms. Using the commercial software GAMBIT, we obtained the C-O type structured grids with the local grid refinement technology, shown in Fig. 4. We also adopted the CFD package FLUENT and followed the similar method described in Yang et al. (2014) to acquire the viscous hydrodynamic parameters. Fig. 5 shows the velocity pathline when the AUV model, as simulated in FLUENT, turns at the yawing rate of 0.3036 rad/s. Viscous forces fv and moments mv acting on the vehicle are part of external forces τ1 and moments τ2 , and can be expressed in the bodyfixed frame as follows:
Fig. 4. C-O type structured grids in GAMBIT.
Fig. 5. Velocity pathline in FLUENT.
vehicle system. In the forthcoming numerical analysis, the simulation software ADAMS is adopted. ADAMS can solve the kinematic and dynamic problems with impact processes according to the above modelling method. Afterwards, the crucial point of modelling the docking process is to search for the explicit expressions of the external forces and moments acted on the AUV. Total external forces and moments can be classified into hydrostatic terms (i.e. the weight and buoyancy of the AUV and their corresponding moments), propeller thrust and torque, hydrodynamic terms (i.e. added mass and hydrodynamic damping) and contact force during impact. We only discuss the hydrostatic terms, the propeller thrust and torque in this subsection owing to the relatively complex hydrodynamic terms and contact force. Hydrostatic terms, namely, restoring forces due to Archimedes, mainly consist of weight W and buoyancy B(both W and Bare threedimensional force vectors expressed in the earth-fixed reference frame), whose magnitude and direction almost remained unchanged in the submerged fluid. We know the hydrostatic force from a previous assumption as the resultant force of the weight and buoyancy that may vanish because of the approximate magnitude and opposite direction of the two component forces. However, in the case of the separate weight and buoyancy centres, the resultant moment causes a trimming torque useful for roll stability. In total, hydrostatic terms can be expressed in the body-fixed reference frame as
⎛ Xv ⎞ ⎜ ⎟ fv = ⎜Yv ⎟ ⎜ ⎟ ⎝ Zv ⎠ ⎛ Kv ⎞ ⎜ ⎟ mv = ⎜ Mv ⎟ ⎜ ⎟ ⎝ Nv ⎠
(6)
We choose 0.5ρV 2L2 and 0.5ρV 2L3 as the dimensionless factors to non-dimensionalise the viscous forces and moments as
Xv′ = Kv′ =
Xv 0.5ρV 2L2 Kv 0.5ρV 2L3
,
Yv′ =
,
Mv′ =
Yv 0.5ρV 2L2
Zv
,
Z v′
,
N ′v =
Mv 0.5ρV 2L3
0.5ρV 2L2 Nv 0.5ρV 2L3
The non-dimensional coefficients of these forces and moments can be obtained using linear derivative regression afterwards. According to the notational convention for aircraft (Nelson, 1998; Pamadi, 2004), the viscous coefficients with non-dimensional quantities can be provided as follows:
Xv′ = CX (α ) = CX0 + CXα1α + CXα 2α 2 + CXα3α 3 + CXα 4α 4
FHS ≈ 0
Kv′ = CK (β , p , r , δr ) = CKββ + CKp p + CKr r + CKδrδr T
MHS = rG × (RIB W )
Yv′ = CY (β , p , r , δr ) = CYββ + CYp p + CYr r + CYδrδr
(4)
Mv′ = CM (α , q , δe ) = CMα α + CMq q + CMδeδe
