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# Team NCTU: Toward AI-Driving for Autonomous Surface Vehicles - From
Duckietown to RobotX

Yi-Wei Huang1, Tzu-Kuan Chuang1, Ni-Ching Lin1 Yu-Chieh Hsiao1, Pin-Wei Chen1,
Ching-Tang Hung2,
Shih-Hsing Liu1, Hsiao-Sheng Chen1, Ya-Hsiu Hsieh1,
Ching-Tang Hung2, Yen-Hsiang Huang2,
Yu-Xuan Chen3, Kuan-Lin Chen3, Ya-Jou Lan3,
Chao-Chun Hsu1, Chun-Yi Lin1, Jhih-Ying Li1,
Jui-Te Huang1, Yu-Jen Menn1, Sin-Kiat Lim1,
Kim-Boon Lua3, Chia-Hung Dylan Tsai3, Chi-Fang Chen2, and Hsueh-Cheng Wang∗,1
1Department of Electrical and Computer Engineering, National Chiao Tung
University, Taiwan. Corresponding author email:
<EMAIL_ADDRESS>of Engineering Science and Ocean
Engineering, National Taiwan University, Taiwan. 3Department of Mechanical
Engineering, National Chiao Tung University, Taiwan.

###### Abstract

Robotic software and hardware systems of autonomous surface vehicles have been
developed in transportation, military, and ocean researches for decades.
Previous efforts in RobotX Challenges 2014 and 2016 facilitates the
developments for important tasks such as obstacle avoidance and docking. Team
NCTU is motivated by the AI Driving Olympics (AI-DO) developed by the
Duckietown community, and adopts the principles to RobotX challenge. With the
containerization (Docker) and uniformed AI agent (with observations and
actions), we could better 1) integrate solutions developed in different
middlewares (ROS and MOOS), 2) develop essential functionalities of from
simulation (Gazebo) to real robots (either miniaturized or full-sized WAM-V),
and 3) compare different approaches either from classic model-based or
learning-based. Finally, we setup an outdoor on-surface platform with
localization services for evaluation. Some of the preliminary results will be
presented for the Team NCTU participations of the RobotX competition in Hawaii
in 2018.

##  I Introduction

RobotX competition has brought together the top schools among the nations
around oceans, and enhanced the developments of both hardware designs and
software algorithms for perceptions and propulsions of unmanned surface
vehicles. Perceptions play an important role together with state estimation
and motion planning for autonomous vehicles. The participated teams have been
working toward robustness to degradation caused by motion, scale and
perspective transformation from different viewing positions, warp and
occlusion, and variants of color from light condition, and speed and accuracy
to support real-time decision-making.

Nevertheless, Building an autonomous unmanned marine system is challenging in
many aspects. The hardware should be robust enough to maintain functionalities
in different weather conditions. Waterproof design, compact electronics,
together with cooling system are crucial for weather conditions of heavy rain,
strong winds and the blistering sun. Due to the resource constrained of power
and computation, realtime algorithms should be adapted for overall
performance. Those challenges remain due to the uncertainties of the marine
environments, and the lack of baselines and standardized evaluations because
benchmarking in marine environments is hard. More importantly, there are still
big questions arisen from the previous RobotX competitions.

Figure 1: We proposed an autonomous surface/underwater system with modular
design and is compatible both with ROS and MOOS. The system is capable of
running in real robots, minitured robots and simulations. The capability of
running in multiple platforms provide us better tools to develop deep learning
algorithms.

  1. 1.

What are the basic principles to manage multiple tasks and to advance the
developments, instead of just a set of clever hacks on individual tasks?

  2. 2.

Many of the tasks have some hand-tuned parameters that were optimized for the
tasks during the competition. How could the developed system/techniques be
generalized to other scenarios, on other robots, or in other environments?

  3. 3.

Can we use simulation environments to facilitate the developments? What are
the gaps between real and virtual environments and how to bring the gaps
closer?

Team NCTU’s technical approaches are motivated from the challenges and big
questions above. The recent mega trends of AI have fostered researchers in
robotics, machine learning, and other fields together. In particular, we wish
to adopt the principles of the AI Driving Olympics (AI-DO) [1, 2] hosted in
NIPS 2018 into RobotX competition. The AI-DO is developed by the Duckietown
community. The project was initiated in MIT in 2016 and is now offered as
university courses in ETH Zurich, University of Montreal, and Toyota
Technological Institute at Chicago, and National Chiao Tung University (NCTU)
in 2017. Duckietown [3] is an open, reproducible, and inexpensive robotic
education and research platform. A team of vehicles are built upon Robot
Operation System (ROS) and include an onboard monocular camera and an embedded
computer. A miniaturized city (Duckietown) with roads, signage, and obstacles
is designed to tackle the problems of autonomy. The Duckietown platform
started to embrace Docker and deep learning in 2018 and host the competitions
of a few tasks via learning approaches such as Convolution Neural Network
(CNN) and Deep Reinforcement Learning. Here we wish to transform such
methodologies into the domain of unmanned surface vehicles.

We summarize our contributions as follows:

  1. 1.

With the principles of containerization (Docker), we designed and built an
autonomous unmanned marine system with the hardware and software that is
compatible for two commonly-used middlewares: ROS and MOOS. The
containerization allows to a) develop under different middlewares, b) deploy
on real and simulation environments, and c) modularize and compare algorithms
for the RobotX tasks.

  2. 2.

The uniformed AI agent framework with observations and actions facilitate
comparisons between classic and learning-based algorithms. In particular, we
tackle the problems of a) the placard detection and 3D object recognition
carried out in classic feature-based vs. learning-based methods, b) obstacle
avoidance via classical methods vs. deep reinforcement learning approaches.

  3. 3.

We built an outdoor on-surface motion capture system based on 3D LiDAR and 2D
vision-based approaches as benchmarks for further research purposes.

Figure 2: From duckietown to RobotX

##  II Literature Review

###  II-A RobotX 2014 and 2016

RobotX has already been held for 2 times in 2014 and 2016. The 2014
championship team MIT-Olin’s [4] uses IvP-helm [5] to achieve multi-objective
optimization, such as transit to target waypoint while avoiding obstacles. The
MOOS [6] framework operates the speed and heading which are generated by IvP
Helm and also process data, for instance, GPS, object map, PID controller, and
so on. The 2016 championship team Team NaviGator AMS [7] utilize ROS [8] as
middleware. That year added a new mission about underwater shape
identification. The team designed underwater vehicle Anglerfish [9] by
themselves which can be controlled by the NaviGator ASV via a 30-metered
tether providing power and ethernet. Most of the teams in the past two
competitions apply the algorithms about detection and motion without using
machine learning methods.

