REPORT TOPIC MODELING AND SIMULATING THE THREEWHEELED MOBILE ROBOT

Introduction

Wheeled Mobile Robot

Wheeled Mobile Robots (WMR) are advanced systems that require precise torque application to their wheels for optimal platform movement Effective motion control algorithms must account for the dynamic characteristics of these systems Typically, this challenge is addressed through cascade control schemes, where an outer controller manages velocity control and an inner controller regulates torque, force, or motor current.

The outer controller sets the necessary system velocities for navigating to the reference pose or following the designated trajectory, while the inner, faster controller computes the required torques to achieve these velocities.

Some typed of Wheeled Mobile Robot

A different wheeled robot is a mobile robot is a mobile robot whose movement is based on separately driven wheels placed on their side of the robot body

It can change its direction by varying the relative rate of rotation of its wheels and hence does not require an additional steering motion

Robots with such a driven typically have on or more castor wheels to prevent the vehicle from tilting

Bicycle Drive features two wheels arranged in a straight line, similar to a bicycle, where typically only one wheel is powered while the other controls the steering angle, utilizing a differential drive system.

This type of robot is rarely used cause of its backwardness in reality applications

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control algorithms, and performance metrics essential for effective navigation and operation By utilizing advanced simulation techniques, the study aims to enhance the robot's maneuverability and efficiency in various environments The findings will contribute to the development of more sophisticated robotic systems capable of performing complex tasks autonomously Overall, this research highlights the significance of modeling and simulation in advancing mobile robotics technology.

DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT

Tricycle Drive is a combination of WMR mentioned above, it has 3 wheels:

The vehicle features two coaxially arranged rear wheels and a front steering wheel Of the three wheels, two are connected to an actuator for control, while the third wheel remains free, allowing for adjustments in speed and steering angle.

WMR has a structure similar to a car with 2 front wheels that can change the steering angle

The Omni Directional Wheel is a versatile wheel designed to move in multiple directions effortlessly While there are various types of Wheeled Mobile Robots (WMR), the Omni Directional Wheel represents just one of the many innovative examples in this category.

This article focuses on the modeling and simulation of three-wheeled mobile robots, exploring their design, functionality, and applications The study emphasizes the importance of accurate modeling techniques to enhance robot performance and navigation capabilities Additionally, it discusses various simulation tools that facilitate the testing and optimization of robotic systems in virtual environments By understanding the dynamics of three-wheeled mobile robots, researchers can improve their efficiency and adaptability in real-world scenarios The findings aim to contribute to advancements in robotic technology and its practical implementations across diverse fields.

Choosing WMR three wheels

In this topic, We choose a Tricycle Drive with 2 rear wheels as active wheels attached with actuators to control and front wheel as free wheel.

Modeling the Moblie Robot Three Wheels

Kinetic Model

WMR is illustrates as in the figure H2.1:

This article focuses on the modeling and simulation of three-wheeled mobile robots, exploring their design, functionality, and applications It highlights the importance of accurate modeling for predicting robot behavior and improving performance in various environments Additionally, the article discusses simulation techniques that facilitate the testing and validation of robotic systems before real-world implementation By employing advanced algorithms and software tools, researchers can enhance the efficiency and effectiveness of three-wheeled mobile robots in tasks such as navigation and obstacle avoidance.

ICR: instantaneous center of rotation of vehicle

R(t): instantaneous radius of vehicle’s trajectory

 : angular speed of vehicle around the center of ICR v : longitudinal vehicle velocity r : wheel’s radius

 : the vehicle’s orientation – angle between WMR and O m X m axis

The model is placed in a general coordinate system  X g ,Y g  , and the coordinate system of motion associated with WMR  X m ,Y m  The state vector of the vehicle in the general coordinate system is:

Because the movement of the vehicle through transmission of 2 rear wheels that moniting the WMR direction; therefore, the vehicle's longitudinal velocity is determined by:

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study aims to explore the dynamics and control mechanisms essential for the effective operation of such robots By employing advanced simulation techniques, we analyze the robot's movement patterns and responsiveness to various environmental conditions The findings will contribute to the development of more efficient navigation algorithms and enhance the overall performance of three-wheeled mobile robots in real-world applications.

