Omnidirectional Robot Odometry

This repository contains the first laboratory project for the Robotics course 2021/2022 of the Polytechnic University of Milan.

The project is implemented in ROS, an open-source robotics middleware suit.

Requirements

• ROS Melodic (Noetic is okay too)
• C++
• Ubuntu 18.04 (20.04 is okay too)

Project structure

The project contains one package (omnidirectional_robot_odometry), which root folder is the src/omnidirectional_robot_odometry/ folder. We will consider this as root folder.

The source files are under the src/ folder:

• compute_odometry.cpp: it deals with computing and resetting the odometry. It also broadcasts the odometry with the TF transforms.
• compute_velocities.cpp: it computes the robot velocities starting from the wheels information provided by the bag files.
• compute_wheel_speed: it computes the angular velocity of each wheel starting from the robot velocities.

Under the include/omnidirectional_robot_odometry/ folder there are all the header files, plus an utility file used for some constants.

The launch file starts together the three nodes and is also used for static transforms and ROS parameters.

Under srv/, msg/ and cfg/ there are, respectively, the reset odometry service definition, the custom message definition for the RPMs, and the dynamic configuration definition for changing the integration method at runtime.

Finally are defined CMakeLists.txt and package.xml for compilation purposes.

If you want to run the bags, you can find them under the bags/ folder.

Getting Started

You can either clone the repository and change directory:

$ git clone https://github.com/davide-giacomini/omnidirectional-robot-odometry.git
$ cd omnidirectional-robot-odometry/

Or you can download the zip file, and unzip it where you prefer and change the name of the directory in omnidirectional-robot-odometry/. Then, you change directory:

$ unzip <directory_name.zip> -d <destination_folder>
$ cd <path/to/destination_folder>
$ mv <directory_name/> omnidirectional-robot-odometry/
$ cd omnidirectional-robot-odometry

Build the environment with catkin:

$ catkin_make

Add ROS worspace to your system. Add the end of the bashrc file the path to the devel/setup.bash file:

$ echo "source </path/to/project/folder/>omnidirectional-robot-odometry/devel/setup.bash" >> ~/.bashrc
$ source ~/.bashrc

Warning: In case you have already define in your bashrc file a path for another workspace, comment or delete it. Each machine must have only one workspace defined.

With the launch file you can start all the nodes at the same time:

$ roslaunch omnidirectional_robot_odometry odom.launch

Once started, you can use the bags to read from the topics. Notice that the launch file has three different transforms, depending on the bag file used. If you want to correctly visualize the translation from the GT world to the odom frame, uncomment only the static transformation correspondent to the bag you are using. For example, the static transformation of the first bag is this one:

<node pkg="tf2_ros" type="static_transform_publisher" name="back_right" args="0.00815962441265583 0.0030597213190048933 0.3687083423137665 -0.011577633209526539 -0.02075166068971157 -0.019595127552747726 0.9995256066322327 world odom " />

Uncomment it when you want to use the first bag.

Using reset odometry service

To reset the odometry at runtime, you can type on command line:

rosservice call /reset_odom <x> <y> <theta>

Where you put numbers inside the brackets. For example:

rosservice call /reset_odom 2 2 0

Notice that if you want to put a negative number, you must type -- before the parameters. For example:

rosservice call /reset_odom -- -1 2.1 1.3

Using dynamic reconfigure

If you want to change at runtime the odometry integration method, you can type on command line:

rosrun rqt_reconfigure rqt_reconfigure

It will open a window where you can easily choose between Euler and Runge-Kutta integration method:

Project Description

In this project I was required to read from a bag file some information and calculate the odometry and other parameters of an omnidirectional robot. A semple is illustrated below.

