Path planning and obstacle avoidance for auv: a review
Modeling and analysis of AUV
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OceanEngineering2021-cheng
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In this section, the kinematic and dynamic models of AUV control are introduced, which put many constraints and steering characteristics
Ocean Engineering 235 (2021) 109355 3
Fig. 2. Autonomous Underwater Vehicle. Source: Reproduced from Vibhute ( 2018 ). on AUV. This makes it challenging to implement path planning methods on AUV and different from other robot platforms on land or in the air. The models are based on Fosson’s comprehensive work ( Fossen ,
), including general two dimensional and three dimensional kinematics transformation and in-depth derivation of dynamics motion equations.
Kinematics is based on the geometric method to study the motion of vehicles, without considering the influence of force and mass. To describe the kinematic characteristics of AUV, we will apply the inertial North-East-Down (NED) reference frame and the Body frame. Fig. 2
describes AUV as a six degree of freedom (DOF) vehicle with two rotational and translational velocity components in each dimension ( Fossen
, 2011
). As shown in Fig. 2
, the Body frame is attached to the vehicle, and has its axes forward (surge), to starboard (sway) and towards the keel (heave) ( Wiig
, 2019
). The translation velocities along the
𝑋 ,
and
directions are expressed as 𝑢 ,
and
respectively, and the rotation velocities are expressed as
,
and
respectively. The rotation angles of each axis are expressed as
,
and
respectively, and
,
and
represent the moment in 𝑋 ,
and
direction respectively ( Vibhute
, 2018
). The rotation matrix of 6-DOF AUV is composed of the basic rotation matrix of
,
and
axes. In the geometric analysis, the basic rotation matrix of
,
and
axes are: 𝑅 𝑥 (
) = ⎡
⎢ ⎣ 1 0 0 0 𝑐𝑜𝑠 (
) −
( 𝜙 ) 0 𝑠𝑖𝑛 (
)
(
) ⎤
⎥ ⎦ (1) 𝑅 𝑦 (
) = ⎡
⎢ ⎣
(
) 0 𝑠𝑖𝑛 (
) 0
0 −
(
) 0 𝑐𝑜𝑠 (
) ⎤
⎥ ⎦ (2) 𝑅 𝑧 (
) = ⎡
⎢ ⎣
(
) − 𝑠𝑖𝑛 (
) 0
( 𝜓 )
(
) 0 0 0 1 ⎤ ⎥ ⎥ ⎦ (3)
Combining these principal rotations gives the rotation matrix 𝑅 as:
𝑅 =
𝑧 (
)
(
)
(
) (4)
The relationship between the orientation and angular velocity is: 𝐽 = ⎡ ⎢ ⎢ ⎣ 1 𝑠𝑖𝑛 (
)
(
)
(
)
(
) 0
( 𝜙 ) − 𝑠𝑖𝑛 (
) 0
( 𝜙 )∕
(
)
(
)∕
(
) ⎤ ⎥ ⎥ ⎦ (5) Hence, the AUV kinematics in 6-DOF are: ̇𝜂 = [ 𝑅 0 3×3 ℎ𝑒𝑙𝑙𝑜𝑐ℎ𝑒𝑐𝑘𝑡ℎ𝑒𝑐𝑜𝑚𝑚𝑎𝑛𝑑 3×3
𝐽 ]
(6) In the formula, the generalized velocity vector and position vector are respectively represented by the following matrix: 𝜂 = [
𝑋, 𝑌 , 𝑍, 𝜙, 𝜃, 𝜓 ] T (7) 2.2. Dynamics Referring to the Fossen (
) maneuvering model, the nonlinear equation of the dynamic motion for AUV has the following general form:
(
) +
(
)
+
+ g
𝜂 ) =
𝐵𝑓 , (8)
where 𝑀 denotes the inertia matrix, 𝐶 contains Coriolis and centripetal terms, and
indicates the hydrodynamic damping matrix. Vector 𝑔 denotes a combination of gravity and buoyancy, vector 𝑓 is the control input variable of AUV, which is transformed into the force and moment of control motion by matrix B. The control input vector is:
= [
𝑇 𝑢 , 𝑇 𝑞 , 𝑇 𝑟 ] T , (9)
where, 𝑇 𝑢 is the thrust force produced by rotating the propeller, 𝑇 𝑞 is the
