The 3rd International Conference on Transportation Information and Safety, June 25 – June 28, 2015, Wuhan, P. R. China
On the Velocity Obstacle Based Automatic Collision Avoidance with Multiple Target Ships at Sea Yanfei Tian
Yong Xiong
School of Navigation, Wuhan University of Technology Hubei Key Laboratory of Inland Shipping Technology Wuhan 430063, China *
[email protected]
School of Navigation, Wuhan University of Technology Hubei Key Laboratory of Inland Shipping Technology Wuhan 430063, China *
[email protected]
Liwen Huang
Shuang Li
School of Navigation, Wuhan University of Technology Hubei Key Laboratory of Inland Shipping Technology Wuhan 430063, China *
[email protected]
School of Computer Science and Technology Wuhan University of Science and Technology Wuhan 430066, China collision avoidance is still rare. The literature [12] studied ship collision avoidance algorithm based on speed barrier under the relative coordinate. Given the similarity of collision avoidance problems, this article will apply the speed barrier method to the collision avoidance field to analysis the steering measures of avoiding multi-target ships. And further the mathematics model of the local ship collision avoidance with automatic control under the circumstances of multi-objective ships at sea was constructed. Finally, the model was verified by simulation on ECDIS.
Abstract—To find out solutions to automatic collision avoidance with multiple targets, which would promote ship automation and intelligence, the basic principle of velocity obstacle theory was applied for the own ship to avoid collision with multiple moving or static targets. The principle of ship collision avoidance was analyzed and solution of demanded course for the own ship to navigation with at current to avoid collision was proposed based on velocity obstacle. With kinematics equations of own ship structured by law of response type mathematical model and an increment PID algorithm presented for automatic course control, simulations on ECDIS were executed to test the validation of the proposed model, which indicated it was available for the own ship to avoid collision with both the moving and static targets. The study showed that concept for collision avoidance at circumstance of multiple ships based on velocity obstacle was effective and could provide support for automatic ship collision avoidance system.
II.
Considering it has already developed systematic and mature, the coordinated system and variables and their meaning used to reflect the kinematics characteristic of the ship are quoted by default in the following sentences and equations without being repeated.
Keywords—Velocity Obstacle, Multiple Target Ships, Collision Avoidance, Automatic Control
I.
A. Basic principle For brief expression, the symbols introduced were listed in TABLE I with their meanings.
INTRODUCTION
The research of intelligent collision avoidance technology has been a hotspot and advancing topic in the research field of Intelligence Navigation (I-NAV) for long, which is one of the key technologies of realizing ship automation. As it involves many factors, although people have put a lot of effort in the field, the progress of intelligent collision avoidance technology is still relatively slow and mature and universal intelligence collision avoidance model adapted to complex navigation environment has not been fully established. For example, Ship collision avoidance decision-making encountering multiple target ships has not been satisfactorily solved [1].
In this section, the subscript [k ] was omitted for brief expression. Fig.1 and Fig.2 demonstrate the scenes for the own ship to avoid collision with a single target ship and multiple target ships at current time, where all target ships (or called mobile obstacles) were simplified as circular. According to the principle of velocity obstacle, absolute motion of both the own ship and target ship(s) in inertial coordinate system can be converted in body-fitted coordinate system to a relative movement of own ship to target ship(s) treated as static obstacles and the process to avoidance collision with the obstacles is one to enable the relative velocity out of the relative collision zone. With speed of own ship supposed not change while maneuvering, and altering course utilized alone for the own ship to avoidance collision with the target ship(s), the strategy taken by the own ship to avoidance is to
From the eighties of last century, the method of Velocity Obstacle is widely used in the research of robot path planning in order to achieve avoidance of fixed and moving obstacles [29] . In addition, people did many researches in the areas of aircraft route planning, obstacle avoidance and so on[10-11]. The study of speed barrier in the ship route planning and automatic This work is supported by both the Fundamental Research Funds for the Central Universities (Financially supported by self-determined and innovative research funds of WUT, Grant No. 2014-JL-010) and the Natural Science Foundation of Hubei Province (Grant No. 2014ZFB878). The authors would like to thank the funds for the financial support for this project.
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DEMANDED COURSE FOR COLLISION AVOIDANCE BASED ON VELOCITY OBSTACLE
The 3rd International Conference on Transportation Information and Safety, June 25 – June 28, 2015, Wuhan, P. R. China
steer at a demanded course demanded relative velocity zone. TABLE I. No.