The equation of external kinematic of WMR on the general coordinate system is determined as follows:

In order to eleminate the complex in presentation, we temporarily ignore the dependence of the quantity into time, the above equation can be rewritten as:

Or we can write as following matrix:

Thus, within control input as velocity vector v   v   T , we have a matrix S being vector fields representing the possible travel directions of the WMR:

This article focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It explores various techniques for accurately representing the dynamics and kinematics of these robots, emphasizing the importance of simulation in optimizing performance and control strategies By examining case studies and real-world implementations, the report underscores the potential of three-wheeled mobile robots in diverse fields, including logistics, surveillance, and autonomous navigation Ultimately, the article aims to provide insights into the advancements in robotic technology and the future prospects of three-wheeled mobile robots in various industries.

In which the directions of motion are:

System equation 2.5 is rewritten as follows:

Beside, the WMR can only move along the wheels, not drift Therefore, the motion of the WMR is constrained:

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study aims to analyze the robot's dynamics, control systems, and navigation capabilities By utilizing advanced simulation techniques, we can predict the robot's behavior in various environments and improve its performance The insights gained from this research will contribute to the development of more efficient and effective mobile robotic systems.

The relationship between (x 2 ,y 2 ) with (x,y) as following:

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study aims to analyze the robot's dynamics and control mechanisms to enhance its performance By employing advanced simulation techniques, we can visualize the robot's behavior in various environments The findings will contribute to the development of more efficient navigation strategies for mobile robots, ultimately improving their applications in real-world scenarios This research is crucial for advancing robotics technology and understanding the complexities of mobile robot systems.

From 2.11, we have constrain matrix A as following:

Dynamic Model

Model 3-wheel mobile robot is considered within 2 rear wheels as active driven by two engines, font wheel as free one These actuators will generate torques

The dynamic model of WMR’s motion is described by the Lagrange formula as follows:

: the difference between the kinetic and potential energy of the system

P : the power lost due to friction k : the index of the general coordinate component q k

This article focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles, control mechanisms, and performance evaluation of these robotic systems By utilizing advanced simulation tools, researchers can analyze the dynamics and kinematics of three-wheeled robots, enhancing their functionality in various applications The findings contribute to the development of more efficient and reliable mobile robots, paving the way for innovations in automation and robotics.

DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT d g k : gravity analysis in the direction of q k

 : disturbance component in direction of q k

 k : component Lagrange associated wih he jth constrain according to q k a jk : constrain cefficient according to q k

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study aims to analyze the robot's dynamics, control mechanisms, and navigation capabilities By employing advanced simulation techniques, we can effectively predict the robot's performance in various environments The findings will contribute to the development of more efficient robotic systems, enhancing their application in real-world scenarios Overall, this research highlights the importance of modeling and simulation in advancing mobile robotics technology.

The dynamic model 2.13 can be rewritten in matrix as follows:

M  q  : positive definte matrix of mass and inertia

V  q,q  :vector of Coriolis force and centrifugal force

E  q  : matrix tránition form actuation space to coordinate space u : input torque vector

In order to simplify 2.16 , we temporarily ignore the dependence on q Then 2.16 becomes

Beside, taking derivative both sides od 2.7 we have : q  S.v  S.v Then 2.17 becomes:

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Phần 2: Mô hình hóa đối tượng Mobile Robot 3 bánh

Multiplying both sides of 2.18 with S T we have:

From 2.7 and 2.21, we can describe the state space

Consider for the dynamic modeil, within m, J are mass anf torque around ICR respectively; and ignore disturbance component in formula 2.15

This report focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles, control strategies, and performance analysis necessary for effective operation By utilizing advanced simulation techniques, we can predict the robot's behavior in various environments, enhancing its navigation and task execution capabilities The findings aim to contribute to the development of more efficient and autonomous robotic systems, showcasing the importance of accurate modeling in robotics research and application.

Meanwhile, we consider that WMR just run on even surface That means its potential energy is constant and q k component disappeared in equation 2.15

The WMR’s kinetic energy is:

The Lagrangian function is calculated by:

This report focuses on the modeling and simulation of a three-wheeled mobile robot, emphasizing its design, functionality, and operational efficiency The study explores various modeling techniques to accurately represent the robot's dynamics and control systems Through simulation, we analyze the robot's performance in different scenarios, highlighting its maneuverability and adaptability The findings aim to enhance the understanding of three-wheeled mobile robots and contribute to advancements in robotics technology.

