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Racing Vehicles
1 Introduction
Over the last few decades, the autonomous driving has become one of the most
active research areas in the field of computer science. The self-driving systems
are being developed to provide a safe and robust driving strategies for highways
and demanding urban areas.
However, if we consider an racing of autonomous vehicles problem where the
self-driving vehicles are competing against each other in a predefined track their
performance becomes as essential as their safety. The autonomous vehicle needs
to be controlled at its limit with self-driving controlling algorithms requiring to
consider the following aspects:
– dynamic environment with static and dynamic obstacles
– performance constraints (e.g. minimising lap time)
– autonomous car safety
The overall aim of this project is to investigate the application of autonomous
driving algorithms to the problem of vehicle racing. One of the main approaches
to controlling an autonomous car is based on the concept of the model-predictive
control [2]. The main idea behind model-predictive control is finding an optimal
driving trajectory by expressing racing as an optimisation problem. There are
few main features of the model-predictive control as visualised in Fig. 1.
– a mathematical model of the autonomous system; often expressed as a system
of differential equations (e.g. Equations 1-3).
– a cost (or objective) function which assigns a value to a particular vehicle
trajectory (e.g. time-to-goal)
– constraints are user provided predicates which limit the domain of modelpredictive
control optimization search
– an optimiser is a search engine which attempts to efficiently analyse the
dynamical model based on user provided constraints, evaluate results based
on the cost function and produce the most optimal system inputs.
2 Sergiy Bogomolov, Milad Kazemi, Sadegh Soudjani and Paulius Stankaitis
Fig. 1. A visual representation of the model-predictive control workflow [3]
2 Developing Model-Predictive Control Systems within
the F1Tenth Simulator
In this project, your team will develop a model-predictive controller of a virtual
autonomous vehicle within the F1Tenth simulator. Your developed controlling
system will improve autonomous vehicles performance by performing a modelbased
vehicle trajectory optimisation in a real-time. In order to complete your
project you are required to complete following tasks (Tasks 1 - 5):
Task 1: Literature Study Perform a literature review on the model-based
predictive control and the possible applications to the domain of self-driving
vehicles. Summarise a few techniques used in the literature to finding optimal
driving strategies and describe their features and properties. Make sure that you
understand the concepts and techniques. Include the details of your literature
study in your final group report. We provide some starting reading below:
– Camacho et al.: Model predictive control [2]
– Video MPC Overview: https://youtu.be/YwodGM2eoy4
– Rosolia and Borelly: Learning How to Autonomously Race a Car: a Predictive
Control Approach [6]
– Brunke: Learning Model Predictive Control for Competitive Autonomous
Racing [1]
Task 2: Download and Install F1Tenth ROS Simulator The Robot Operating
System (ROS) only runs natively in Linux so we are only supporting using
the simulator in Ubuntu at this time. If you do not have ROS Melodic installed,
follow the instructions from website below:
http://wiki.ros.org/melodic/Installation/Ubuntu
Optimal and Safe Control of Autonomous Racing Vehicles 3
Dependencies You will need the following dependencies:
– tf2-geometry-msgs
– ackermann-msgs
– joy
– map-server
Open the command line and install these packages using
sudo apt-get install ros-melodic-tf2-geometry-msgs
ros-melodic-ackermann-msgs ros-melodic-joy
ros-melodic-map-server
The full list of dependencies can be found in the package.xml file.
Package To install the simulator package, clone the simulator repository into
your catkin workspace:
cd ~
mkdir catkin_ws
cd catkin_ws
mkdir src
cd ~/catkin_ws/src
git clone https://github.com/f1tenth/f1tenth_simulator.git
Then run catkin make to build it:
cd ~/catkin_ws
catkin_make
source devel/setup.bash
Quick Start To run the simulator on its own, run:
roslaunch f1tenth_simulator simulator.launch
This will launch everything you need for a full simulation: roscore, the simulator,
a preselected map, a model of the racecar, and the joystick server.