###  II-B Learning Approaches for Mobile Robots

Recently, deep Convolutional Neural Networks (CNN) have been used to achieve
autonomous trail or lane following. Giusti et al. [10] tackled autonomous
forest or mountain trail-following using a single monocular camera mounted on
a mobile robot, such as a micro-aerial vehicle. Unlike the previous
literature, they focused on trail segmentation and used low-level features to
develop a supervised learning approach using a deep CNN classifier. The
trained CNN classifier was shown to follow unseen trails using a quadrotor.
Deep driving [11] categorizes the autonomous driving work into three
paradigms. _Behavior Reflex_ is known as a low-level approach for constructing
a direct mapping from the image/sensory inputs to produce a steering motion.
This is done by means of a deep CNN trained by labels generated from human
driving along a road or in virtual environments. _Mediated perception_ is the
recognition of driving-relevant objects, e.g., lanes, traffic signs, traffic
lights, cars, or pedestrians. The recognition results are then combined into a
consistent world representation of the cars and immediate surroundings.
_Direct perception_ falls between mediated perception and behavior reflex. It
proposes to learn a mapping from an image to estimate several meaningful
states of the road situation, such as the angle of the car relative to the
road and the lateral distance to lane markings. With the state estimation,
other filters or FSMs and controllers can be applied. The forest-trail-
following vehicle in [10] belongs to behavior reflex, whereas the Duckietown
falls into the direct perception paradigm.

In the context of deep learning, the most commonly used method for simulation
to real environment is transfer learning [12, 13]. By gathering data from the
target domain in addition to the source domain closes the gap between
simulation and the reality. [14, 15] uses data alignment to tackle with
simulation to real problems for robotics arm pose estimation. [16, 17] proved
that doing simple but precise tasks in simulations can be transferred to real
world robots for more complex and general tasks. [18] connected the layers of
deep learning models trained with simulation data and real world data
together. It resulted features trained in virtual environments usable in real
world scenarios.

##  III Design Strategy

###  III-A Enabling Hardware Systems for AI Computing

For the first time building such a sophisticated system, it is very crucial to
do every possible evaluation beforehand. It just happens that we’ve been
working on a project called ”Duckietown”, a miniaturized AI self-driving car
platform that runs on ROS. The cars a.k.a ”duckiebots” use AI to navigate
around and communicate with other duckiebots. We think it would be interesting
to apply the AI technology to our Autonomous Maritime System(AMS). The
duckiebots could provide a miniaturized environment for testing our
algorithms.

###  III-B From Simulation to Real Environments

In addition to the duckietown platform as an simulation, using software
simulation is also important for our proof of concept. We use ROS as
middleware, so Gazebo [19] is the obvious solution due to the compatibility to
ROS. Using the advantage of ROS, we could simply interface with simultation
and real robots by publishing and subsribing corresponding messages. A few
parameters should be adjusted to fit the real environment.

###  III-C Containerized Algorithms for Deployable Softwares

To deploy a variety of different algorithms on various environments, software
dependencies may be troubling. A decent solution for it is to containerize
algorithms. By using Docker, every algorithm is like a building block, which
is easy to switch to one another. The plug and play feature on docker
containers provide us with simple deployment on both simulation and real
environments.

###  III-D Comparing Deep Learning to Classic Approaches

Deep learning has influenced the robotic research in the past few years. The
challenge has always been proving deep learning is better than classic
approaches. We believe that both are good but in different aspects. Classic
approaches may deal with a problem with a really great performance, on the
other hand deep learning methods might be more reliable to unexpected
environment changes. Our goal is to compare the two and discuss the pros and
cons of each method.

##  IV Vehicle Design

The WAM-V system has one multi-enclosures on payload which can be seen in Fig.
3, which split into two power enclosures, one sensor enclosure, one controller
enclosure, and one hydronphone enclosure.

Figure 3: Hardware

###  IV-A Propulsion

Two forward thrusts are used for the differential drive system. Each motor is
capable of 80 lbs of thrust. It is the simplest to implement with the least
amount of cost. We once considered holonomic drive which enables the mobility
of the USV, but it requires at least three thrusters and it has much more
complicated control motion. In addition, we think there must be some reason
that no holonomic drive USV is currently working in the ocean.

###  IV-B Sensor System

The sensor system is build as an sensor tower and an independent sensor for
underwater acoustic array for the competition. The sensor tower has 4 levels,
each mounted with different sensors. (shown as Fig. 3) One 3D LiDAR, three
depth cameras, an IMU, and a GPS are used to sense the environment. These
sensors could localize our USV and target objects. There is also an underwater
hydrophone array for detecting underwater pingers.

###  IV-C Computation

This paper presents a multi-computing-unit system. A Industrial Personal
Computer(IPC) served as the main computing unit. Through ethernet it
communicates with all other computing units, such as Nvidia Jetson TX2, and
Raspberry Pi 3 for different purposes. The Nvidia Jetson TX2 is used to gather
depth camera sensor data and sent back to the IPC. The Raspberry Pi 3 is used
to control motors. Every unit in the system is connected by ethernet and
communicate with ROS.

TABLE I: Computation Units Computation Units |  Number |  Processor |  Spec/Used
---|---|---|---
ASUS Laptop (GX501) | 1 | GPU | GeForce GTX 1050 Ti
NVidia Jeson TX2 | 3 | GPU | Pascal 256 CUDA cores
Raspberry Pi 3 (Ne- | 9 | VPU | Myriad 2 Vision
ural Compute Stick) |  |  | Processing Unit
Raspberry Pi 3 | 1 |  | Propulsion
Raspberry Pi 3 | 1 |  | Visual Feedback
Raspberry Pi 3 | 1 |  | Launching and Recovery
Raspberry Pi 3 | 1 |  | Detect and Deliver

##  V Software system design

Figure 4: The software architecture

###  V-A Overall System

The software is built upon the ROS interface, several nodes are built for
distinct functionalites and they communicate with each other via ROS messages
and services. The ROS package tree contains nodes shown in Figure 4

There are nodes that deal with path planning, localization, control,
perception, classification, etc. Some of the ROS nodes are contained in docker
for easier deployment.

###  V-B AI Agent

To generalize the usage of this system, we introduce the concept of AI agent.
The idea is to build it so its compatible for OpenAI gym [20].

Figure 5: The relationship between the AI agent and the environment

Figure 5 shows that the agent should output observations and rewards for each
input action. The design of the agent should output higher rewards for correct
actions. Then the algorithm tries to interact with the agent and learn what
the AI agent wants it to learn. So for each task there is at least one AI
agent and each agent could have different observation from various of sensors.

###  V-C MOOS and ROS

The Mission Oriented Operating System (MOOS) [6] and the Robot Operating
System (ROS) [8] are both robotic frameworks which provide the communication
between different robots and components.

ROS is an open source project which is compatible of using C++ and Python as
development languages. In ROS, processing units are called ”Nodes” and they
communicate with each other by ”Messages” and ”Services”. A central monitor
program named ”ROS Master” controls all the status of nodes and handles all
the ”messages” and ”services” exchanged among the ROS ”nodes”. Since there are
majority of users and thousands of modules have been developed, ROS already
became the most commonly-used middleware for robotics. Lots of robots such as
PR2, Atlas, UR5, Turtlebot use this open source software as their software
framework.