In the ideal condition, ignoring the friction that means lost power equal 0 (P=0)

In order to 2 rear wheels can run with longitudinal velocity

The combined force to pull the WMR moving is ; considering in two components x and y we have:

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control strategies, and performance evaluation of the robot, emphasizing its applications in various fields The study aims to provide insights into the dynamics of three-wheeled robots, highlighting their maneuverability and stability Additionally, it discusses the software tools used for simulation, which aid in optimizing the robot's design and functionality By analyzing different scenarios, the report seeks to enhance the understanding of three-wheeled mobile robots and their potential in real-world applications.

In a WMR's motion coordinate system, the traction force from the two wheels generates a torque (M) that causes the vehicle to rotate around its axis.

Subtituting 2.27, 2.28 and 2.29 into 2.26 we have:

Knematic model 2.30 is writen in the matrix as follow:

Modeling and simulating a three-wheeled mobile robot involves creating a detailed representation of its dynamics and control systems This process allows for the analysis of the robot's performance in various scenarios, enhancing its design and functionality By utilizing advanced simulation tools, engineers can predict the robot's behavior, optimize its movements, and improve navigation capabilities Effective modeling is crucial for developing algorithms that ensure precise control, enabling the robot to operate efficiently in real-world environments Overall, the integration of modeling and simulation is essential for advancing mobile robotics technology.

From that, state space 2.22 can be represented as following:

Because of the non-linear of system, in order to design controller, we normally separated model into 2 parts, including:

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study aims to analyze the robot's dynamics, control mechanisms, and navigation strategies By utilizing advanced simulation techniques, we can optimize the robot's performance in various environments The findings will provide insights into the design and implementation of efficient mobile robotic systems, enhancing their functionality and adaptability in real-world applications.

Where matrixs M,E, V are defined by 2.32

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control strategies, and performance evaluation of the robot The study emphasizes the importance of accurate modeling to enhance navigation and maneuverability By utilizing advanced simulation techniques, the report aims to optimize the robot's functionality in various environments Additionally, it discusses the implications of these simulations for real-world applications, highlighting the potential for improved efficiency and adaptability in robotic systems.

Methods Wheel Mobile Robot

Control Overview

As mentioned above, to facilitate control design, we often divide the state model of the vehicle into two component models, kinematics and dynamics

Therefore, the construction of control options is also based on these two models

To design the controller for a Wheeled Mobile Robot (WMR), we typically employ a classic control scheme utilizing a cascade control strategy with two control loops The outer loop functions as the speed control loop, while the inner loop serves as the torque control loop The kinematics controller in the outer loop computes the desired speed, which then acts as the set value for the inner loop's dynamic control The system is represented through a block diagram that illustrates this relationship.

Beside, the above control system can also be represented in another way according to the EMR method as follows:

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Basic approaches

Let the angle of direction at time t is φ(t) và and desired angle is φ ref (t), the control angle deviation :

In this case, the variable to be controlled is φ(t) and in order to control φ(t) to reach the desired value we need to control the bias 𝑒𝜑(𝑡) to zero

The direction angle of the robot is expressed through the system of differential equations of the direction angle as follows:

In this case, the control variable is selected as   t  , it is determined corresponding to the angular deviation 𝑒 𝜑 (𝑡) through proportional controller as follow:

This equation is approximated to:

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To effectively follow a predetermined trajectory or state, translational control is essential, particularly in longitudinal vehicle control A suitable solution for achieving this control is a proportional control system, where the control output is directly proportional to the distance between the vehicle's current position and the desired reference position.

This report focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It explores the dynamics and control mechanisms essential for effective navigation and task execution Additionally, the report examines various simulation techniques that enhance the understanding of robot behavior in different environments By analyzing performance metrics, the study aims to provide insights into optimizing three-wheeled mobile robots for various practical uses.

This section discusses practical approaches for controlling a robot to a reference state by integrating angular and translational control methods Specifically, it focuses on the technique of controlling the robot to a set point.

In this scenario, the WMR is tasked with reaching a reference position without needing the final direction angle The robot's direction angle is continuously adjusted to align with the reference location, with the angle from the robot's current position to the reference, denoted as φr, being determined accordingly.

Vận tốc dài và góc lái của bánh trước được điều khiển như sau:

The longitudinal velocity and steering direction of the front wheel are controlled as following:

This report focuses on the modeling and simulation of a three-wheeled mobile robot, exploring its design, functionality, and potential applications The study emphasizes the importance of accurate modeling techniques to predict the robot's behavior in various environments Additionally, simulations are conducted to assess performance metrics such as speed, maneuverability, and stability By integrating advanced algorithms and control systems, the research aims to enhance the robot's operational efficiency and adaptability Ultimately, this work contributes to the development of more sophisticated mobile robotic systems for diverse tasks.

