Abbreviations Meaning | MPC Model Predictive Control 2 AVs Autonomous Vehicles 3 ODEs Ordinary Differential Equations 4 IVPs Initial Value Problems 5 ABS Anti-lock Braking System 6 ESC E
INTRODUCTION 1015 e ố
“BARRIER GUARD” ADVANCING AUTONOMOUS VEHICLE MODELS WITH OBSTACLE AVOIDANCE.
- Nguyén Xuân Thế - 21070106 - ICE2021A — 21070106@vnu.edu.vn
- Than Ngọc Tuấn Anh — 21070240 — ICE2021A — 21070240@vnu.edu.vn
- Giap Lê Hoang — 21070836 — ICE2021B — hoanggl@vnuis.edu.vn
- Nguyén Thanh Trung — 21070126 — ICE2021A — 21070126@vnu.edu.vn
- Nguyén Lưu Anh Tuan - 21070364 — ICE2021A — 21070364@vnu.edu.vn
CONTENT Ặ LH HH HH HH HH HH HH ch 9 | Ttroductions 0018
1 The urgency of the subject
The development of technology in the twenty-first century led to the rise of many automated systems especially in transportation Unmanned vehicles are starting to appear in many research fields and even in daily life from underwater, ground, and aerial Each system is utilized for its purpose such as rescue missions [13][14], military missions [15], servicing in restaurants, and scientific research And in today’s society,the importance of autonomous transportation has been increasing rapidly However, this system is not always autonomous since it still needs human interference in some circumstances Moreover, the system cannot replicate how a human mind processes since there are problems in communication Delay, signal noise, or bandwidth limitation can easily make the system fail Thus, a suitable control algorithm should be implemented in the system to minimize the error and also adapt to hazardous conditions.
Model Predictive Control (MPC) stands out as a promising solution for autonomous vehicle control Unlike traditional methods, MPC optimizes control inputs by considering future system behavior and constraints Its predictive capabilities enable it to handle complex systems effectively, managing nonlinear dynamics, uncertainties, and limitations MPC's advantages include its ability to handle complex systems, maximize efficiency, and ensure safety in dynamic and unpredictable environments Additionally, it offers simultaneous constraint handling and control output, further enhancing its suitability for autonomous driving systems.
Above all, safety is a crucial aspect of autonomous vehicles [11] The collision avoidance system has been an important field of research for researchers because of the need to improve traffic safety [17] With constraints, the MPC model can successfully navigate through complex environments Also, it can optimize the traveling cost which includes energy consumption and time Moreover, when combining MPC with other sensors or technology, the control problem can be solved more effectively.
Some research uses Nonlinear Model Predictive Control to solve point- stabilization and obstacle avoidance problems [9], [10] But in this research, we have simplified the algorithm so that we can get a successful result without wasting computational resources In this report, we design an MPC-based obstacle-avoidance algorithm that needs the initial position of the vehicle and the destination The approach can handle static and dynamic obstacles since it considers obstacle avoidance as a constraint.
The purpose of this research is to apply Model Predictive Control to create a sophisticated model of an autonomous vehicle that excels in adhering to road lanes and avoiding obstacles under simulated real-road conditions.
- Establishing a four-wheeled self-propelled vehicle model, researching and synthesizing methods that have been published domestically and internationally.
- Proposing a new control structure for autonomous vehicles in working conditions with changing model parameters.
- Provide a trajectory-following adaptive control algorithm for self-propelled vehicles in working conditions with changing model parameters and affected by disturbances and semi-slip friction.
3 Subject and scope of research of the study
- The study subject is the 4-wheeled self-propelled vehicle with 2 axles, which is described using a kinematic equation and the dynamics of a nonlinear, nonholonomic system.
- The scope of the study:
+ Develop a mathematical model for a four-wheeled system + Develop, test, and refine algorithms specific to lane detection, lane- keeping, obstacle detection, and obstacle avoidance control
4 Scientific and practical significance of the study
- Integrate control algorithms into a unified lane-keeping and obstacle avoidance control program, thereby enhancing the vehicle's operational efficacy and safety in complex driving environments
- Enhancing the vehicle's operational efficacy and safety in complex driving environments
- Ensures a robust platform for future advancements in autonomous vehicle technology.