MOOS-IvP is the combination of two open source projects: MOOS and Ivp Helm.
MOOS is developed by the University of Oxford which and is designed to be the
core of autonomy middleware. While IvP Helm is developed by MIT used for
multi-objective optimization between competing behaviors. Most of the MOOS-IvP
projects are applied in the field of unmanned surface vehicle and underwater
acoustics and large influence in the field of marine robots for years.

This paper [21] from Georgia Tech presented some advantages and disadvantages
of these two middlewares. MOOS is more oriented towards onboard publish-
subscribe architecture by using its community database ”MOOSDB” and more
lightweight. In addition, there are hundreds of executable behaviors,
simulations, and MOOS Apps developed by the marine robotics community. This
leads to easy development of your own algorithms for USVs. On the other hand,
ROS is more general and provides multi-platform services which is less painful
for system integration. Moreover, it has many of the low-level device control
interfaces and components int the hardware abstraction layer. ROS also
included Gazebo, a 3D simulation for general robotics application, on the
contrary MOOS only offers 2D simulation. However, development in Gazebo is
much complicated than in MOOS.

We chose to use both frameworks for taking advantages from each. In order to
cooperate the two frameworks, we use MOOS-ROS Bridge [22] to communicate these
two robotics middlewares. We modified and added a few features for better
performance in applications needed by our system.

###  V-D Localization

One of the critical things to do is to obtain the vessel’s pose. Without the
poses, the vessel wouldn’t know where it is not to mention navigate to a
position. We implement the localization with a Hector GPS and a microstrain 9
DoF IMU. GPS datum and IMU datum are fused together using a Gaussian filter.
This filter stablizes the localizaton output. Posistion and Orientation are
calculated separately.

###  V-E Control and Navigation

Another crucial feature is to control the vessel and to navigate from one
point to another. We designed our WAM-V’s with a differential drive motion
model, therefore linear and angular could be controlled separately. We use a
PID controller for heading control and a cascade PID controller for the
position. We chose the cascade PID controller to control position because with
both position and velocity feedback, it could provide better performance for
tasks i.e. station keeping.

For navigation, we implement the pure pursuit algorithm for waypoint
navigation. The pure pursuit algorith makes the trajectory smoother by
reducing sharp turns. Figure 6 shows the trajectory for our WAM-V executing
waypoint navigation. The waypoints are a the points of a square with a 15
meter edge. It show the turns on the corners are smoothed out.

Figure 6: The green line shows trajectory of the vessel executing a square
movement. Other colored points are the pointcloud from the LiDAR data.

###  V-F Object Classification

Due to the precarious weather and changeable lighting conditions which can
strongly impact the color of the object, we chose to use the pointclouds
gathered from the LIDAR for object classification. A brief introduction of the
algorithm pipeline is as follows. First, for the preprocessing stage, we apply
RANSAC and noise filter to remove the points from the sea level and random
noises, leaving the objects remaining in the pointcloud. After the
preprocessing process, we apply a clustering algorithm to separate each object
for each another. Then we project each object’s pointcloud to X-Y, Y-Z and X-Z
planes (according to the LIDAR’s coordinate frame) and saved each plane
projection to one of the RGB channels of an image. (Figure 7) We now obtain
the RGB image and named it as the ”flattened pointcloud”. This ”flattened
pointcloud” remains some of the 3D information and at the same time is a more
compact datatpe compared to the raw pointcloud.

Figure 7: Each target object’s pointcloud is projected to the X-Y, Y-Z and X-Z
planes then the three flattened images saved to the R, G, B channels of a
2D-image

However, the projection is related to the LiDAR’s orientation, different
rotations of the WAM-V cause the ”flattened pointcloud” of the same object to
differ a lot. This may lead to bad performance for classification afterwards.
To cope with this problem, we simply transform the coordinate frame to the
object’s frame which sets the origin to the center of the object and the x
axes. This resulted the flatted image be consistent as the WAM-V change the
orientation. Figure 8.

Figure 8: With the rotation technique, the flattened pointcloud from the same
object but 4 different viewing angles looks almost identical compared to those
with out the rotation process. This improves our classification performance.

For each class we gather approximately 700 ”flatten pointcloud” images, with
500 images from Gazebo virtual environment and 200 images from the real world
(Bamboo lake in NCTU, Taiwan). We have 5 different classes, which are obstacle
buoys, totem buoys, the dock and the box for the detect and deliver task.

After collecting our dataset, we train them with CaffeNet and got an accuracy
of 95.4% in gazebo testing dataset Figure 9 and 87.7% in real world testing
dataset. The decrease of accuracy in the real world testing dataset is mainly
because the object is too far from the LIDAR. The obtained sparse pointcloud
leads to worse performance. But overall, it is still a decent algorithm for
the tasks in RobotX.

Figure 9: We test the object classification in marine Gazebo environment, and
get an well performance

###  V-G Placard Detection

For the placard detection algorithm in the task identify the dock, most of the
traditional methods based on feature matching suffered from illumination
variance, perspective transformation, and occlusion. And the methods were
limited to scaling up with more types of placards. To overcome those
challenges, a deep CNN classifier was utilized to identify the placards. The
training data was collected from virtual and semi-realistic environments which
are more accessible. We collect data by driving the vehicle in different
trajectories shown in Fig. 10, the data contained different perspective
transformation, and some with occlusion. Our CNN model is based on CaffeNet
[23] but using network surgery techniques to reconfigure it for having 10
output classess. The 10 classes represent nine different types of placards and
one background. After training from virtual and semi-realistic environments,
the CNN classifier is applied to perform placard identification with MSER
region proposals input in real-world environment. As shown in Fig. 11, the
green, black, and white boxes represent the green circle class, background
class, and predictions under threshold respectively.

Figure 10: The training data for CNN placard classifier was collected from
virtual and real environments by driving vehicle following different
trajectories. The data contains data with a variety of perspective
transformation, with occlusion, and illumination variance. Left: semi-
realistic environment Duckietown [24]. Right: virtual environment Gazebo.
Figure 11: The CNN classifier trained from virtual and semi-realistic
environments is applied to identify placard in real-world environments. Green
boxes: green circle class. White boxes: predictions under threshold. Black
boxes: background class.

###  V-H Docking Motion

Inspired by the previous work [25], an end-to-end deep CNN model was deployed
to predict three motion probabilities with single RGB image input. The
imitation learning process is to gather training data by contolling a vehicle
mounted with three different heading cameras torwards a docking bay. Shown in
the left of Fig. 12, the data collected from three cameras was automatically
labelled into three classes: turn left, go straight, turn right. The
probabilities of three motion classes outputs were then calculated to the
motor commands of the differential-driven vessel. The right Fig. 12 showed the
images from a single camera mounted on ASV with different heading angles to
the docking bay in real-world environments. And the images could be predictied
into correct motion classes for the following docking motion control.