where FHS and MHS are the hydrostatic force and moment respectively, and rG is the vector from the centre of gravity to the origin of the bodyfixed reference frame (i.e. centre of buoyancy). The rotary propeller for marine vehicles not only generates the thrust for the surge motion but also the propeller torque, though it is generally counteracted. Afterwards, the directions of the thrust and the torque are aligned with the X axis in the body-fixed reference frame. According to a simple propulsion model (Kerwin and Hadler, 2010), the magnitudes of the thrust and the propeller torque can be shown as
Z v′ = CZ (α , q , δe ) = CZαα + CZq q + CZδeδe Nv′ = CN (β , p , r , δr ) = CNββ + CNp p + CNr r + CNδrδr where α , β are the attack and sideslip angles; p , q , r are the dimenpL qL rL sionless angular velocities defined as p = V , q = V , r = V ; and δr , δe are the rudder and elevator angles. The rest on the right side of the equal sign are the computed viscous coefficients of the AUV as listed in Table 2. 179
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Table 2 Viscous coefficients of the AUV. Notation
Value (×10−3)
Notation
Value (×10−3)
CX0
- 2.5933
CKβ
−0.2211
CXα1 CXα2 CXα3 CXα4 CYβ CYp CYr
2.7339
−0.0621
CYδr CZα CZq CZδe
−11.02
CKp CKr CKδr α CM q CM δe CM β CN CNp CNr CNδr
- 8.3656 - 91.791 165.11 −32.329 −1.2958 −7.4285 −26.228 6.23
0.0595 −0.001 −2.4682 4.0153 5.0858 −1.484 0.3554 4.3013 5.1003
10.975
Fig. 6. Difference between, and q0,q and d. (For interpretation of the references to color
Table 3 Inviscid coefficients of the AUV. Notation
Value (×10−3)
Notation
Value (×10−3)
X′u̇ Y′v̇ Z′ẇ
−0.1236 −6.9286 −6.8543
N′r ̇ Y′r ̇ Z′q̇
−0.3564 0.0890 −0.0612
K′ ṗ
−0.0181
M′ẇ
−0.0612
M′q̇
−0.3512
N′v̇
0.0890
According to the SNAME notation (Fossen, 1994), inviscid hydrodynamic parameters are the components of the generalised added inertia matrix. Owing to the vehicle symmetry and considering the mainly effective terms, the generalised added inertia matrix can be simplified as
⎛M f M f = ⎜⎜ C ⎝ f
⎛ Xu ̇ ⎜ ⎜0 T⎞ ⎜0 Cf ⎟=−⎜ ⎟ Jf ⎠ ⎜0 ⎜0 ⎜⎜ ⎝0
0 0 Yv ̇ 0 0 Z ẇ
0 0 0
0
0
K ṗ
0
Mẇ
0
Nv ̇
0
0
Fig. 7. Simulation model in ADAMS.
x-shaped configuration. Furthermore, the vehicle's hull is approximated as a spheroid, whereas the appendages, including antenna housing and control planes, are approximated as flat plates. Then the inviscid coefficients can be calculated as follows (Shi, 1995):
0 0⎞ ⎟ 0 Yr ̇ ⎟ Z q̇ 0 ⎟ ⎟ 0 0⎟ Mq ̇ 0 ⎟ ⎟⎟ 0 Nr ̇⎠
z ap π BH H π l b [1 + ( )2]K44 − ∑fv μ(λ ) ( )2( )2 60 L L 2 L L L L y ap π l b − ∑fh μ(λ ) ( )2( )2 2 L L L xap πBH π l b π BH H π l b Yv′ ̇ = − K − ∑fv μ(λ ) ( )2 Mq′ ̇ = − [1 + ( )2]K55 − ∑fh μ(λ ) ( )2( )2 3 L L 22 2 60 L L 2 L L L L L L x ap πBH π l b π BH B π l b Z w′ ̇ = − K − ∑fh μ(λ ) ( )2 Nr′̇ = − [1 + ( )2]K66 − ∑fv μ(λ ) ( )2( )2 3 L L 33 2 60 L L 2 L L L L L L π l b xap π l b xap Yr′̇ = Nv′ ̇ = ∑fv μ(λ ) ( )2 Z q′ ̇ = Mw′ ̇ = − ∑fh μ(λ ) ( )2 2 2 L L L L L L
Xu′ ̇ = −
πBH K 3 L L 11
K p′ ̇ = −
where Yr ̇ = Nv ,̇ Z q ̇ = Mẇ , and the component submatrices Mf , Jf and Cf represent added mass, added inertia and hydrodynamic coupling matrixes, respectively. The fluid inertia forces and moments, which are also part of external forces and moments, can be described as (Li, 2007)
where K11, K22, K33, K44, K55, K66 are the added mass coefficients, obtained by looking up the map of added mass in Shi (1995); and the rest on the right side are the geometrical parameters of AUV. Calculation results are presented in Table 3.