The research methodology of this study is theoretical research combined with simulation to evaluate the quality of the new controllers proposed in the study:
- Theoretical research: Analyze and research on Model Predictive Control applied to self-propelled vehicles as a basis for proposing new control algorithms.
- Apply numerical simulations in different scenarios with different parameters to evaluate the analysis based on theory From the results, we evaluate the capabilities of the controllers in practice.
6 Layout of the study The research has 5 chapters with the main content summarized as follows:
Chapter 1: Literature review and theoretical background:
This chapter introduces the Euler forward method, Model Predictive Control, and LIDAR — some of the components and techniques we will be using in our model.
Chapter 2: System design and data measurement:
This chapter provides us with a detailed overview of the system's architecture, including the vehicle's dynamic model, its multidirectional movement, and the tire model that we employ Above all, we take a close look at the MPC system's architecture to assist the car in avoiding obstructions.
In this section of the study, we present our simulation outcome Here, we build a simulation using our determined input parameters, and the output is displayed
Literature Review and Theoretical Background
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The Euler forward method is a numerical technique used to solve ordinary differential equations (ODEs) with a given initial value It is a first-order method where its error per step is proportional to the square of the step size and the error at a given time is proportional to the step size The Euler forward method is considered suitable for our system because of a few reasons.
First of all, the simplicity of the method makes it require less computational resources, which can increase the calculating speed The method only needs the initial state and the differential equation It can also easily be implemented into the system since it only needs basic arithmetic operations Secondly, many different types of ODEs, including non-linear and time-varying systems, may be handled by the Euler forward technique It is a flexible tool for numerical simulations and modeling that may be used for a wide range of scientific and engineering applications Finally, the method is suited for problems with initial values (IVPs) It offers a simple method for propagating the answer from the starting state forward in time. solution curve Slope = F (X,,Y.) tangent line
Model Predictive Control (MPC) is an advanced control strategy used to predict future behavior and optimize control input over a finite time horizon MPC implicitly determines the control rule by resolving an optimization problem, which may be limited.This causes the process of designing a controller to be redirected toward modeling the process that needs to be regulated.
Measured Output Predicted Control Input Past Control Input
Figure 2 Model Predictive Control Scheme
MPC models forecast how changes in the independent variables will affect the modeled system's dependent variables To estimate future changes in the dependent variables, MPC makes use of the current plant data, the process's dynamic state at the time, its MPC models, and the process variable objectives and limitations These adjustments are computed to respect limitations on both independent and dependent variables and maintain the dependent variables near to goal Usually, the MPC only sends out the initial adjustment for each independent variable that has to be changed and iterates the computation whenever a new modification is needed.
In MPC, following the implementation of the initial state and the computation of the subsequent stage, the plant state is sampled once again, and the calculation is repeated from the new current state, producing a new control and new anticipated state route The prediction horizon keeps being shifted forward.
To implement MPC, we need an internal dynamic model of the process, a cost function J over the receding horizon and an optimization algorithm minimizing the cost function using the control input.
At the core of model predictive control (MPC) lies the solution to an optimization problem at each time step The efficiency of the control output depends on the quality of this solution, which typically involves minimizing control effort, accommodating performance criteria, and incorporating a cost function that penalizes deviations from desired setpoints To guarantee system safety, the optimization problem further incorporates constraints on inputs and system states.
These days, MPC applications can be found in wide range of industries including power systems, robotics and most of all, autonomous vehicles where flexibility,
Figure 3 Structure and working principle of Model Predictive Control
The concept of the forecast horizon, denoted as N, plays a pivotal role in Model Predictive Control (MPC), as it defines the number of future time steps considered for decision-making During each forecast step, the controller implements a specific control task spanning from the current time t to t+N The selection of an appropriate forecast horizon is essential for effective control; for instance, in a scenario where an automobile travels at 80 km/h with an emergency stopping requirement of 5 seconds, a forecast horizon shorter than this duration, such as 2 seconds, would be inadequate, potentially resulting in the vehicle halting only post-collision Conversely, an excessively lengthy horizon could lead to unnecessary computational demands on the system.
The sampling time, represented by At, refers to the smallest time interval for executing the control algorithm This parameter critically influences the controller's processing velocity and its capacity to timely address disturbances or changes in input signals A large sampling interval might impede the controller's response to disturbances, whereas an excessively small interval could enable faster reactions to variations and noise, raising the risk of computational overload.
