Orient_Tbot_Polaris

This project aims to autonomously orient the Turtlebot3 to Polaris (the North Star) from any given location on Earth.

Problem statement

The Polaris star is aligned with True North from anywhere on Earth. However, Magnetic North and True North are not the same almost anywhere on Earth. This is caused by the fact that the Earth's magnetic poles are not aligned with its axis of rotation, and drift on a yearly basis. Therefore, to compute True North heading, knowing the Magnetic Declination is necessary in addition to magnetic heading. By adding the Magnetic Declination to the Magnetic North heading, we can obtain the True North heading. The Magnetic Declination can be computed using the World Magnetic Model 2020-2025, and is a function of latitude, longitude and altitude above sea level.

The Turtlebot3 can execute velocity commands in x and y and can rotate on itself around the z axis. It is equipped with an IMU incorporating a magnetometer, which allows it to compute its absolute heading with respect to magnetic North, in the ENU frame of reference. To achieve its objective, this ROS implementation performs the following tasks:

• Given a latitude, longitude and altitude, calculate the True North heading, corresponding to the North Pole.
• Orient the Turtlebot to the True North heading, observe data from the /odom topic and publish angular velocity commands to the /cmd_vel topic.
• Simulate the Turtlebot in the Gazebo simulator in order to validate the implementation.

Setup

Dependencies

This package requires ROS Melodic and Gazebo 9 and was tested on Ubuntu 18.04. It also requires the turtlebot3 packages, which can be installed with

sudo apt install ros-melodic-turtlebot3-*

Installation

First clone the repository into your catkin workspace src folder. From your catkin workspace, build and source the package using

catkin build turtle_polaris

source devel/setup.bash

You will also need to setup an environment variable to define which Turtlebot3 model you want to use (this package works for all). For example, to set up the burger model as your default model in your .bashrc, do:

echo "export TURTLEBOT3_MODEL=burger" >> ~/.bashrc

source ~/.bashrc

Execution

The package is designed to run directly on the Turtlebot3 or in parallel with a simulated model in Gazebo.

To run on the Turtlebot3, launch: roslaunch turtle_polaris turtlebot3_controller.launch

To launch the simulation environment, launch: roslaunch turtle_polaris turtlebot3_sim.launch

Alternatively, you can launch both at the same time using: roslaunch turtle_polaris turtle_to_polaris_main.launch

turtlebot3_controller.launch and turtle_to_polaris_main.launch accept 3 launch arguments: lat, lon, and alt. They represent latitude (deg_dec), longitude (deg_dec) and altitude above sea level (m). They are set to 0.0 by default.

turtlebot3_sim.launch accepts 1 launch argument: yaw (rad). It represents the initial yaw of the robot and is set to 0.0 by default (due East).

Implementation details

The controller is implemented in the turtle_polaris_node.py file and incorporates methods to obtain the current yaw from the /odom topic and send an appropriate yaw rate command through the /cmd_vel topic. Additionally, the node depends on 3 other files:

• utils.py: contains the Utils class. The class initialises the publisher, subscriber and loads the ROS parameters.
• PI_controller.py: contains the PI class. The class is a PI controller that allows to compute appropriate yaw rate commands for the robot. Although, in this case, it seems that a simple unit P controller gives the best results. Therefore the I gain is set to 0.
• lib/mag_declination/declination_wrapper.py: A wrapper file that contains functions to determine the True North Heading from computing the Magnetic Declination. The function computing the magnetic declination given a latitude, longitude and altitude is implemented in C, and is stored in the compiled library file declination.so. It is based on the World Magnetic Model (WMW) for the years 2020-2025 and on open-source software released by NOAA (the National Oceanic and Atmospheric Administration). As far as the author is aware, this makes it the only publicly available library to compute True North in ROS (using Magnetic North, longitude, latitude and altitude as inputs).

declination.so is created from the declination.c file using coefficients and functions made publicly available by NOAA in the WMM.COF and GeomagnetismLibrary.c files. If required, declination.so can be recompiled from the src/turtle_polaris/src/lib/mag_declination folder using:

cc -fPIC -shared -o declination_test.so declination.c GeomagnetismLibrary.c

Test cases

Several tests cases are designed to check that the robot attains the correct orientation from different locations on Earth. The test is considered successful if the current yaw rate and the error between the True North heading and the current yaw are both under 0.1 rad/s and rad, respectively. The test automatically fails if it does not reach a successful state within 10 seconds.

5 test cases are implemented and described in the table below. The True North Heading is defined as the heading of True North in the ODOM ENU reference frame, that represents Magnetic North as pi/2. It is obtained by first calculating the magnetic declination using the World Magnetic Model at epoch 2021. The declination is then converted to radian and added to the Magnetic North value (pi/2).

Test	Location	Comment	Latitude	Longitude	Altitude (m)	True North Heading (deg)
1	Equator	Default	0.0	0.0	0.0	85.4945
2	The North Face HQ	Just a pun	40.29377	-121.66497	0.0	103.7333
3	The Mariana Trench	Preparing for the amphibious update	11.35	142.2	-10984	90.5167
4	The North Pole	Here any heading works	90.0	0.0	0.0	95.7333
5	The Magnetic North Pole	Would be impossible in the real world (see Limitations)	86.83	164.07	0.0	-78.3333

Known limitations

The following limitations are identified in the current implementation:

• The Turtlebot3 does not have a GPS, so the latitude, longitude and altitude information need to be inputted manually by the user on launch.
• The Turtlebot3 will not adjust its heading if it is displaced after launch. However this is intentional as estimates of distance travelled would be inaccurate without a GPS.
• The computed magnetic declination is only accurate for the year 2021 as the location of the Magnetic North Pole drifts on a yearly basis. However it is possible to update the year by changing a single line in the code. It was not implemented as an autonomous change as it would greatly complexify the testing architecture.
• In the real world, the reading from the magnetometer would become inaccurate around the North and South magnetic poles. This is due to the fact that the vertical component of the magnetic field becomes larger than the horizontal component in those areas, which are known as Blackout Zones. Both test case 4 and 5 are located in Blackout Zones and therefore would not be practical in the real world. They are present to ensure that the controller is able to handle edge cases without crashing or getting stuck.

Future work

In the future, the following improvements could be achieved:

• Validate the implementation on a real Turtlebot3 robot, as it was only ran in the Gazebo simulator so far.
• Add a GPS module in order to automatically obtain the latitude, longitude and altitude information. Most modern GPS chips incorporate the World Magnetic Model and therefore the computation of the magnetic declination may become obsolete. Additionally, the GPS could be used as an heading source if two precise and far apart GPS antennas are used. Alternatively the heading may also be recovered by analysing the past GPS data after some movement of the robot. This would allow for a more accurate heading estimation anywhere on Earth, but in particular in the Blackout Zones.
• The above would also enable the robot to be moving while conserving a notion of where the True North heading is located.
• The above improvements may require a slight rework of the implementation structure, for example by enabling separate threads for each publisher, to allow for a reduction of the delay between messages or commands.
• There was only a single global integration test implemented in this version due to time constraints. More test cases should be implemented that perform unit tests on each of the methods and classes.

References

1. Chulliat, Arnaud, et al. "The US/UK World Magnetic Model for 2020-2025: Technical Report." (2020).

2. WMM software: https://www.ngdc.noaa.gov/geomag/WMM/soft.shtml