⎡ f⎤ ⎡ v1̇ ⎤ ⎢ i ⎥ = − Mf⎢ ⎥ ⎣ mi ⎦ ⎣ v2̇ ⎦
3.3. Contact force
(7)
Given that 0.5ρL3, 0.5ρL 4 and 0.5ρL5 are selected the dimensionless factors, the inviscid hydrodynamic coefficients are as follows:
Xu′̇ = Yv′̇ = Z w′ ̇ =
Xu ̇
K p′ ̇ =
0.5ρL3 Yv ̇
Mq′̇ =
0.5ρL3 Z ẇ
Nr′̇ =
0.5ρL3
Yr′̇ = Nv′̇ =
Yr ̇ 0.5ρL 4
Contact force generally consists of impact and friction forces. Coulomb's law is frequently used to describe the friction phenomenon with static and dynamic friction coefficients for the impact problem. Describing the impact process is quite complicated. The most widely used approaches to complete this work are the impulse-momentum model and the contact force-indentation model (Gilardi and Sharf, 2002). We adopted the latter one here. Therefore, in its general form, impact force may appear as follows (Faik and Witteman, 2000):
K ṗ 0.5ρL5 Mq ̇ 0.5ρL5 Nr ̇ 0.5ρL5
Z q′̇ = Mw′ ̇ =
Zq̇
F = Fc(δ ) + Fv(δ, δ )̇ + Fp(δ, δ )̇
0.5ρL 4
Potential flow theory (Lewandowski, 2004) is widely adopted to calculate inviscid coefficients. According to the superposition principle, the total inviscid coefficients of the AUV are the sum contribution of the three subsections: hull, antenna housing and four control planes in the
(8)
where Fc is the elastic part of the impact force F , Fv is the viscous damping part, Fp is the dissipative part because of plastic deformation ̇ andδ andδ are the penetration and its rate respectively. Owing to the relatively low speed and rigidity of the colliding bodies (i.e. the AUV 180
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1 1 1 = + R R1 R2
Table 4 Model's initial configurations. Category
Notation (Unit)
Value
Cone Angle
ϑ(°)
75
Material Characteristics
k (N /mm1.5) *e *Cmax(N ⋅s /mm )
5700
Position Deviation
1 − μ12 1 − μ2 2 1 = + E1 E2 E* where R1 and R2 are the curvature radius of two rigid bodies at contact point; and E1 and E2 , μ1 and μ2 represent the material properties of the two contact bodies as the elastic modulus and the Poisson ratio respectively. Considering the complexity of the colliding detection and the contact zone recognition, we adopted the commercial software ADAMS to simulate the docking process. The simplified impact model (9) in ADAMS can be shown as
1.5
5 × 10−3
μs
0.08
μd
0.04 2
* ΔSξ(m )
⎧ 0 q > q0 F=⎨ e k ( q − q ) − c ( dq / dt ) step ( q , q − d , 1, q , 0) q ≤ q0 ⎩ 0 max 0 0 ⎪
Posture Deviation
ΔSη(m )
0.35
ΔSζ (m )
0
0
ψ (°)
0.8
u (m / s )
Angular Velocity
v (m / s )
0
w (m / s )
0 0 0 480
*q(°/s ) *r (°/s ) n(r /min)
Propeller Rotation Speed
and the dock), plastic deformation, which vanishes in the third part in (8), is negligible. Combined with the analogy of spring and damper, the above model can be simplified as the linear spring damper model as follows:
F = kδ e + cδ ̇
4. Numerical results and discussion
(9)
Note that the ADAMS model only contains the last section of the docking phase, where the distance of the two origins (i.e. O and E in Section 3) along theξ direction is less than 2 m. The entire discussion in this paper is based on the assumption that the dock is rigidly fixed on the ocean bottom mentioned at the beginning of Section 3. The ADAMS model is illustrated in Fig. 7 in accordance to the reference frame with the exerted total external forces and moments acquired in Section 3. A number of interesting terms, such as velocities, displacements and contact forces, have also been measured in the ADAMS model. The general configurations of the model are shown in Table 4, although part
where e and c are the force exponent and damping coefficient respectively, and k is the contact stiffness, which can be obtained as follows (Chatterjee, 1997):
k=
(10)
where q0 denotes the original distance of the two colliding bodies, whereas q corresponds to the actual distance; cmax indicates the maximum damping coefficient, d represents the penetration depth, k and e meet the previous definitions and step is a function in the ADAMS library. To show the difference between q0 and q, and d, Fig. 6 demonstrates the relevant variables. The dark spots in Fig. 6 indicate the mass centres of the impact bodies, and the dotted lines represent the line of impact. The left part where the bodies are represented with solid curves illustrates the state before impact, whereas the right part represents the state after the impact occurred. The red zone indicates the contact zone. Relevant variables are measured along the line of impact and marked in Fig. 6. ADAMS also adopts Coulomb's law to define the friction force usually determined by the static friction coefficient μs and the dynamic friction coefficient μd during impact simulation. The explicit expressions of the external forces and moments were recently obtained. They are shown in Eqs. (4–7) and (10) for further details.