vertical motion control force generated by the left and right rudders, 𝑇 𝑟 is the horizontal motion control force generated by the upper and lower rudders. Assuming that the center of gravity ( 𝑥 𝑔 , 𝑦 𝑔 , 𝑧 𝑔 ) and buoyancy of AUV are rigid bodies at one point, the 6-DOF translational and rotational motions will be expressed as follows: 𝑚 [
−
+
−
(
2 +
2 ) +
𝑦 𝑔 (
−
) +
𝑧 𝑔 (
+
)] =
𝑋 𝑡𝑜𝑡𝑎𝑙 𝑚 [
−
+
−
(
2 +
2 ) +
𝑧 𝑔 (
+
) +
𝑥 𝑔 (
+
)] =
𝑌 𝑡𝑜𝑡𝑎𝑙 𝑚 [
𝑤 −
+
−
𝑔 (
2 +
2 ) +
𝑥 𝑔 (
−
) +
𝑦 𝑔 (
+
)] =
𝑍 𝑡𝑜𝑡𝑎𝑙 𝐼 𝑥 ̇𝑝 + (
𝐼 𝑧 −
𝑦 )
− (
+
)
+ (
𝑟 2 − 𝑞 2 ) 𝐼 𝑦𝑧 + (
𝑝𝑟 −
)
+
[
(
𝑤 −
+
) −
𝑧 𝑔 (
−
+
)] =
+ (
𝐼 𝑥 −
𝑧 )
− (
+
)
+ (
𝑝 2 − 𝑟 2 ) 𝐼 𝑧𝑥 + (
𝑞𝑝 −
)
+
[
(
−
+
) −
(
𝑤 −
+
)] =
𝑀 𝑡𝑜𝑡𝑎𝑙 𝐼 𝑧 ̇𝑟 + (
𝐼 𝑦 −
𝑥 )
− (
+
)
+ (
𝑞 2 − 𝑝 2 ) 𝐼 𝑥𝑦 + (
𝑟𝑝 −
)
+
[
(
−
+
) −
(
−
+
)] =
where
𝑚 is the mass of the vehicle, 𝐼 is the inertia in the specific axial or transverse direction, and (
) and (
𝐾 𝑡𝑜𝑡𝑎𝑙 , 𝑀 𝑡𝑜𝑡𝑎𝑙 , 𝑁 𝑡𝑜𝑡𝑎𝑙 ) are the total external forces on each degree of freedom. The above modeling of AUV put some unique constraints in its motion control with path planning methods which makes it different from other mobile robots. On the one hand, as a highly nonlinear system, AUV is affected by the change of mass center, buoyancy center and hydrodynamic coefficient ( Xiang et al. , 2014
). On the other hand, AUV has underactuated characteristics, and parts of its speed cannot be directly controlled, but can only be generated when the propeller and rudder angle are manipulated. For example, when AUV rotates, part of the forward speed will be converted into swing speed, and the heave motion is controlled in a similar way. In addition, the collected sensory data will affect the performance of path planning methods for AUV. General mobile robots use the electromagnetic wave generated by laser sensor to navigate and avoid obstacles Ye and Borenstein ( 2002
), and some of them use the camera ( Biswas and Veloso , 2012
) to obtain images directly to judge the position of obstacles. However, because AUV works in the marine environment, and it detects the surrounding obstacles according to the ultrasonic wave generated by Ocean Engineering 235 (2021) 109355 4
sonar sensor ( Kimball and Rock , 2008
). Data collected with sonar sensors will be interfered by underwater sound waves, which will result in inaccurate information and low-quality data received and largely affect the accuracy of obstacle avoidance for AUV. In addition, AUV path planning also needs to consider the influence of ocean currents. Moreover, underwater tasks performed by AUVs usually need to follow some specific path patterns. For example, when AUV completes some unknown search and detection missions, there is usually an algorithm to generate a coverage path in the task editor, which requires AUV to bypass unforeseen obstacles when executing this path mode ( Bagnitckii et al.
, 2017
). In some situation, multi-AUV also needs to follow a certain formation mode to improve the efficiency of the mission ( Ding et al. , 2014 ). Although these make it more challenging to implement general path planning methods for AUV compared to other mobile robots, many re- searchers have proposed effective path planning methods to overcome these challenges. In Sections 3 and 4 , we will review most popular path planning methods for AUV in terms of global path planning with known static obstacles and local path planning with unknown and dynamic obstacles.
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