F1TENTH gym environment ROS communication bridge For using gym environment
you can follow the steps of following repository to install the required
packages locally or as a docker.
https://github.com/f1tenth/f1tenth gym ros
The F1TENTH Gym environment For using gym environment without the ROS
communication you can follow the steps of the following repository.
https://github.com/f1tenth/f1tenth gym
4 Sergiy Bogomolov, Milad Kazemi, Sadegh Soudjani and Paulius Stankaitis
Building ROS Melodic with Python3 support If we look at ROS Melodic and
Kinect minimum requirement, they work with Python 2.7. In order to get Python
3 support in ROS Melodic, you can follow the steps of this article.
https://www.miguelalonsojr.com/blog/robotics/ros/python3/2019/08/20/
ros-melodic-python-3-build.html
By using the following command you can make sure you use the correct ROS
distribution and python:
printenv | grep ROS
Task 3: Model-based Analysis of Dynamical Systems Before your team
starts implementing a model-predictive vehicle controller, it is paramount to
understand how dynamical systems can be simulated, as it is an essential part
of model-predictive controllers. In this exercise, you are required to consider a
kinematic single-track model, which models a vehicle with on two wheels (front
and rear wheels are combined into a single wheel) as shown in Figure 2.
Fig. 2. Mathematical representation of the Kinematic Single-Track Model [5]
The kinematic single-track model has a number variables, which are used to
mathematically define the dynamical model. In this part of project, your group
should complete following tasks:
Task 3.1 Understanding Kinematic Model Your team will need to understand
the kinematic single-track model (Equations 1 - 3). More information
about the Kinematic Single-Track Model can be found in:
– Chapter 2 of Vehicle dynamics and control [5] book
– https://github.com/MPC-Berkeley/barc/wiki/Car-Model
– https://gitlab.lrz.de/tum-cps/commonroad-vehicle-models/blob/master
/vehicleModels commonRoad.pdf
Optimal and Safe Control of Autonomous Racing Vehicles 5
x˙ = v · cos(ψ + β) (1)
y˙ = v · sin(ψ + β) (2)
ψ˙ =
v
lr
· sin(β) (3)
Task 3.2 Modeling and Simulating Kinematic Model You will need to
model and simulate Kinematic Single-Track Model with the Python or C++
programming language. There are a number of available libraries, which simplify
dynamical system modelling and enable simulating them given initial system
states.
Task 4: Linearisation of Dynamical Systems A lot of real-world physical
systems, cannot easily be specified with differential equations or the set of differential
equations are complex and cannot be easily analysed. In particular, for
the model-predictive control efficiently simulating a model of a dynamical system
is crucial, as inputs to the actual system have to be derived repeatedly and
quickly. One of the more popular ideas for making model-predictive systems or
optimation engines more efficient is approximating complex system dynamics.
The basic idea is that (in most circumstances) one can approximate the
nonlinear differential equations that govern the behavior of the system by linear
differential equations. We can solve the resulting set of linear ODEs, whereas we
cannot, in general, solve a set of nonlinear differential equations. Therefore, in
this exercise, you are required:
Task 4.1: Understand Dynamical System Linearisation Your first tasks
is to understand the process of approximating complex dynamical systems.
Task 4.2: Approximating Kinematic Model Simplify the dynamical system
presented in the previous task by applying the mathematical method of
linearisation.
Task 4.3:Compare You should compare an approximated and an actual
model of the kinematic single-track model.
Task 5: Implementing a Reference Tracking Algorithm by using MPC
The main deliverable of this project is a reference trajectory tracking controller
which should be implemented by using a model-based predictive control approach
(see Fig. 3). Your team will be provided with a F1Tenth simulator map
(Skirk) and a reference trajectory - a set of x, y coordinates stored in a .csv file.
A screenshot of the map, provided trajectory and vehicle is shown in Fig. 4.
In the following paragraphs a high-level description sub-tasks of the reference
trajectory tracking algorithm are provided.
Task 5.1: Localising Vehicle In the first step, a control system of your autonomous
vehicle should be able to localise itself, or in order words, determine
its coordinates (xv, yv). F1Tenth simulator provides a virtual odometry device
as a ROS node with communication topic (/odom) which can be subscribed to.
6 Sergiy Bogomolov, Milad Kazemi, Sadegh Soudjani and Paulius Stankaitis
(xv, yv)
(xr, yr)
Fig. 3. A visual depiction of the reference trajectory tracking based on the modelpredictive
control
Therefore, as the first step, your control algorithm should subscribe to the /odom
and receive coordinates of the vehicle.