0
θ(°)
Linear Velocity
⎪
4 1/2 * R E 3
where R and E * are the equivalent radius of the contact and equivalent elastic modulus calculated by 18
Resultant Impact Force (kN)
15
12
9
6
3
0
3
6
9
12
15
Time (s) Fig. 8. Resultant impact forces on the AUV in simulation. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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12
t
Fmax
c
10
21
19 8 17
Time Cost (s)
Maximum Impact Force (kN)
23
6 15
13 50
60
70
80
4 100
90
Cone Angle (deg) Fig. 9. Influence of different cone angles on the docking process.
of them are unmarked with an asterisk and would be modified to coincide with the various simulation situations discussed below. An appropriate thrust force Fprop , determined by the coefficient of thrust force CF and the propeller rotation speed n , have been exerted on the AUV to guarantee that the vehicle can reach the parking zone (indicated with a red box in Fig. 2) with a constant speed before contact. Five elements based on the ADAMS model, including cone angle, material characteristic, deviation, velocity and propeller force, will be discussed to verify the influence of impact on the docking process. The most considerable factor when docking is whether the AUV can
Table 5 Friction coefficients. μs
μd
0.05 0.08 0.13 0.15 0.25 0.30 0.50
0.03 0.04 0.09 0.10 0.20 0.25 0.43
18.5
t
9
c
18
8
17.5
7
17
Time Cost (s)
Maximum Impact Force (kN)
Fmax
6
16.5 0.05
0.1
0.15
0.2
5 0.3
0.25
Static Friction Coefficient
Fig. 10. Friction coefficient influences on the docking process.
Maximum Impact Force (kN)
Fmax
15
tc
27
13
22
11
17
9
12
7
7 2000
4000
6000
8000 Stiffness Coefficient (N/mm
10000 1.5
12000
)
Fig. 11. Influence of stiffness coefficient on the docking process.
182
14000
5
Time Cost (s)
32
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Fig. 12. Influence of position deviation on the docking process.
Fig. 13. Influence of posture deviation on the docking process.
Fig. 14. Influence of translational velocity in x direction on the docking process.
between two special moments (i.e. the first and last contact instances). We sampled the dynamic simulation by adopting the initial configurations in Table 4. Fig. 8 shows the resultant impact force in simulation during the last docking phase. From this figure, is 17.28 kN at the second contact moment stamped with red rectangle, and is about 9.3 s between the first and last contact moments marked with red circles. Following the same method, Fmax and can be obtained under various configurations.
complete the docking mission or not. Mission failure means that the AUV fails to reach the parking zone in the docking station. This phenomenon can occur in the case where relative configurations such as cone angle, material characteristic, deviation, velocity and propeller force are not reasonable, all of which were discussed in the following. The other two evaluation indexes are proposed to assess the docking process: maximum resultant impact forceFmax and time costtc .indicates the maximum of resultant impact force, and represents the duration 183
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Fig. 15. Influence of translational velocities in the y and z directions on the docking process.