Figure 12: An end-to-end deep CNN model was used to predict motion classes for
the docking process with a single RGB image as input. Left: training data
collected by three cameras with different mounting angles. The datum is
automatically labeled into three motion classes. Right: real-world motion
class predictions with images of a single camera equipped on the ASV.

###  V-I Totem Circling

For the totem circling task, we implemented it in the classical way. Totem
detection is achieved by the object detection discussed in previous subsection
therefore we could get the spatial information of the totems. Then we
formulate the circling problem as figure 13. The two variables d and phi are
used to describe the vehicle’s position. If the vehicle is performing a
circulating action, d will be the rotating radius R and phi would be zero.
Therefore, by using 2 PID controllers to control d and phi, the circulation
motion is done.

This algorithm is implemented in both the Duckietown and Gazebo
simulations(Figurefigure 13). Both of them are robust enough to complete at
least 30 rounds.

Figure 13: Robots doing totem circling in two simulation environments. The red
lines show their trajectories Top Left: Duckietown. Lower left: Gazebo. Top
right: the problem formulation of robot state: d and phi. Lower right: The d
and phi through time for the gazbebo simulation.

###  V-J Obstacle Avoidance

Obstacle avoidance is one of the basic features for mobile robots and there
are plenty of different algorithms to solve this problem. In this section, we
are discussing three algorithms for this problem: MOOS obstacle manager,
minimum angle real-time path planning and deep reinforcement learning.
Different techniques may all solve the problem, but the meaning behind it
could be quite different. The first method is the obstacle avoidance feature
included in MOOS. It is mainly composed of three parts. The pFeatureTracker
App manages objects’ convex polygon, position, and map. The pObstacleMgr App
sends the OBSTACLE_ALERT to the behavior. The BHV_AvoidObstacle is the
behavior function in MOOS-IvP Helm which maneuvers the vehicle to avoid the
obstacles. In response to different situations, the user has many
configuration parameters to adjust for the AvoidObstacle Behavior. This method
is based on a priority policy to avoid obstacles which may be useful in many
scenarios.

The second method we implemented the minimum angle real-time path planning,
which is based on [26]. Basically, the algorithm forms a line segment by
connecting the start point and the goal point, then checks whether this line
collides with objects or not. If collision occurs, then it finds the points on
the right side and left side of the obstacle as candidates. Then the turning
angles of both the candidates are calculated. The candidate with a smaller
angle will be picked and considered as a new starting point. Then we repeat
the process of checking the new line segment that is connecting the new
starting point and goal point. By doing this iteratively until the starting
point is close to the goal point, we could find a path that connects the
original starting point to the goal point without hitting obstacles.

The last method we implemented for obstacle avoidance by Reinforcement
learning. This is a well known problem for reinforcement learning. Work [27]
has been done to solve this problem using a 2D LiDAR as input with two classic
reinforcement learning algorithms: Q learning and SARSA. Results are very
promising in simply built simulation environments. However, with a more
complex sensor input, it is common that there are thousands or even millions
of robot states. This resulted in the traditional reinforcement learning
almost impossible to train. Deep reinforcement learning overcomes this problem
by replacing policy tables with Deep Neural Networks(DNN). We’ve designed our
software as an AI agent(mentioned previously), so it is simple to implement it
for deep reinforcement learning. For this task, first we set the action space
as ⟨go_straight, turn_left, turn_right ⟩. Then we downsampled the LiDAR data
as the observation. Finally, we set the reward as r a function of observation
o and action a.The design of the reward function is simply penalize collisions
and rewarding more for straight movement compared to turns for preventing the
agent spinning on the same spot. By training iteratively, the DNN learns the
policy. On an average of 100 episodes the agent learns to avoid obstacles in
100 steps. While this method seems workable and simple. However, some strange
behaviors sometimes occur on some agents, for example, some agents only turn
right to avoid obstacles. The agents only learn from the reward functions, so
it makes total sense it would learn this result. Therefore it is important to
carefully design the reward function.

###  V-K Underwater Manipulation

For the underwater manipulation task we modified the inspector 2 from Seadrone
Inc as our AUV. The AUV is equipped with 5 thrusters which provided 3 DoF in
translation and 1 dof in orientation(yaw) movement. Onboard sensors include a
pressure sensor, leak sensors, IMU and a camera with extra led lighting. We
added an underwater gripper from Blue Robotics for grasping rings for the
task.

Using classic image processing algorithms, we are able to detect the pose of
the ring, steer the AUV to grasping point using PID control and retrieve the
ring to the surface.

Figure 14: AUV detecting and retrieving ring autonomously

##  VI Experimental Results

All the tests and trials of our AMS are done in the lake located in our
campus. This is our first year doing this so we did a lot to get our WAM-V in
the lake. We managed to build a launching platform which consists of a slope
with a winching system. Neither of us had any experience so it was a trial-
and-error process. We also built the equipments from totems buoys to docks by
hand.

After the WAM-V is launched into the lake, we did some test for basic
functionalities(e.g. localization, motion control and perception), the problem
we encountered is that we couldn’t do a quantitative analysis for all the
experiments related to localization. We could only do qualitative analysis and
just come up to a more general conclusion. For instance, we did a trial of 10
rounds for the WAM-V performing obstacle avoidance and it completed 9 rounds.

Therefore, later we decided to build a vision-based localization system
Figure. 15 by placing apriltags [28] on floating pontoon cubes anchored with
concrete blocks. This could provide us more quantitative results for our AMS
localization, giving us more prove whether our algorithms work better.

Figure 15: The system to localize marine robotics using RGB camera with
AprilTag [28]. Top left: Vision-based localization system in real environment
with our WAM-V. Top right: Vision-based localization tower with and RGB
camera. Lower left: Trajectory in real environment using vision-based
localization system. Lower right: WAM-V velocity calculate from the vision-
based localization system.

##  VII CONCLUSIONS

Our development of the whole system for the RobotX 2018 competition is
meaningful for us being part of the unmanned autonomous vessel research. We
focus not only on making our system work in the competition but also building
a foundation for further researches. Our final goal is to bring a better
platform and modularized software for easier development and deployment that
every developer could use. This could bring the community closer together by
sharing work based on the same framework and also let researchers focus on
parts they care about. In our case we brought some deep learning / deep
reinforcement learning algorithms and hope to bring more cutting-edge deep
learning technologies to the field of marine robotics.

## ACKNOWLEDGMENT

The research was supported by National Chiao Tung University Innovative
Creative Technology (NCTU-ICT), Ministry of Science and Technology, Taiwan
(grant numbers 107-2623-E-009 -005 -D and 105-2511-S-009-017-MY3), . We are
also grateful for the help by Santani Teng, Robert Katzschmann, Ilenia
Tinnirello, and Daniele Croce.