ψd
ψ dr
, which will cause the
out of the relative collision
NTRODUCED SYMBOLS WITH PRESCRIBED MEANINGS
symbols
meaning
1
k
a symbol that indicates the current time
2
TS
target ship
3
ST
static target
n
total number of the targets (obstacles) a number between 1 and
4 5
i
6
TSi
the
i − th
7
STi
the
i − th static target
8
Vos[ k ]
speed of the own ship at current
9
ϕ[ k ]
course of the own ship at current
10
VTS [ k ] / VST [ k ]
11
ϕTS [ k ] / ϕ ST [ k ]
12
Vri[ k ]
13
ϕ ri[ k ]
14
l(2 i −1)[ k ] / 䯴l 2 i +1)[ k ]
15
16
17
Vdr (2i −1)[ k ] / Vdr (2i +1)[ k ]
ϕdr (2i −1)[ k ] / ϕdr (2i +1)[ k ] ψ u[k]
x
X
I
VTS Vr
OS
y
target ship
Fig. 1. Collision avoidance with a single target ship
x
X ĂĂ
speed of the target ship/static target at current course of target ship/static target at current relative speed of own ship and TSi (or STi) at current relative course of own ship and TSi (or STi) at current left/right line of relative motion of own ship and target ship at current demanded relative speed of own ship and TSi (or STi) at current for collision avoidance
TSn
O
OS
Fig. 2. Collision avoidance with multiple target ships
B. Calculation steps
to l(2 i −1)[ k ] / 䯴l 2 i +1)[ k ] universal set of courses expressed in inertial coordinate at current,
Similar to the statements in section 2.1, the subscript [ k ] was omitted for brief expression. The following steps were proposed to approach to ψ d base on the above analysis:
= [0°, 360°]
ψ ci[ k ]
19
ψ c[ k ]
set of the courses which will make the own ship collide with TSi (or STi) at current set of courses which will make collision happen
20
ψ [ k ] ˄ψ ˅
the current course of own ship
21
ψ a[k ]
22
ψ d[k ]
Step 1.
k =k,
calculate ψ dr (2i −1) and ψ dr (2i +1) according
to current motion features of the ships in scene.
ψ ci = (ψ 2i −1 , ψ 2i +1 ) , where the two endpoints and ψ 2 i +1 corresponding to ψ dr (2 i -1) and ψ dr (2i +1) are
Step 2.
ψ 2 i −1
set of the courses available for collision avoidance with TSi (and STi) at current demanded specific course for the own ship currently to steer at to avoid collision with TSi (and STi)
calculated according to the triangle of velocities. Step 3. ψ c
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Y y
demanded relative course of own ship and TSi (or STi) at current for collision avoidance corresponding
18
TSi
TS1
l(2 i −1)[ k ] / 䯴l 2 i +1)[ k ]
u[k ]
Y
-VTS
O
n ( i = 1, 2, 3" n )
ψ
TS
VOS
n
= ∪ψ ci , which is a set of closed interval. i =1
The 3rd International Conference on Transportation Information and Safety, June 25 – June 28, 2015, Wuhan, P. R. China
ψ a = ψ c = ψ u −ψ c ,
Step 4. interval. Step 5.
ψ d = {ψ d ψ d ∈ψ a & min ψ d −ψ
will be exported and executed. Step 6. III.
° X = Vi ⋅ cos (ψ i + N ) ® °¯Y = Vi ⋅ sin (ψ i + N )
which is a set of closed
},
The plus vi represents the speed of the target ship(s). Variable N is assumed to be a small quantitative value submit to normal distribution, represents the random noise to reflect course variation of the target ship(s).
k = k +1 , turn to step 1 to continue.
ADOPTED KINEMATICS EQUATIONS OF SHIP MOTION
Since planar position and motion parameters were primarily considered, so we built up the kinematics equations of ship motion with 3 degrees of freedom (DOF).
IV.
disturbance
feedback
(1)
Fig. 3. Automatic control process to alter course by increment PID
Referring to [13], the increment PID algorithm was designed as:
§ ©
δ d [k ] = δ r[k −1] + ¨ KP +
KI · + KD ¸ ⋅ eψ [ k ] 2 ¹
KI § · + ¨ − KP + − 2 KD ¸ ⋅ eψ [k −1] 2 © ¹ + KD ⋅ eψ [ k − 2]
(2)
The plus letters K and T represent the turning ability index and turning lag index. K = 26 , T = 0.3 were applied to simulation. Letter β represents the drift angle and is equal to
kinematics equations of ship motion
PID
And:
°u = V ⋅ cos ( β ) ® °¯v = V ⋅ sin ( β )
DESIGNED PID CONTROLLER
The increment PID algorithm was used for the ship to automatically alter course toψ d . The control process is shown in Fig.3.