Fig. 16. Influence of propeller force on the docking process.
the dock, the cone angle should not be as small as possible. 4.2. Material characteristic Two typical material characteristics, namely, friction coefficient and stiffness, are considered below. The typical friction coefficients are chosen based on general references and are shown in Table 5. The corresponding influence is depicted in Fig. 10, whose abscissa is selected as a static friction coefficient. Both the maximum resultant impact force and the time cost grew with an increasing friction coefficient, although the variation range of the maximum resultant impact force was minimal. However, the docking mission failed under the last friction coefficient set (i.e. μs = 0.50 and μd = 0.43), which indicates that the poor friction condition can challenge the docking process. Fortunately, the friction coefficient during docking is quite small in reality because of the surrounding fluid. Stiffness, the other material characteristic, greatly influences the docking process, as illustrated in Fig. 11. Similar to the simulation results under the friction coefficient configuration, the maximum resultant impact force and the time cost sharply increase, albeit with larger variation ranges as the stiffness coefficient rises. With a six-fold growth in static friction coefficient, the maximum resultant impact force and the time cost increased up to 1.08 and 1.7 times respectively, as displayed in Fig. 10. By contrast, the corresponding increase could reach 4 and 2.8 times given the same stiffness growth, as depicted in Fig. 11. These results illustrate that stiffness has a greater influence than friction coefficient. Once stiffness coefficient becomes larger than 14250N / mm1.5, the docking failure rate will significantly increase with
Fig. 17. Pool trial in Xixi Campus.
4.1. Cone angle In accordance with the AUV size and the control precision, the cone entry diameter is set as a constant at 1.2 m. Afterwards, the variable cone angles can make a difference on the docking process. Fig. 9 reveals the influence tendency under diverse cone angles by merely changing the cone angle. All the situations with different cone angles shown in this figure complete the docking mission. Considering the cone angle growth, both the maximum resultant impact force and the time cost increase with markedly large rates. Simulation results indicate that a relatively small cone angle is advantageous to optimise the docking process. However, considering the length of the cone and the balance of 184
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Fig. 18. Velocity comparison between the simulation results and the experimental data. The blue curve represents the simulation results, and the red curve indicates the experimental data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 19. Comparison of time-series pictures in the experiment and the simulation for one docking attempt. The red lines in the simulation pictures indicate the gravity and buoyancy exerted on the AUV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
is not much different under the η and ϛ direction deviations when the absolute value of abscissa is within 0.35 m. However, the maximum resultant impact force, especially under the η direction deviation, increases sharply when the abscissa falls outside that region. The increase rate of time cost under the η direction deviation is larger than that under the ϛ direction deviation within the entire process, and turned especially gradient when the absolute value of the position deviation is between 0.3 and 0.4 m. In comparison, it is much better to decrease the position deviation and thus improve the control requirements, better promoting the docking success rate and optimising the docking process. The perfect posture of a docking AUV is when the longitudinal axis can coincide with the central axis of the cone before the AUV makes contact with the dock. However, the appearance of some posture deviations during docking is inevitable. Fig. 13 depicts the changes in the maximum resultant impact force and the time cost under different posture deviations, which fail to consider the position deviation discussed above. The influence is also symmetric because of the structural characteristics already mentioned above. Apart from the
the rise of stiffness coefficient. Collectively, the above discussion shows it is better to use a material with small stiffness and friction coefficients to construct the dock, such as acrylic and nylon, instead of steel or aluminium, although the influence of the stiffness coefficient is more obvious than that of the friction coefficient. 4.3. Position and posture deviation Both position and posture deviations exert immense influence on the docking process, which will be discussed respectively. The entry radius of the cone has been set as 0.6 m and the main AUV diameter is 0.2 m. Afterwards, the position deviation is limited from −0.5 to 0.5 m to guarantee a successful docking. The detailed influence of the position deviation is illustrated in Fig. 12. The influence of the position deviation in the η direction and the ϛ direction is coincident and symmetric between the negative and positive position bias because of the characteristic symmetry of the AUV and the cone. The maximum resultant impact force and the time cost increase with the rise of absolute value. The change rate of the maximum resultant impact force 185
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absence of posture deviation, the maximum resultant impact force under pitch deviation is larger than that under yaw deviation. A sharp change of the force under pitch deviation occurs when the absolute value of pitch angle exceeds 12°. During the entire zone change, the time cost under yaw deviation is slightly greater than that under pitch deviation. Neither the pitch deviation nor the yaw deviation can actually reach 20° in most cases, which aids the docking process.
but the maximum resultant impact force and the failure rate of docking sharply increase until 900 r/min. The proper propeller force, just like the propeller rotation speed between 420 and 660r /min , is a good compromise between the time cost and the maximum resultant impact force.