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# Is the Spiral Galaxy a Cosmic Hurricane?

CAO Zexin11affiliation<EMAIL_ADDRESS>College of Science, Shenyang
Aerospace University, Shenyang 110136, China  LIU Ling, ZHENG Tingting
College of Physics Science and Technology, Shenyang Normal University,
ShenYang 110034, China

###### Abstract

It is discussed that the formation of the spiral galaxies is driven by the
cosmic background rotation, not a result of an isolated evolution proposed by
the density wave theory. To analyze the motions of the galaxies, a simple
double particle galaxy model is considered and the Coriolis force formed by
the rotational background is introduced. The numerical analysis shows that not
only the trajectory of the particle is the spiral shape, but also the
relationship between the velocity and the radius reveals both the existence of
spiral arm and the change of the arm number. In addition, the results of the
three-dimensional simulation also give the warped structure of the spiral
galaxies, and shows that the disc surface of the warped galaxy, like a
spinning coins on the table, exists a whole overturning movement. Through the
analysis, it can be concluded that the background environment of the spiral
galaxies have a large-scale rotation, and both the formation and evolution of
hurricane-like spiral galaxies are driven by this background rotation.

Galaxy:background rotation — Galaxy:spiral galaxy — Galaxy:Coriolis force —
Galaxy:warped structure— Galaxy:spiral arm

=100

##  1 Introduction

The beautiful and unusual spiral structure of spiral galaxy attracts people’s
attention all the time. Conjecture and hypothesis of the formation mechanism
have been made by many people, and a lot of investigations and verifications
have been carried out. Among those works, the density wave theory developed by
C.C. Lin and others has been acknowledged by many people(Lin & Shu (1964,
1966)). The density wave theory holds that the rotation speed and density of
the stars around the center vary in a wave motion, which forms a density
wave(Pasha (2004)).

The wave travels both along the center circle and at the same time along the
radius, therefore, the peaks with the highest density are in a spiral shape
and thus form a spiral arm. After coming into the arm area the star materials
would slow down their velocity because of the dense stars and the strengthened
gravitational field; on the other hand, the slowed down velocity of the stars
would make the stars to crowd together, which would cause the density
increases, and then the gravitational field would be strengthened further.
Thus the stability of the arms which is made up of areas of greater density
would be maintained self-consistently. According to the model of the density
wave theory, the quasi-steady solutions can be obtained from the gravitational
field equations and dynamical equation of galaxies, to demonstrate the spiral
structure of the galaxies.

The spiral structure observed from the spiral disc galaxies, such as the
galaxy M81 and M74, can be explained by the density wave theory. However, it
is difficult for the density wave theory to explain clearly for the flocculent
spiral galaxies, such as M33 and NGC 7793, which have no obvious arms
accumulation areas, but still show the spiral shapes(Puerari & Dottori (1992);
Kennicutt (1981); Sellwood (2011)). For the initial phase of the particles is
random, The simulating results according to the density wave theory should
show a variety of non-spiral structures, but the ratio of the spiral galaxies
is so high. To illustrate this case, the density wave theory is not
sufficient. In addition to the above problems, there are still no reasonable
explanations based on the density wave theory for the spiral galaxy with
multi-arms structure and for the ubiquitous warped structure of the
galaxy(Terquem & Papaloizou (2000); Kim (2014); Elmegreen (1982);
Grosb$\phi$l, Patsis & Pompei (2004)). There are other theories, which do not
yet explain the spiral structure very well(Toomre (1972); de Souza (2013);
Sellwood & Carlberg (1984); Baba, Saitoh, & Wada (2013); Reshetnikov (2016);
Gamaleldin (1995)).

The density wave theory is proposed mainly for the formation of the spiral
arm. However, the existence of the spiral arm does not mean that the
trajectory of the single moving particle will exhibit a spiral structure. It
is considered in density wave theory that the particle in the spiral galaxies
is doing the elliptical motion in the central potential. Nevertheless, even if
the spiral structure is formed, it is difficult for the galaxy to keep the
stability and sustainability of the spiral arm. Relatively, a spiral galaxy
tends to be stable. Both the local damage and the deformation of spiral
structure are difficult to be observed(Dobbs & Baba (2014)). However, the
observations show that the spiral structure of the galaxy is very stable, and
no damage phenomenon of the structure is observed. Therefore, there must be
other reasons for the formation of the spiral structure and the spiral arm.

In this work, a new view for the general existence of the spiral galaxies is
proposed that it is due to the large scale rotation of the background, and
then the spiral galaxy is not a relatively isolated system during its
evolution process. The rotation of its physical background makes the galaxies
more like a cosmic hurricane.

Based on this view point, a physical mechanism which is very different from
the density wave theory is proposed for the formation of the spiral structure
in the spiral galaxy. the problem of the galactic evolution is reduced to a
viscous two-body problem in a non-inertial system. The viscous two-body system
is simulated for researching the force upon the galactic particle and its
influence to the galaxies. The trajectory of a single galactic particle is
calculated under the actions of the gravitational force, the galaxy viscous
force and the Coriolis force. The results show that the trajectory of galactic
particle under the background rotation is a spiral structure itself, not an
elliptic orbit. And the origin of both the spiral arm and the warping
structure can be demonstrated self-consistently. Under the effect of the
rotation background, the transverse velocity of the galactic particle rotating
around the centre is mainly the result of the Coriolis force, rather than the
effect of the rotating velocity of the elliptical orbit under the action of
central gravitational force. And this transverse velocity does not need to be
explained with dark mater(Turner (2000)).

##  2 The physical mechanism in the motion of Galaxies

In the density wave theory, the formation of spiral arm is a combined results
of particles doing elliptical motion under the central potential, which
actually considers the galaxies as a relatively isolated system. Aiming at
this point, it is proposed that the spiral galaxy in cosmos is not a
relatively isolated statistical system, and its evolution is also driven with
the motion of the background. A non-inertial force evoked from the universal
background motion participates in the evolution of the galaxies, which is the
significant reason for the galactic spiral structure. Therefore, the inertial
force should be taken into account when the structure and evolution of the
galaxies are simulated. A galactic particle in its movement is attracted by
other particles with the force of gravitation. Because of the central
symmetry, the net force on every particle is centripetal. However, there is no
enough huge mass in the center to provide this kind of gravitational force to
make the particle moving in an elliptical orbit. Therefore, the galaxy is
considered as a many-body system in classical mechanics while analyzing its
kinetic mechanism.

a net viscous force is also provided from the interactions between the
galactic particles for a single particle other than both the central net force
and the non-inertial force exerted by the rotational background(Lynden-Bell &
Pringle (1974); Hofner & Sparke (1994); C. B. New, K., et al (1998); Flebbe
(1994)). This viscous force is actually produced from the gravitational forces
of other matters around the particle, i.e., the viscous force is one component
of the gravitational force. Up to now, there are no sufficient theoretical and
experimental data to give the explicit expressions for the viscous force of
the galaxies. Therefore, the viscous coefficient is taken as a free parameter,
and the viscous force is considered as proportional to the velocity of the
particle. The viscous force here is one kind of the inner gravitational force
of the whole galaxies, so the total mechanical energy of the galactic system
does not changed while a particle is under the viscous force. And the lost
energy of the single particle will make the change of the rotational velocity
of the whole galaxy. It is neglected in simulation cause its effect on the
single particle is very little.