A. Kinematics Equations of Own Ship With response type mathematical model based on, the Kinematics equations of own ships with 3 DOF are:
° X = u ⋅ cos (ψ ) − v ⋅ sin (ψ ) ° ®Y = u ⋅ sin (ψ ) + v ⋅ cos (ψ ) ° t °ψ = K ⋅ δ ⋅ (1 − e − T ) ¯
(4)
which
Where, k represents the current time;
0° for simplification.
rudder angle to be executed;
The real-time rudder angle during steering is calculated by:
eψ
δd
(5)
is the demanded
represents the deviation
between the demanded course ψ d [ k ] and the current real-time
δ = (δ d − δ ) / τ
course ψ [ k ] , which is:
eψ [ k ] = ψ d [ k ] −ψ [ k ]
(3)
After parameters tuning, we adopted KP=2.1 ˈ KI=0.01 and KD=0.9DŽ
Where: δ d represents the required rudder angle provided by an increment PID algorithm depicted in sectionIV; τ represents the time constant ( τ = 2.5 applied in simulation) which reflects performance of the steering gear.
V.
SIMULATION AND RESULT ANALYSIS
Simulations on ECDIS were executed to test the validation of the above mentioned model andalgorithm, where the radiuses of circulars representing various obstacles were equal
B. Kinematics Equations of Target Ships Target ship(s) is (are) supposed to make uniform linear motion, so the kinematics equations of target ship(s) are:
to 500m and the random noise into account.
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(6)
N ∼ N (0.1,0.12 ) was taken
The 3rd International Conference on Transportation Information and Safety, June 25 – June 28, 2015, Wuhan, P. R. China
A. Scenario 1 Initial settings are listed in TABLE II. The scenario where the own ship acted to avoid collision with two target ships was shown in Fig.4. TABLE II. Items Own ship(OS) Target ship 1(TS1) Target ship 2(TS2)
I
NITIAL SETTINGS FOR SCENARIO 1
X(m) 101.37 4548.59 4378.98
Y(m) -0.36 3.85 2769.86
(°) 0.14 180.00 225.03
V(m/s) 6.07 6.17 5.15
Fig. 5. Scenario 2
In Fig.5, (a) demonstrated the initial scene when the ships started to navigate with the given course and speed. (b) Showed the moment when the own ship started to act under constraints from both TS2 and the static target (ST) to avoid collision with TS1. (c) Showed currently OS was taking measures to avoid collision with TS2 at the same time. (d) Indicated that it was capable for the own ship to pass the moving two without collision with the static one at current. It can be seen that the proposed model and algorithm were available for the own ship to avoid collision with both the moving and static targets.
Fig. 4. Scenario 1
In Fig.4, (a) demonstrated the initial scene when the ships started to navigate with the given course and speed. (b) Showed the moment when the own ship started to act to avoid collision with TS1. (c) Showed the time when the own ship was clear from TS1 and continually act to avoid collision with TS2. (d) Indicated that the own ship was clear from both the two targets. It can be seen that the proposed model and algorithm were available for the own ship to avoid collision with two moving targets. B. Scenario 2 Initial settings are listed in TABLE III. The scenario where the own ship acted to avoid collision with two target ships and one static target was shown in Fig.5. TABLE III. Items Own ship(OS) Target ship 1(TS1) Target ship 2(TS2) Static target(ST)
NITIAL SETTINGS FOR SCENARIO 2
X(m) 60.33 4515.01 3652.37 3808.26
Y(m) -0.29 266.97 -1871.67 1281.74
(°) 0.13 180.00 140 0
V(m/s) 5.78 6.17 5.15 0
VI.
This paper analyses the collision avoidance principle in steering based on velocity obstacle, and develops the mathematical model of automatic collision avoidance control for local ship under the circumstance of multi-objective ships at sea. The simulation results show that the goal of automatic collision avoidance control for local ship can be achieved with the achieved demanded course and control scheme. In practice, people measure the risk of collision mainly with distance to the closest point of approach (DCPA) and time to the closest point of approach (TCPA), then determine the priorities of collision avoidance according to the risk level and take measures to avoid collision. From the principle point of I view, the collision avoidance method based on velocity obstacle just keeps the local ship at a safe distance outside of the target ships to avoid collision at any time, but failure to treat the target ships discriminatorily according to TCPAs. The achieved demanded course available for collision avoidance may not be the best solution. In addition, the model adopted in this paper is relatively simple, and without considering the
471 978-1-4799-8694-1/11/31.00 © 2015 IEEE
CONCLUSION AND OUTLOOK
The 3rd International Conference on Transportation Information and Safety, June 25 – June 28, 2015, Wuhan, P. R. China
constraints such as weather, sea conditions, water depth, ordinary practice of seaman, collision regulation and so on, and the follow-up study will focus on comprehensive consideration of multiple constraints and improving the model in details.
[6]
[7]
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