Task 5.2: Determining Reference Coordinate In the second step, your
vehicle control algorithm should determine the next reference coordinate (xr
, yr)
from the set of coordinates provided in the trajectory .csv file. The (xr
, yr) coordinate
should be determined, so it reflects the correct vehicle travelling direction.
Fig. 4. A Skirk map with a visualised trajectory to be followed [4]
Task 5.3: Implementing MPC Problem In the third and the main step,
you should implement a model-based predictive control system. There are a num-
Optimal and Safe Control of Autonomous Racing Vehicles 7
ber of existing model-predictive control Python, C++ programming languages
libraries, therefore, it is highly suggested to investigate and evaluate few of existing
libraries. Nonetheless, regardless of the library or skeleton code selected
your will still be required to define the following in your algorithm:
Define Vehicle Dynamics
Define Cost Function
Define MPC Constraints
Task 5.4: Actuating In the last step, your virtual vehicle should be actuated
with controller inputs generated by your developed model-based predictive
control system. F1Tenth simulator provides a ROS node with communication
topic (/drive) which can be published to. Therefore, as the last step, your control
algorithm should publish velocity and driving angle to the /drive in order
to actuate virtual vehicle.
References
1. Brunke, L.: Learning model predictive control for competitive autonomous racing
(2020)
2. Camacho, E.F., Alba, C.B.: Model predictive control. Springer Science & Business
Media (2013)
3. El Ferik, S.: Automation technology in hydrocarbon fuel processing plant. In:
Khan, M.R. (ed.) Advances in Clean Hydrocarbon Fuel Processing, pp. 463 – 495.
Woodhead Publishing Series in Energy, Woodhead Publishing (2011)
4. Norouzi, P.: https://github.com/pnorouzi/rl-path-racing
5. Rajamani, R.: Vehicle dynamics and control. Springer Science & Business Media
(2011)
6. Rosolia, U., Borrelli, F.: Learning how to autonomously race a car: a predictive
control approach (2019)
Racing Vehicles
1 Introduction
Over the last few decades, the autonomous driving has become one of the most
active research areas in the field of computer science. The self-driving systems
are being developed to provide a safe and robust driving strategies for highways
and demanding urban areas.
However, if we consider an racing of autonomous vehicles problem where the
self-driving vehicles are competing against each other in a predefined track their
performance becomes as essential as their safety. The autonomous vehicle needs
to be controlled at its limit with self-driving controlling algorithms requiring to
consider the following aspects:
– dynamic environment with static and dynamic obstacles
– performance constraints (e.g. minimising lap time)
– autonomous car safety
The overall aim of this project is to investigate the application of autonomous
driving algorithms to the problem of vehicle racing. One of the main approaches
to controlling an autonomous car is based on the concept of the model-predictive
control [2]. The main idea behind model-predictive control is finding an optimal
driving trajectory by expressing racing as an optimisation problem. There are
few main features of the model-predictive control as visualised in Fig. 1.
– a mathematical model of the autonomous system; often expressed as a system
of differential equations (e.g. Equations 1-3).
– a cost (or objective) function which assigns a value to a particular vehicle
trajectory (e.g. time-to-goal)
– constraints are user provided predicates which limit the domain of modelpredictive
control optimization search
– an optimiser is a search engine which attempts to efficiently analyse the
dynamical model based on user provided constraints, evaluate results based
on the cost function and produce the most optimal system inputs.