By doing so, the evolution of galactic system can be considered as a many-body
problem under these three forces now. The spiral structure of the galaxy can
be given by many multi-body and fluid simulations coming from some galactic
theory such as the density wave theory. Nevertheless, the influence of an
inertia force can not be clearly investigated by the more complicated multi-
body and fluid simulations, and the relationship between the forces and the
galactic evolution can not be comprehended intuitively. In this work, the
kinetic properties of galaxy under those forces is analyzed with the simplest
galactic system only consisting of two particles. The research on the
evolution of the overall galaxy in detail requires further simulations of a
system with more particles. However, the simplified two-particle galaxy can
not only give the explicit conclusion, but also make the relationship of the
forces and the evolution of the galaxy comprehended more intuitively and
easier when the effect of those forces is investigated. Then the reduced
galactic system consisted of two particles makes the conclusion more
convincing. Therefore, it is necessary to carry out such analysis before the
many-body or Hydrodynamic simulations is given.

The main forces exerted on the galactic particle are the gravitational force,
viscous force and non-inertial force, so the net force on one galactic
particle can be represented as

$\vec{F}={{\vec{F}}_{g}}+{{\vec{F}}_{v}}+{{\vec{F}}_{c}}$ (1)

Where ${{\vec{F}}_{g}}$ is the net gravitational force on the particle,
${{\vec{F}}_{v}}$ is the viscous force, and ${{\vec{F}}_{c}}$ is the non-
inertial force exerted by the rotational physical background. The force
${{\vec{F}}_{c}}$ is an important factor for the galactic evolution here.
Because of the rotational symmetry of a spiral galaxy, the net gravitational
force exerted on a galactic particle by all the other galactic particles is a
centripetal force. In this simplified two-particle galaxy, the net
gravitational force is represented with the gravitational force between two
particles, so the gravitational term in equation (1) can be written as

${{\vec{F}}_{g}}=-G\frac{{{m}_{1}}{{m}_{2}}}{{{r}^{3}}}\vec{r}$ (2)

where $G$ is the gravitational constant,${{m}_{1}}$and${{m}_{2}}$ are the
masses of the two particles respectively, $\vec{r}$ is the distance vector
between two particles.

When a particle moves in a galaxy, it is also pulled by a residual
gravitational force from other particles, which forms the viscous force
exerted on this particle. The viscous force is introduced in our double
particles galaxy model, and the viscous force is supposed to be proportional
to the velocity of the particle empirically, i.e.

${{\vec{F}}_{v}}=-\eta\vec{v}$ (3)

where $\eta$ is the viscosity coefficient for the galactic particles.
According to the data from current galaxy researches, there is not yet a
convincing numerical value for $\eta$, which is taken as a free parameter
here.

As an assumption, it is not suitable to generate the inertial force from the
cosmic background in a complicated way. There are two simple ways to provide
an inertia force, one is the uniformly accelerated motion, and another is the
uniform rotation. The same inertia acceleration is provided to each particle
in uniformly accelerated motion, which can not exert an influence on the self
evolution of the galaxy. Therefore, the influence of the background in
uniformly accelerated motion is regardless. And the inertia force provided by
the cosmic background in an uniform rotation is taken into account for the
effect of the galaxy evolution. With respect to the large scale background
rotation, the galactic scale $D$ is far less than the radius of the background
rotation $R$, i.e., $D\ll R$. So the difference of centripetal force produced
by the rotational background on each particle is omitted. Thus the inertial
force on each galactic particle produced by the uniform rotation of the
background is only Coriolis force, which can be expressed as

${{\vec{F}}_{c}}=-2m\vec{\omega}\times\vec{v}$ (4)

where $m$ is the mass of the galactic particle, and $\vec{v}$ is the velocity
of galactic particle relative to the galactic centroid in the background
rotation frame, and $\vec{\omega}$ is the angular velocity of the background
rotation. In this case, the forces on the galactic particle under the large
scale rotation of the background are one gravitational force, one viscous
force and one Coriolis force. The net force can be expressed as

$\vec{F}=-G\frac{{{m}_{1}}{{m}_{2}}}{{{r}^{3}}}\vec{r}-\eta\vec{v}-2{{m}_{1}}\vec{\omega}\times\vec{v}$
(5)

Based on these reasonable assumption, a reduced galactic system consisted of
two particles is produced. Those particles have the same mass because of the
rotational symmetry of the galaxy, and the initial relative velocity of each
particle is set as zero. The movement of the galactic particle can be
numerically simulated with the net force in equation (5).

##  3 Simulation and analysis about viscous two-body problem

Because the main physical properties of the model is focused on here, the
dimensionless unit is used in simulating the equation (5), i.e.,
$G={{m}_{1}}={{m}_{2}}=m=1$. The dynamical equations for particles of a two-
particle galaxy can be represented as

$\left\\{\begin{aligned}
&\frac{{{d}^{2}}{{{\vec{r}}}_{1}}}{d{{t}^{2}}}=-\frac{{{{\vec{r}}}_{12}}}{r_{12}^{3}}-\eta{{{\vec{v}}}_{1}}-2\vec{\omega}\times{{{\vec{v}}}_{1}}\\\
&\frac{{{d}^{2}}{{{\vec{r}}}_{2}}}{d{{t}^{2}}}=\frac{{{{\vec{r}}}_{12}}}{r_{12}^{3}}-\eta{{{\vec{v}}}_{2}}-2\vec{\omega}\times{{{\vec{v}}}_{2}}\\\
\end{aligned}\right.$ (6)

Where ${{\vec{r}}_{12}}$ is the displacement vector of particle 1 relative to
particle 2, both ${{\vec{v}}_{1}}$ and ${{\vec{v}}_{2}}$ are the relative
velocities of particle 1 and particle 2 in the non-inertial system,
respectively, $\eta$ and $\vec{\omega}$ are the adjustable parameters. In the
simulation, the trajectories of particles in equation (6) can be calculated by
setting the initial position and the adjustable parameters, and the properties
of galactic evolution are investigated. The important results are given via
the simulating calculation.The spiral structure is conspicuous and stable in
the trajectories of particles. but also that the formation of the spiral arm
can be explained specifically through relation between the velocity and the
radius. Moreover, the unusual physical phenomenon, such as distinct warped
structure, is given by the three-dimensional simulation, which is consistent
with the real warped galaxies.