4.4. Velocity
The preliminary docking experiment was conducted in a pool in the Xixi Campus of Zhejiang University (Fig. 17) to demonstrate the validity of the cone-shaped docking method. The pool is 50 m long, 30 m wide and nearly 1.7 m deep, dimensions which sufficiently and completely submerge the AUV. The weather was sunny with no wind in most cases during the study, leading to still water, which is the appropriate environment for docking. Based on upfront surveys, the cone angle was determined as 75°, and the stave materials in the cone and the fairing in the bow of the AUV were chosen as fibreglass and polycarbonate respectively. Owing to the limitations of the pool condition, only dock, housing and some necessary accessories were tested and submerged in water, and the dock was fixed in the temporary base without the steering mechanism. During the experiments, the AUV worked in orientation mode and constant speed mode followed by the expected orientation and velocity specified by the matched upper computer, while the specified velocity was much less than that in the wide area like in a lake. By adjusting the position, orientation and velocity of the AUV, we examined the docking processes under different situations. The maximum impact force and time cost are both difficult to measure in actuality. However, the velocities recorded by the AUV and photographs shot by an underwater camera were compared with the simulation results. Fig. 18 presents the comparison of the vehicle velocities in the body-fixed frame between the simulation results and the experiment data. Simulation results were acquired by configuring the initial velocity as 0.67m /s in the x direction, initial position deviation as 0.05 m in the η direction and −0.35 m in the ζ direction, with no posture deviation in ADAMS. The first contact time in simulation failed to coincide with that in the experiment because of the different initial moments selected in the two curves. After this first impact, the resultant velocity and velocity in the x direction vanished immediately in the simulation and experiment. In comparison, the corresponding velocities in the y and z directions increased in absolute values, although the increase rate in the simulation was much larger than that in the experiment. Owing to the positive deviation in the direction, the negative deviation in the direction and the velocity measurement at the centre of buoyancy, the velocities in the y and z directions coincided with the corresponding directions of the position deviation. In the simulation, two distinct acceleration processes with a similar acceleration occurred in the x direction before 4.3 and 8.7 s, namely the second and third contact moments respectively; several acceleration processes in the x direction were also found between 2.68 and 8.54 s in the experiment. With these three main contacts in the simulation, the vehicle completed the docking mission with a time cost of about 6.75 s, while the contact times before completing the docking mission were not intuitional in the experiment. Apart from the last impact at 10.42 s in the experiment, at which moment the vehicle actually entered the dock completely, the vehicle spent almost 6.14 s completing the docking mission. Finally, based on the above analyses, the simulation velocity tendencies coincided with the experimental velocity data as a whole, although some discrepancies, such as contact times and velocity magnitudes, occurred as a result of the differences in the model, initial configurations and circumstances, among others. Time-series pictures corresponding to the above velocities are compared to validate the posture changes during the docking process. These are shown in Fig. 19. The successes of the docking attempts in the experiment and the simulation are intuitionistic as well. A number of relevant postures in the simulation can coincide with those in the
5. Experiment validation