2 Sergiy Bogomolov, Milad Kazemi, Sadegh Soudjani and Paulius Stankaitis
Fig. 1. A visual representation of the model-predictive control workflow [3]
2 Developing Model-Predictive Control Systems within
the F1Tenth Simulator
In this project, your team will develop a model-predictive controller of a virtual
autonomous vehicle within the F1Tenth simulator. Your developed controlling
system will improve autonomous vehicles performance by performing a modelbased
vehicle trajectory optimisation in a real-time. In order to complete your
project you are required to complete following tasks (Tasks 1 - 5):
Task 1: Literature Study Perform a literature review on the model-based
predictive control and the possible applications to the domain of self-driving
vehicles. Summarise a few techniques used in the literature to finding optimal
driving strategies and describe their features and properties. Make sure that you
understand the concepts and techniques. Include the details of your literature
study in your final group report. We provide some starting reading below:
– Camacho et al.: Model predictive control [2]
– Video MPC Overview: https://youtu.be/YwodGM2eoy4
– Rosolia and Borelly: Learning How to Autonomously Race a Car: a Predictive
Control Approach [6]
– Brunke: Learning Model Predictive Control for Competitive Autonomous
Racing [1]
Task 2: Download and Install F1Tenth ROS Simulator The Robot Operating
System (ROS) only runs natively in Linux so we are only supporting using
the simulator in Ubuntu at this time. If you do not have ROS Melodic installed,
follow the instructions from website below:
http://wiki.ros.org/melodic/Installation/Ubuntu
Optimal and Safe Control of Autonomous Racing Vehicles 3
Dependencies You will need the following dependencies:
– tf2-geometry-msgs
– ackermann-msgs
– joy
– map-server
Open the command line and install these packages using
sudo apt-get install ros-melodic-tf2-geometry-msgs
ros-melodic-ackermann-msgs ros-melodic-joy
ros-melodic-map-server
The full list of dependencies can be found in the package.xml file.
Package To install the simulator package, clone the simulator repository into
your catkin workspace:
cd ~
mkdir catkin_ws
cd catkin_ws
mkdir src
cd ~/catkin_ws/src
git clone https://github.com/f1tenth/f1tenth_simulator.git
Then run catkin make to build it:
cd ~/catkin_ws
catkin_make
source devel/setup.bash
Quick Start To run the simulator on its own, run:
roslaunch f1tenth_simulator simulator.launch
This will launch everything you need for a full simulation: roscore, the simulator,
a preselected map, a model of the racecar, and the joystick server.
F1TENTH gym environment ROS communication bridge For using gym environment
you can follow the steps of following repository to install the required
packages locally or as a docker.
https://github.com/f1tenth/f1tenth gym ros
The F1TENTH Gym environment For using gym environment without the ROS
communication you can follow the steps of the following repository.
https://github.com/f1tenth/f1tenth gym
4 Sergiy Bogomolov, Milad Kazemi, Sadegh Soudjani and Paulius Stankaitis
Building ROS Melodic with Python3 support If we look at ROS Melodic and
Kinect minimum requirement, they work with Python 2.7. In order to get Python
3 support in ROS Melodic, you can follow the steps of this article.
https://www.miguelalonsojr.com/blog/robotics/ros/python3/2019/08/20/
ros-melodic-python-3-build.html
By using the following command you can make sure you use the correct ROS
distribution and python:
printenv | grep ROS
Task 3: Model-based Analysis of Dynamical Systems Before your team
starts implementing a model-predictive vehicle controller, it is paramount to
understand how dynamical systems can be simulated, as it is an essential part
of model-predictive controllers. In this exercise, you are required to consider a
kinematic single-track model, which models a vehicle with on two wheels (front
and rear wheels are combined into a single wheel) as shown in Figure 2.
Fig. 2. Mathematical representation of the Kinematic Single-Track Model [5]
The kinematic single-track model has a number variables, which are used to
mathematically define the dynamical model. In this part of project, your group
should complete following tasks:
Task 3.1 Understanding Kinematic Model Your team will need to understand
the kinematic single-track model (Equations 1 - 3). More information
about the Kinematic Single-Track Model can be found in:
– Chapter 2 of Vehicle dynamics and control [5] book
– https://github.com/MPC-Berkeley/barc/wiki/Car-Model
– https://gitlab.lrz.de/tum-cps/commonroad-vehicle-models/blob/master
/vehicleModels commonRoad.pdf
Optimal and Safe Control of Autonomous Racing Vehicles 5
x˙ = v · cos(ψ + β) (1)
y˙ = v · sin(ψ + β) (2)
ψ˙ =
v
lr
· sin(β) (3)
Task 3.2 Modeling and Simulating Kinematic Model You will need to
model and simulate Kinematic Single-Track Model with the Python or C++
programming language. There are a number of available libraries, which simplify
dynamical system modelling and enable simulating them given initial system
states.