###  3.1 spiral structure

In the case of plane motion, the direction of $\vec{\omega}$ is set as Z axis,
and the centroid location of the two particles is taken as the original point.
The line connecting two particles is perpendicular to $\vec{\omega}$, and the
initial velocities of the particles are all zero, and then the motion of the
system can be investigated.

By setting without the viscous force, i.e., $\eta=0$, and giving some initial
conditions, there have no spiral structure in the trajectory calculated from
the equation (6), and the result is shown in figure 1. The trajectories show a
petal-shaped structure with sharp end, which is similar to the trajectory of
Foucault Pendulum with a zero initial velocity(Somerville (1972)). The reason
for appearing this petal shape is that only the direction of the particle
velocity is changed by Coriolis force, while the energy of the system can not
be influenced. When the particle is attractive by another one and moves
towards the center, the magnitude of the particle’s velocity is increased, and
the direction of the particle’s velocity also keeps changing under the action
of Coriolis force.

At the position where is the nearest neighborhood from the center, the
particle’s radial velocity decreases to zero, and its tangential velocity
reaches the maximum value. At this time, Coriolis force also reaches it’s
maximum value. At the tip position, the potential energy comes up to the
maximum value, both the velocity and Coriolis force are zero. this process is
repeated and the particle’s moving direction is always changed by the Coriolis
force. Then a petal-shaped structure around the center is formed in the
trajectory of the particle. It can also be seen from this trajectory that
Coriolis force does not change the energy of the system.

Figure 1: Moving trajectories of double particles with $\eta=0$

when the viscosity coefficient does not equal zero, the galactic particle
surrounds and tends to the original point because the particle’s energy loses
continuously for the action of viscous force. Then a spiral structure appears
in the trajectory of the particle, which is displayed in figure 1.

Figure 2: Trajectories of the double particles with $\eta=0.06$

Various shapes of the spiral structure can be given by adjusting the viscosity
coefficient and the angular velocity of the galactic background, and these
spiral structures are very similar to that in the spiral galaxies observed at
present and the tropical hurricanes. The trajectory of the spiral structure in
figure 2, for instance, is extremely consistent with that of the spiral galaxy
NGC 6814(or the Milk Way) and hurricane Alberto(2000) shown in figure
3(Hurricane Alberto (2000); NGC 6814 (2018)).

(a) Hurricane Alberto

(b) NGC 6814

Figure 3: The similar spiral structure in Hurricane Alberto and NGC 6814

It is also showed that this spiral trajectory is very in accord with that of a
logarithmic spiral function in the simulation calculation. One particle’s
trajectory in the double-particle galaxy with the initial position of
$\text{(}\pm 5,\mp 5)$ is represented as that shown in figure . The trajectory
can be fitted very well with the logarithmic spiral function

$r=2.015{{e}^{0.531\theta}}$

Therefore, that the initially static particle looks likes rotating around the
center of galaxy, is the result of Coriolis force, rather than of be attracted
by the galactic matter as an isolated system. Moreover, the previous
assumption of introducing dark matter to explain the particle’s motion as the
effect of center gravitational force should be reevaluated.

It is shown that the trajectory of the particle generated from the equation
(6) has a spiral structure consistent with that of a spiral galaxy in the
above analysis. Unlike in the density wave theory, the particle’s trajectory
is not an elliptical orbit, but is initially a spiral shape, which could
explain why there exists a similar spiral structure in the flocculent galaxy
without any explicit spiral arms. The spiral structure of the galaxies is so
stable without any broken case, primarily because the trajectory of the
particle is originally spiral, not an elliptical shape.

Figure 4: The logarithmic spiral curve fitting for a particle’s trajectory

###  3.2 The formation and evolution of spiral arm

It is impossible to simulate the formation of the spiral arm in a galaxy of
two particles, because the number of particles is too small. Nevertheless, the
velocity changing with the radius is represented in figure 5, and it can be
seen that the velocity-radius curve of the particle have some turning-back.
Considering the trajectories with $\eta=0$ in figure 1, it can be observed
that the turning-back area actually change from those endpoint driven by both
the Coriolis force and the viscous force. While the particles in a galactic
disc move along the trajectories of the spiral curve, the foregoing particle
with the turning-back will gather together near the orbit with the subsequent
particle in the same trajectory and those nearby. As a result, the higher
density area is generated, which then forms the galactic spiral arm.

Figure 5: the relationship between velocity and radius of particle motion

The hurricane on the earth also has the similar spiral shape and the similar
spiral arm under the action of Coriolis force generated from the earth spin.
Just because of this turning-back of the velocity, the clouds area with
different density is generated and forms the spiral arm-like structure of the
hurricane. Furthermore, the hurricane’s spiral arm can be explained only with
Coriolis force, while both the density wave theory and the dark matter are
needless.

If the large-scale background rotation existed, the spiral arm of the galaxy
should be formed by the turning-back driven by Coriolis force, and which is
very different from the explanation of the density wave theory. Moreover, all
the particles move steadily along their spiral trajectories, which could
explain the general existence of the spiral arm and the time stability of the
spiral structure. the broken spiral arm caused by the moving particle in an
elliptical orbit supposed in density wave theory has never been observed in
astronomy.

Further, the turning-back drives the formation of the spiral arm, and along
the circumference there have many turning-back location which can be seen in
figure 1, so the arm number in the original galaxy might be more than two.
However, during the evolution of the galaxy’s multi-arm structure, the nearby
spiral arms get together continuously due to the sustained impact of those
turning-back, and the number of arms is reduced to two.

###  3.3 The origin of thin disc structure

The thin disc structure is an significant feature of the spiral galaxies. By
analysis the physical model in equation 6, it is obtained that the formation
of the disc structure is directly associated to the viscous force
$-\eta\vec{v}$ and Coriolis force $\vec{\omega}\times\vec{v}$. During the
particles falling to the center, the velocity component perpendicular to
$\vec{\omega}$ reduces slowly due to the turning-back evoked by Coriolis
forces. However, in the direction parallel to $\vec{\omega}$, there have no
turning back for the component of Coriolis force being zero, and this energy
loss is more than the one perpendicular to $\vec{\omega}$ under the only
viscous force at the same time. The velocity component parallel to
$\vec{\omega}$ decrease more rapidly.

In this case, the particles in the direction parallel to the $\vec{\omega}$
accumulate in the thin disc plane soon. however, the particles perpendicular
to the $\vec{\omega}$ direction are still doing spiral motion far from the
center at the same time. Therefore, a thin disc is formed before long during
the evolution of the galaxy by this way.