The initial translational velocity also exerts an important effect on the docking process; it has been evaluated in the body-fixed frame as a component velocity as well. Fig. 14 depicts the influence of the translational velocity in the x direction. The maximum resultant impact force increases almost linearly with the x-component velocity growth, whereas the time cost decreases without a distinct linear relation. However, when the x-component velocity is larger than 1.7m / s , the time cost nearly remains constant, though the maximum resultant impact force continues to increase rapidly. Moreover, if the translational velocity continues growing, the failure rate of docking and the possibility of damage will increase. The actual cruising speed of the AUV is approximately 3 knots (Zhang et al., 2014), which is almost the middle abscissa value in Fig. 14. Combined with the minimum speed for buoyancy balance required, the speed for docking can be selected between 0.8 and 1.5 m/s. The lateral and vertical velocities also affect the docking process. Fig. 15 synthesises the evaluation indexes in the y and z directions. The maximum resultant impact force and the time cost increase in quite a small rate from negative to positive velocity in the y direction. The docking process can benefit from the negative velocity in the y direction as the corresponding positive velocity becomes the obstacle because of the position deviation under the positive η direction. Owing to the approximate symmetry in the x−y plane of the AUV and the absence of the position deviation in the ϛ direction, the influence of translational velocity in the z direction is almost symmetrical between the positive and negative velocity configurations. The two evaluation indexes increase and the time cost augments with a large rate with the growth of the absolute velocity value in the z direction. The velocity variations in the y and z directions exert much more obvious influences on the time cost than on the maximum resultant impact force. The influence of time cost in the z direction is much worse than in the y direction because of the position deviation in the positive y direction. Although the negative velocity in the y direction has the beneficial influence on the docking process, eliminating the lateral and vertical velocities by reducing the sideslip angle and angle of attack for instance is better considering the difficulty of controllability. 4.5. Propeller force The propeller rotation speed is deliberately set in the above configurations to ascertain that the AUV can go ahead at constant speed before contact so that the propeller force can balance the viscous drag. In this subsection, the propeller rotation speed is changed under the same initial velocity 0.8m / s to evaluate the influence of different propeller forces. Moreover, if the uniform velocity before contact is necessary, the propeller rotation speed 480r /min is configured. Fig. 16 depicts the influence of the propeller force as delegated by diverse propeller rotation speeds. The time cost is negatively related to the propeller rotation speed, whereas the maximum resultant impact force indicates a positive relation. With regard to the time cost, the propeller rotation speed is a demarcation point, and the rate of descent before this point is four times as large as that after this point. When the propeller rotation speed is larger than 680r /min , the growth rate of the maximum resultant impact force can be up to 20.01kN /(r /min), which is nearly two times larger than that of the previous segment. However, if the propeller rotation speed continues to grow, time cost varies weakly 186
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Cowen, S., 1997. Flying plug: a small uuv designed for submarine data connectivity (Report documentation). Space and Naval Warfare Systems Center, San Diego, CA. Chatterjee, A., 1997. Rigid body collisions: some general considerations, new collision laws, and some experimental data. Cornell University, New York. De Barros, E., Dantas, J.L., Pascoal, A.M., De Sá, E., 2008. Investigation of normal force and moment coefficients for an AUV at nonlinear angle of attack and sideslip range. IEEE J. Ocean. Eng. 33 (4), 538–549. Li, D., 2007. Ship Motion and Modelling second edition. National defense industry press, Beijing. Faik S., Witteman H., 2000. Modeling of impact dynamics: a literature survey. In: International ADAMS User Conference. Orlando, FL, pp. 1–11 Fossen, T.I., 1994. Guidance and Control of Ocean Vehicles. John Wiley & Sons Inc, New York. Fukasawa, T., Noguchi, T., Kawasaki, T., Baino, M., 2003. "MARINE BIRD", a new experimental AUV with underwater docking and recharging system. MTS/IEEE Oceans. IEEE, San. Diego, CA, 2195–2200. Gilardi, G., Sharf, I., 2002. Literature survey of contact dynamics modelling. Mech. Mach. Theory 37 (10), 1213–1239. Kerwin, J.E., Hadler, J.B., 2010. Principles of Naval Architecture Series: Propulsion. The Society of Naval Architects and Marine Engineers (SNAME), Alexandria, VA. Lambiotte, J.C., Coulson, R., Smith, S.M., An, A., 2002. Results from mechanical docking tests of a Morpheus class AUV with a dock designed for an OEX class AUV. MTS/ IEEE Oceans. IEEE, Biloxi, MS, 260–265. Lewandowski, E.M., 2004. The dynamics of marine craft: maneuvering and