Task 4: Linearisation of Dynamical Systems A lot of real-world physical
systems, cannot easily be specified with differential equations or the set of differential
equations are complex and cannot be easily analysed. In particular, for
the model-predictive control efficiently simulating a model of a dynamical system
is crucial, as inputs to the actual system have to be derived repeatedly and
quickly. One of the more popular ideas for making model-predictive systems or
optimation engines more efficient is approximating complex system dynamics.
The basic idea is that (in most circumstances) one can approximate the
nonlinear differential equations that govern the behavior of the system by linear
differential equations. We can solve the resulting set of linear ODEs, whereas we
cannot, in general, solve a set of nonlinear differential equations. Therefore, in
this exercise, you are required:
Task 4.1: Understand Dynamical System Linearisation Your first tasks
is to understand the process of approximating complex dynamical systems.
Task 4.2: Approximating Kinematic Model Simplify the dynamical system
presented in the previous task by applying the mathematical method of
linearisation.
Task 4.3:Compare You should compare an approximated and an actual
model of the kinematic single-track model.
Task 5: Implementing a Reference Tracking Algorithm by using MPC
The main deliverable of this project is a reference trajectory tracking controller
which should be implemented by using a model-based predictive control approach
(see Fig. 3). Your team will be provided with a F1Tenth simulator map
(Skirk) and a reference trajectory - a set of x, y coordinates stored in a .csv file.
A screenshot of the map, provided trajectory and vehicle is shown in Fig. 4.
In the following paragraphs a high-level description sub-tasks of the reference
trajectory tracking algorithm are provided.
Task 5.1: Localising Vehicle In the first step, a control system of your autonomous
vehicle should be able to localise itself, or in order words, determine
its coordinates (xv, yv). F1Tenth simulator provides a virtual odometry device
as a ROS node with communication topic (/odom) which can be subscribed to.
6 Sergiy Bogomolov, Milad Kazemi, Sadegh Soudjani and Paulius Stankaitis
(xv, yv)
(xr, yr)
Fig. 3. A visual depiction of the reference trajectory tracking based on the modelpredictive
control
Therefore, as the first step, your control algorithm should subscribe to the /odom
and receive coordinates of the vehicle.
Task 5.2: Determining Reference Coordinate In the second step, your
vehicle control algorithm should determine the next reference coordinate (xr
, yr)
from the set of coordinates provided in the trajectory .csv file. The (xr
, yr) coordinate
should be determined, so it reflects the correct vehicle travelling direction.
Fig. 4. A Skirk map with a visualised trajectory to be followed [4]
Task 5.3: Implementing MPC Problem In the third and the main step,
you should implement a model-based predictive control system. There are a num-
Optimal and Safe Control of Autonomous Racing Vehicles 7
ber of existing model-predictive control Python, C++ programming languages
libraries, therefore, it is highly suggested to investigate and evaluate few of existing
libraries. Nonetheless, regardless of the library or skeleton code selected
your will still be required to define the following in your algorithm:
Define Vehicle Dynamics
Define Cost Function
Define MPC Constraints
Task 5.4: Actuating In the last step, your virtual vehicle should be actuated
with controller inputs generated by your developed model-based predictive
control system. F1Tenth simulator provides a ROS node with communication
topic (/drive) which can be published to. Therefore, as the last step, your control
algorithm should publish velocity and driving angle to the /drive in order
to actuate virtual vehicle.
References
1. Brunke, L.: Learning model predictive control for competitive autonomous racing
(2020)
2. Camacho, E.F., Alba, C.B.: Model predictive control. Springer Science & Business
Media (2013)
3. El Ferik, S.: Automation technology in hydrocarbon fuel processing plant. In:
Khan, M.R. (ed.) Advances in Clean Hydrocarbon Fuel Processing, pp. 463 – 495.
Woodhead Publishing Series in Energy, Woodhead Publishing (2011)
4. Norouzi, P.: https://github.com/pnorouzi/rl-path-racing
5. Rajamani, R.: Vehicle dynamics and control. Springer Science & Business Media
(2011)
6. Rosolia, U., Borrelli, F.: Learning how to autonomously race a car: a predictive
control approach (2019)