###  3.4 The formation of the warped structure

Through setting the direction of angular velocity of the background rotation
as the z-axis, and making the straight line between the two particles no
longer in the same plane perpendicular to the $Z$-axis, the 3D trajectory of
particles is simulated too. In addition to the case of plane motion, the
three-dimensional simulation also give some important conclusion, especially
the warped structure which usually appears in the trajectories of the two-
particle galaxy. Therefore, the 3D trajectory is no longer a kind of plane
distribution.

The three-dimensional simulation of the equation (6) can be proceeded by the
following setting: the initial positions of the two particles are located at
${{\vec{r}}_{10}}=(3,5,10)$ and ${{\vec{r}}_{20}}=(5,3,10)$, respectively; the
initial velocities are all zero; and the angular velocity of the background
rotation is set as

$\vec{\omega}=\left(0.36\cos(\frac{\pi}{6}),0,0.36\sin(\frac{\pi}{6})\right)$

which is no longer set as z-axis; the viscosity coefficient is set as
$\eta=0.16$. The three-dimensional spatial trajectory of the particles is
shown in figure 6. It can be seen distinctly from the $XY$ projection that a
spatial warped structure is in the particles’ 3D trajectory. And the different
shapes of the warped structure can be also simulated in the galactic
particles’ trajectories by setting some different initial parameters.

Figure 6: 3D trajectory and its projections of two particles’ motion

When the angular velocity of the background rotation is not parallel to the
normal of the rotational galactic disc, there is a component
${{\vec{\omega}}_{\bot}}$ parallel to the rotational disc, which occurs a
component of Coriolis force $m{{\vec{\omega}}_{\bot}}\times\vec{v}$
perpendicular to the rotational plane. This force component is called as the
leaving-plane force here. The particle will move away from the rotational
plane along its normal direction under the action of this leaving-plane force.

The leaving-plane force reaches the maximum value when the particle’s velocity
are vertical to ${{\vec{\omega}}_{\bot}}$, and it is zero when the particle’s
velocity is parallel to ${{\vec{\omega}}_{\bot}}$. It can be seen that the
leaving-plane force is anti-centrosymmetric in the disc. The direction of the
leaving-plane force on one point is opposite to the one on its centrosymmetric
point. And the leaving-plane force is changed with the particle’s velocity. In
this way, the warped structure is formed by the action of this component of
the Coriolis force.

It is always a tough task to explain the warped structure of the galaxies, and
most of them need to employ dark matter (López-Corredoira, Betancort-Rijo &
Beckman (2002); Debattista & Sellwood (1999); Kerr (1957); Binney (1978)).
Different from the current theory on the warped structure, the spatial warped
structure is derived naturally from the background rotation in this work, and
no additional assumption is required. The influence of the related parameters
such as the background rotational frequency on the warped structure is also
investigated through the numerical simulations. It is shown in the simulating
results that the warped structure is a general phenomenon except the normal
direction of the disc completely parallel to the angular velocity of the
background rotation. This conclusion is consistent with the astronomical
observations(Gamaleldin (1995); Sanchez-Saavedra, Battaner & Florido (1990)).

Due to the existence of the real galactic disc, it should be noted that the
warped structures is different noticeably between the two-particle galaxy and
the many-particle galaxies. The more results approach to the real galaxies
need to be investigated through the N-body simulation. However, on the
physical relationship between Coriolis force and the warped structure, the
result given in this work is more intuitive. If the background were rotating,
the warped structure should appear certainly in the real galaxies.

###  3.5 The whole turning of the galactic disc

In addition to the formation of the warped structure, the whole turning of the
thin galactic disc can be evoked by a torque
$\vec{r}\times(m\vec{\omega}_{\bot}\times\vec{v})$ produced by the leaving-
plane force ${{\vec{\omega}}_{\bot}}$. The sum torque vector is in the thin
disc plane and passes through the center of the thin disc, and is
perpendicular to ${{\vec{\omega}}_{\bot}}$. The direction of the whole turning
of the disc, should be parellel to the torque vector.

It might be an important evidence of the overturning of the disc that the jet-
current from the center of Centaurus A turns into a form with the s-shape
through processional motion. And if there exists the background rotation, the
circumferential band formed by the historical rudiments, i.e., a small amount
of the material left during the galactic overturn process, and the other
related phenomenons about the overturning could be observed as usual. Those
reference need more observed evidence to prove.

##  4 Conclusions and prospects

A model of the simplified galaxy for its evolution is simulated and analyzed
with the existence of the background rotation in this work. The research of
the whole galactic evolution still needs the further many-body simulation or
the hydrodynamic simulation. However, with regard to the properties of the
forces and the resulting spiral structures, spiral arms and warped structures
and so on, the effects of forces can be demonstrated more clearly here, and
the conclusions are more convincing for the simplicity and intuition of the
model.

In the density wave theory, the particle is doing an elliptical motion, and
the particle’s velocity is periodic. The spiral arm is made up of areas of
greater density. Furthermore, the assumption of dark matter is introduced for
explaining the huge centripetal gravitational force for the rotation. However
in this work, the trajectory of a single particle is itself spiral, and the
high tangential velocity is associated to Coriolis force and viscous force,
not contributed by the huge centripetal gravitational force. Therefore, the
dark matter is not required yet. If there is a large scale rotation of the
galactic background indeed, the assumption of dark matter needs to be
reevaluated.

In addition, different from the explanation of the spiral arm in density wave
theory, the spiral arm is associated to turning-back of the particle’s
velocity in this work. the turning-back makes the particles in the same spiral
trajectory and the nearby areas aggregate, and impulses the form of spiral
arm. Moreover, this model can also be applied to explain the spiral arm
structures of the tropical hurricane on the earth, which can not be
demonstrated by the density wave theory under the centripetal gravitational
force obviously.

A tropical hurricane on the earth is mainly a two-dimensional structure as it
keeps close to the ground. However, the three-dimensional galaxies in the
background rotation also have some physical phenomena worthy of attention,
such as warped spiral structure, spiral arm and the whole turning of the
disc(Burns & Price (1983)). Although the background rotation need to be
confirmed by further astronomical observations, if the background rotation
exists, it can be supposed sufficiently that the spiral galaxy is exactly a
cosmic hurricane under the background rotation. According to the widespread
distribution of the spiral galaxies, the large-scale rotation in the universe
can basically be regarded as a normal and general phenomenon.

In our previous work(Cao Zexin, Chen & Liu (2003)), the horizon problem of the
rotation velocity within the Galileo rotating framework had been solved in the
special relativistic rotating frame. No horizon problem restricts a large-
scale rotation in the cosmos now. The results in that paper showed that the
large-scale rotation of the galactic background can exist. Therefore, the
percentage that the transverse Doppler red shift formed by the background
rotation occupies in the Hubble red shift is also a problem worthy of
discussing.

We appreciate the helpful comments from the anonymous referee. We thank the
students CAI Yuanqiang, GONG Jiguang, GUO Juanjuan and ZHANG Jingyu for their
helpful work in computer, and we also thank WANG Heng, JU Liping for their
helpful discussions and comments.

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