I was given:

• Wheels encoder state:
  • RPM (noisy)
  • Ticks (more accurate)
• Nominal robot parameters:
  • Wheel radius (r) = 0.07m (could be a bit off)
  • Wheel position along x (l) = 0.200m
  • Wheel position along y (w) = 0.169m
  • Gear ratio (T) = 5:1
  • Encoder resolution(N): 42 CPR (Counts Per Rev.) (could be a bit off)
• Ground truth (GT) pose of the robot (acquired with OptiTrack)

And I was required to:

• Compute odometry using appropriate kinematics
  • Compute robot linear and angular velocities v, ⍵ from wheel encoders
  • Compute odometry using both Euler and Runge-Kutta integration methods
    • Add ROS parameters for initial pose
  • Calibrate (fine-tune) robot parameters to match ground truth
• Compute wheel control speeds from v, ⍵
• Add a service to reset the odometry to a specified pose (x,y,θ)
• Use dynamic reconfigure to select between the desired integration method

I created a package which contains three different nodes. Each node corresponds to a source code file and it is in charge of a different task, which is explained more in detail in the next sections.

Compute robot velocities

Given the wheel speeds of the robot from the bags, I were required to compute the robot linear and angular velocities. As a reference, I considered the formulas developed by Taheri et al. for a mecanum wheeled mobile robot.

In particular, we are interested in the equations 22, 23 and 24 of the paper, which I report below:

• v_x(t) = ( ω_fl + ω_fr + ω_rl + ω_rr ) ∙ ^r ∕ ₄
• v_y(t) = ( - ω_fl + ω_fr + ω_rl - ω_rr ) ∙ ^r ∕ ₄
• ω_z(t) = ( - ω_fl + ω_fr - ω_rl + ω_rr ) ∙ ^r ∕ _{4(lx + ly)}

Where, in our case, the subscripts refer to the position of the wheel (fl = front left, rr = rear right, etc.).

The node "compute_velocities" takes the wheel ticks published in the topic wheel_states by the bags, and then easily computes the angular velocity of each speed by using this equation:

ω = ( ^Δ_ticks ∕ _Δtime ) ∙ ( ¹ ∕ _N ) ∙ ( ¹ ∕ _T ) ∙ 2π

Where ^Δ_ticks ∕ _Δtime refers to the difference between the number of ticks divided by the period of time that has been measured. Please notice that I divided by the gear ratio because the encoders are located in the motors of the wheels. Once computing each angular velocity, the robot velocities can be computed using the aformentioned three equations, and they are eventually published as topic cmd_vel.

Compute odometry

For this task, I was required to compute the robot odometry starting from the velocities I just calculated in the previous task. Furthermore, I was required to use both Euler and Runge-Kutta integration methods.

After computing the odometry, I published it as topic odom and wrote a TF broadcaster having as father the frame odom and as children the frame base_link (odom ➔ base_link), which is basically the Reference System of the center of gravity of the robot.

All of this can be found in the node "compute_odometry", which reads from the topic cmd_vel the velocities.

Euler integration method

I used as a reference the set of slides of Professor Matteucci [2]. From now on I will consider our odom frame as the fixed frame of the slides, and our base_link frame as the mobile frame of the robot. In case of a differential drive (slide 22), it can be seen that I have the x axis of the base_link frame always parallel to the direction of the velocity of the robot. This is not true for a mecanum wheeled robot, where I have to take into account both the parallel and perpendicular component of the velocity.

At slide number 27, the Euler integration method for differential drive is illustrated. We can see that v_kcosθ_k = v_x(k) and v_ksinθ_k = v_y(k), where v_x and v_y are the velocities relative to the odom reference frame. We could then generalize the Euler integration method in order to use it for the omnidirectional robot. The generalized equations can be recapped in:

• x_k+1 = x_k + v_xk∙ΔT
• y_k+1 = y_k + v_yk∙ΔT
• θ_k+1 = θ_k + ω_k∙ΔT

In case of a mecanum wheeled robot, v_x and v_y have the perpendicular components too. In the image below you can see the base_link as the reference system τ / η and the odom frame as the reference system x / y , as in the slides.

With a bit of Euclidean Geometry, it is easy to obtain:

• v_xk = v_τkcosθ_k - v_ηksinθ_k
• v_yk = v_τksinθ_k + v_ηkcosθ_k

Applying these equations to the above ones, we can obtain the odometry starting from the components of the velocities relative to the base_frame of our omnidirectional robot.