Another crucial design aspect within MPC is the control horizon, denoted as c It encapsulates the number of control actions considered up to a specific future time step m, assuming constant input parameters during this interval Each control action within this horizon is a variable determined through optimization, with a shorter control horizon generally reducing computational load.
In developing an MPC model, it is vital to also consider additional parameters such as constraints and weighting factors Specifically, in autonomous vehicle navigation, the MPC controller must identify a trajectory that closely aligns with a pre- set reference path, maintaining a consistent speed and throttle setting This process involves optimizing an objective function, J, to approximate the desired trajectory. Autonomous systems are required to adhere to both stringent (hard) and flexible (soft) constraints, which help delineate operational limits, environmental adaptability, and safety protocols essential for vehicle movement.
Light Detection and Ranging (LIDAR) is a method for determining ranges by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver LIDAR can operate in both fixed directions or multiple directions which is known as 3D laser scanning.
Typically, a lidar sensor is made up of four major parts: 1 Light source: Usually a laser, or any source of pulsed light emissions; 2 Optical components - There are several optical components For instance, light from the sensor reflects off of an oscillating or spinning mirror, changing its direction to encompass a 360-degree field of vision Light is helped to concentrate on the photodetector by an optical lens; 3 Photodetector: This device detects light and processes it electrically to determine the light's frequency (used for speed measurements) and bounce time; 4 GPS: In order to pinpoint the precise location and orientation of these sensors in three dimensions, a GPS system is required.
Optical rotary encoder Laser source
The equation that LIDAR used to calculate the distance between the sensor and the obstacle is mostly based on Newton’s Second law of motion:
The speed of light is a constant so we replace a = 0,1 = c = 3x 108 and S = d: d=c't
(MPPC, APD, PIN photodiode) mae wee
Fig 5 Time of Flight method
LIDAR is widely used in many aspects of life such as Topographic Graphing, Archaeology and Cultural Heritage, Autonomous Vehicle, etc The reason behind the popularity of LIDAR in many industrial fields is that LIDAR has a high accuracy, even over large areas The mapping ability of the sensor also helps users effectively develops their systems Moreover, it can be used in many types of environments and weather conditions since it can penetrate through clouds and darkness Finally, LIDAR’s ability to adapt to many types of applications makes it one of the most commonly used sensors for both researchers and manufacturers.
CHAPTER 2: System Design and Data Measurement
To research and develop a comprehensive dynamic model of car motion, it is necessary to build a model in three-dimensional space, the car will move in a fixed Oxyz coordinate system In this system, the car's dynamics are represented through six basic elements including 3 elements related to translational motion - moving along each axis
Ox, Oy, Oz, and three other elements related to rotation around the corresponding axes
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In this section of the study, we present our simulation outcome Here, we build a simulation using our determined input parameters, and the output is displayed graphically To help with a better understanding of our model's output, we also assess the results.
Finally, there is the Conclusion and References of the study.
CHAPTER 1: Literature Review and Theoretical Background
The Euler forward method is a numerical technique used to solve ordinary differential equations (ODEs) with a given initial value It is a first-order method where its error per step is proportional to the square of the step size and the error at a given time is proportional to the step size The Euler forward method is considered suitable for our system because of a few reasons.
First of all, the simplicity of the method makes it require less computational resources, which can increase the calculating speed The method only needs the initial state and the differential equation It can also easily be implemented into the system since it only needs basic arithmetic operations Secondly, many different types of ODEs, including non-linear and time-varying systems, may be handled by the Euler forward technique It is a flexible tool for numerical simulations and modeling that may be used for a wide range of scientific and engineering applications Finally, the method is suited for problems with initial values (IVPs) It offers a simple method for propagating the answer from the starting state forward in time. solution curve Slope = F (X,,Y.) tangent line
Model Predictive Control (MPC) is an advanced control strategy used to predict future behavior and optimize control input over a finite time horizon MPC implicitly determines the control rule by resolving an optimization problem, which may be limited.This causes the process of designing a controller to be redirected toward modeling the process that needs to be regulated.