seakeeping. World Scientific, River Edge, NJ. McEwen, R.S., Hobson, B.W., McBride, L., Bellingham, J.G., 2008. Docking control system for a 54-cm-diameter (21-in) AUV. IEEE J. Ocean. Eng. 33 (4), 550–562. Nelson, R.C., 1998. Flight Stability and Automatic Control. WCB/McGraw-Hill, New York. Pamadi, B.N., 2004. Performance, stability dynamics, and Control of Airplanes. AIAA, Reston, VA, 780. Park, J.Y., Jun, B.H., Lee, P.M., Lee, F.Y., Oh, J., 2007. Experiment on Underwater docking of an autonomous underwater vehicle 'ISiMI' using optical terminal guidance. MTS/IEEE Oceans. IEEE, Aberd., 1–6. Park, J.Y., Jun, B.H., Lee, P.M., Oh, J., 2009. Experiments on vision guided docking of an autonomous underwater vehicle using one camera. Ocean Eng. 36 (1), 48–61. Shi, S., 1995. Submarine Maneuverability. National Defense Industry Press, Beijing. Shi, J., Li, D., Yang, C., 2014. Design and analysis of an underwater inductive coupling power transfer system for autonomous underwater vehicle docking applications. J. Zhejiang Univ. -Sci. C. (Comput. Electron. ) 15 (1), 51–62. Shi, J., Li, D., Yang, C., Cai, Y., 2015. Impact analysis during docking process of autonomous underwater vehicle. J. Zhejiang Univ. (Eng. Sci. ) 49 (3), 497–504. Singh, H., Bellingham, J.G., Hover, F., Lerner, S., Moran, B.A., von der Heydt, K., Yoerger, D., 2001. Docking for an autonomous ocean sampling network. IEEE J. Ocean. Eng. 26 (4), 498–514. Stokey, R., Allen, B., Austin, T., Goldsborough, R., Forrester, N., Purcell, M., von Alt, C., 2001. Enabling technologies for REMUS docking: an integral component of an autonomous ocean-sampling network. IEEE J. Ocean. Eng. 26 (4), 487–497. Thomasson, P.G., Woolsey, C.A., 2013. Vehicle motion in currents. IEEE J. Ocean. Eng. 38 (2), 226–242. Timothy, P., 2001. Verification of a six-degree of freedom simulation model for the REMUS autonomous underwater vehicle (Master thesis). Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, Cambridge, MA. Wu, L., Li, Y., Su, S., Yan, P., Qin, Y., 2014. Hydrodynamic analysis of AUV underwater docking with a cone-shaped dock under ocean currents. Ocean Eng. 85, 110–126. Yang, C., Peng, S., Fan, S., 2014. Performance and stability analysis for ZJU Glider. Mar. Technol. Soc. J. 48 (3), 88–103. Zhang, M., Xu, Y., Li, B., Wang, D., Xu, W., 2014. A modular autonomous underwater vehicle for environmental sampling: system design and preliminary experimental results. MTS/IEEE Oceans. IEEE, Taipei, 1–5.
experiment, although with attitude deviations and at different moments because of the previously mentioned discrepancies between the simulation and the experiment. 6. Conclusions Considering the influence of impact on a docking AUV, an underwater impact model in ADAMS was proposed after the hydrodynamic coefficients were identified. Five interesting influence elements, including cone angle, material characteristic, deviation, velocity and propeller force, were discussed. A pool trial was conducted to validate the proposed simulation model. Results of this study can provide some insights into the design of the docking system and the docking control of the companion AUV, including the following: 1) The cone-shaped dock, especially one with a proper cone angle, is a good choice for underwater docking. 2) Docking materials with small friction and stiffness coefficients are suggested. 3) Large deviations in both position and posture serve as obstacles for docking, meaning the remarkable significance of high control accuracy. 4) Lateral and vertical velocities negatively affect docking, whereas an appropriate forward speed can optimise the impact process. 5) A propeller force slightly larger than the need of constant forward speed is beneficial to the impact process. 6) The maximum impact force between the AUV and the docking station can provide some reference to optimise the structure of the docking station to make this station satisfy the use in ocean bottom during the whole docking mission. Our ongoing work is focused on the entire docking system trials in the lake and the shallow sea to realise docking missions with high success rates in water 100 m deep. Acknowledgment This project was supported by the National High-Tech Research and Development Program of China (Grant No. 2013AA09A414) and the Science Fund for Creative Research Groups of National Natural Science Foundation of China (No. 51221004). References Allen, B., Austin, T., Forrester, N., Goldsborough, R., Kukulya, A., 2006. Autonomous docking demonstrations with enhanced REMUS technology. MTS/IEEE Oceans. IEEE, Boston, MA, 1539–1544.
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