Runge-Kutta integration method

Starting from the assumptions made in the section before, I took as a reference the equations for differential drive listed at slide 28 ([2]). In case of a mecanum wheeled robot, I split again the two components. It is illustrated in the image below.

Putting all together, the three equations for Runge-Kutta are:

• x_k+1 = x_k + v_τkcos(θ_k + ^ω_kΔT ∕ ₂)∙ΔT - v_ηksin(θ_k + ^ω_kΔT ∕ ₂)∙ΔT
• y_k+1 = y_k + v_τksin(θ_k + ^ω_kΔT ∕ ₂)∙ΔT - v_ηkcos(θ_k + ^ω_kΔT ∕ ₂)∙ΔT
• θ_k+1 = θ_k + ω_k∙ΔT

ROS parameters for initial pose

I was required to add ROS parameters for defining the initial pose of the robot (x, y, θ). You can find them in the launch file, at line 3-4-5:

<param name="init_pose_x" value="0"/>
<param name="init_pose_y" value="0"/>
<param name="init_pose_th" value="0"/>

Those values are then used for initializing pose in the compute_odometry node.

Notice that the initial pose values are referred to the odom frame. Considered that, at the beginning of the odometry, base_link overlaps odom, those values are put to zero.

TF tree

In the launch file you can also find three different TF static transforms world ➔ odom. This is because the topic robot/pose of the bags refers to the frame world, hence we implemented a static translation taking into account the first values of the ground truth. In this way, our odometry better overlaps the GT odometry when visualized on rviz. There are three different transforms because each bag starts from a different position in world.

Below I show the structure of the final TF tree:

Compute Control

I was required to compute wheel speeds in RPM starting from the velocities calculated in compute_velocities.

The node compute_wheel_speed takes the velocities from the topic cmd_vel and then computes each wheel angular velocity using the system of equations number 20 of Taheri et al.. Those equations find the angular velocities in [rad/sec], and moreover they don't take into account the gear ratio between the motor and the wheel. Hence, I corrected them for our situation multiplying by 60∙T. The final equationsare reported below:

• ω_fl = ¹ ∕ _r ∙ ( v_x - v_y - (l_x + l_y)∙ω_z ) ∙ 60 ∙ T
• ω_fr = ¹ ∕ _r ∙ ( v_x + v_y + (l_x + l_y)∙ω_z ) ∙ 60 ∙ T
• ω_rl = ¹ ∕ _r ∙ ( v_x + v_y - (l_x + l_y)∙ω_z ) ∙ 60 ∙ T
• ω_rr = ¹ ∕ _r ∙ ( v_x - v_y + (l_x + l_y)∙ω_z ) ∙ 60 ∙ T

Subsequently, the node publishes the angular velocities as topic wheels_rpm using a custom message, called CustomRpm.

CustomRpm Structure

The structure of the custom message can be found in the file CustomRpm.msg under the msg/ folder. It has got an Header and one float64 for each wheel. The stamp and the frame_id of the header are filled with the stamp and the frame_id of the message taken from the topic cmd_vel.

Reset Service

I was asked to define a service for resetting the odometry to any given pose (x,y,θ). The file ResetOdometry.srv under the srv/ folder defines a service called /reset_odometry that takes as input the x, y and θ. The function ComputeOdometry::reset_odometry in compute_odometry.cpp takes as input the pose given and resets even at runtime the odometry.

Integration Method Selector

I was finally required to use dynamic reconfigure to select the odometry integration method (either Euler or Runge-Kutta). The reconfiguration is defined in parameters.cfg, under the folder cfg/. The constants "Euler" and "RK" are then used in compute_odometry.cpp for deciding the integration method at runtime.

Author

• Davide Giacomini (GitHub, Linkedin, email)

References

[1] Taheri, Hamid, Bing Qiao, and Nurallah Ghaeminezhad. "Kinematic model of a four mecanum wheeled mobile robot." International journal of computer applications 113.3 (2015): 6-9.

[2] Matteo Matteucci. "Robot Localization - Wheels odometry", http://chrome.ws.dei.polimi.it/images/3/3e/Robotics_03_2021_Odometry.pdf