Measured Output Predicted Control Input Past Control Input
Figure 2 Model Predictive Control Scheme
MPC models forecast how changes in the independent variables will affect the modeled system's dependent variables To estimate future changes in the dependent variables, MPC makes use of the current plant data, the process's dynamic state at the time, its MPC models, and the process variable objectives and limitations These adjustments are computed to respect limitations on both independent and dependent variables and maintain the dependent variables near to goal Usually, the MPC only sends out the initial adjustment for each independent variable that has to be changed and iterates the computation whenever a new modification is needed.
In MPC, following the implementation of the initial state and the computation of the subsequent stage, the plant state is sampled once again, and the calculation is repeated from the new current state, producing a new control and new anticipated state route The prediction horizon keeps being shifted forward.
To implement MPC, we need an internal dynamic model of the process, a cost function J over the receding horizon and an optimization algorithm minimizing the cost function using the control input.
The core of MPC is solving the optimization problem at each time step The better the solution of this problem, the better the control output Typically, the optimization goal involves reducing control effort, additional performance requirements, and a cost function that penalizes deviations from intended setpoints Also, input and state constraints are also included in the optimization problem to ensure the safety of the system.
These days, MPC applications can be found in wide range of industries including power systems, robotics and most of all, autonomous vehicles where flexibility,
Figure 3 Structure and working principle of Model Predictive Control
In Model Predictive Control (MPC), the forecast horizon (N) governs the number of future time steps used for decision-making It impacts the effectiveness of the control system For example, in a car traveling at 80 km/h with a 5-second emergency stopping requirement, a forecast horizon of 2 seconds would be inadequate, as the vehicle would halt after collision Conversely, an excessively long forecast horizon can lead to excessive computational demands.
The sampling time, represented by At, refers to the smallest time interval for executing the control algorithm This parameter critically influences the controller's processing velocity and its capacity to timely address disturbances or changes in input signals A large sampling interval might impede the controller's response to disturbances, whereas an excessively small interval could enable faster reactions to variations and noise, raising the risk of computational overload.
Another crucial design aspect within MPC is the control horizon, denoted as c It encapsulates the number of control actions considered up to a specific future time step m, assuming constant input parameters during this interval Each control action within this horizon is a variable determined through optimization, with a shorter control horizon generally reducing computational load.
In developing an MPC model, it is vital to also consider additional parameters such as constraints and weighting factors Specifically, in autonomous vehicle navigation, the MPC controller must identify a trajectory that closely aligns with a pre- set reference path, maintaining a consistent speed and throttle setting This process involves optimizing an objective function, J, to approximate the desired trajectory. Autonomous systems are required to adhere to both stringent (hard) and flexible (soft) constraints, which help delineate operational limits, environmental adaptability, and safety protocols essential for vehicle movement.
Light Detection and Ranging (LIDAR) is a method for determining ranges by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver LIDAR can operate in both fixed directions or multiple directions which is known as 3D laser scanning.
Typically, a lidar sensor is made up of four major parts: 1 Light source: Usually a laser, or any source of pulsed light emissions; 2 Optical components - There are several optical components For instance, light from the sensor reflects off of an oscillating or spinning mirror, changing its direction to encompass a 360-degree field of vision Light is helped to concentrate on the photodetector by an optical lens; 3 Photodetector: This device detects light and processes it electrically to determine the light's frequency (used for speed measurements) and bounce time; 4 GPS: In order to pinpoint the precise location and orientation of these sensors in three dimensions, a GPS system is required.
Optical rotary encoder Laser source
The equation that LIDAR used to calculate the distance between the sensor and the obstacle is mostly based on Newton’s Second law of motion:
The speed of light is a constant so we replace a = 0,1 = c = 3x 108 and S = d: d=c't
(MPPC, APD, PIN photodiode) mae wee
Fig 5 Time of Flight method
LIDAR is widely used in many aspects of life such as Topographic Graphing, Archaeology and Cultural Heritage, Autonomous Vehicle, etc The reason behind the popularity of LIDAR in many industrial fields is that LIDAR has a high accuracy, even over large areas The mapping ability of the sensor also helps users effectively develops their systems Moreover, it can be used in many types of environments and weather conditions since it can penetrate through clouds and darkness Finally, LIDAR’s ability to adapt to many types of applications makes it one of the most commonly used sensors for both researchers and manufacturers.
CHAPTER 2: System Design and Data Measurement