The existing control law faces challenges, particularly as the speed remains consistently positive, which can lead the robot to inadvertently overshoot the reference point, causing the speed to increase further due to the growing distance from the target Additionally, upon crossing the reference point, the reference direction angle may abruptly reverse To address these issues, it is proposed to modify the formulas for velocity and steering angle, specifically by guiding the robot to a reference pose via an intermediate point.

In this scenario, the robot must not only reach the specified location but also achieve a designated angle of direction This task is relatively straightforward, as the previously established control rules can be applied once more The method involves utilizing an intermediary point (xt, yt) positioned at a distance r from the reference point, ensuring that the direction from this intermediary point to the reference point aligns with the intended reference direction.

The idea of that method is to use an intermediate point  x t , y t  placed a distance r from the reference point

Thuật toán điều khiển robot được chia thành hai giai đoạn Ở giai đoạn đầu tiên, robot di chuyển đến điểm trung gian Khi khoảng cách giữa robot và điểm trung gian giảm xuống dưới một ngưỡng nhất định, robot sẽ chuyển sang giai đoạn tiếp theo.

2, điều khiển robot về điểm tham chiếu

The control algorithm consists of two stages In the first stage, the robot is guided to an intermediate point Once the distance between the robot's position and the reference point is sufficiently small, the robot transitions to the second stage, where it is directed to the reference point.

This report focuses on the modeling and simulation of a three-wheeled mobile robot, exploring its design, functionality, and potential applications The study highlights the importance of accurate modeling techniques to enhance the robot's navigation and movement capabilities By utilizing advanced simulation tools, the performance of the three-wheeled robot can be effectively analyzed and optimized for various tasks This research aims to contribute to the development of more efficient mobile robots in real-world scenarios, paving the way for innovations in robotics and automation.

This article focuses on modeling and simulating a three-wheeled mobile robot, emphasizing the transition from a reference state to a reference trajectory It explores the dynamics and control mechanisms necessary for effective navigation and movement of the robot, providing insights into the underlying principles of robotics and simulation techniques The study aims to enhance the understanding of robotic motion and improve the design of mobile robotic systems.

The trajectory is segmented into multiple small sections, with each terminal serving as a reference state Specifically, a reference orbit consists of a sequence of reference states T_i, where i ranges from 1 to n The robot must navigate sequentially through these reference states, moving from T_1 to T_n.

This article focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles, control mechanisms, and performance evaluation of these robots By utilizing advanced simulation techniques, the study aims to enhance the understanding of their dynamics and operational capabilities The findings contribute to the development of more efficient and effective mobile robotic systems Overall, this research provides valuable insights into the practical applications of three-wheeled mobile robots in various fields.

Orbit Following Control

3.3.1 Following the trajectory using basic approaches

Quỹ đạo tham chiếu có thể được coi là một vị trí chuyển động tham chiếu, trong đó điểm tham chiếu được xác định tại mỗi thời điểm trích mẫu dựa trên tọa độ hiện tại của quỹ đạo tham chiếu theo thời gian, cụ thể là các giá trị x ref(t) và y ref(t).

Việc điều khiển tới điểm tham chiếu này được áp dụng luật điều khiển như công thức (3.2)

In line with section 3.2.2.c, the reference trajectory is defined by the movement positions of the reference points At each sampling interval, the reference coordinates are recalibrated based on the current position of the reference orbit over time, denoted as (x_ref(t), y_ref(t)).

3.3.2 Analysis feedforward and feedback elements

The method outlined in section 3.3.1 is straightforward to implement; however, it is highly vulnerable to disturbances within the control loops, necessitating the inclusion of a feedforward disturbance compensation component.

A planar differential system is defined by its ability to express all states and inputs as functions of flat outputs and a finite number of time derivatives This characteristic allows for the computation of every system variable directly from the flat outputs without the need for integration Therefore, control inputs can be derived from the reference trajectory, simplifying the control process in such systems.

We can easily see that the 3 wheeled mobile robot object in question is a planar differential system Indeed:

This article focuses on the modeling and simulation of three-wheeled mobile robots, exploring their design, functionality, and applications It discusses the importance of accurate modeling techniques to enhance performance and efficiency in various environments The simulation processes are highlighted as essential tools for testing and optimizing robotic behaviors before real-world implementation Additionally, the article emphasizes the potential of three-wheeled mobile robots in fields such as automation, logistics, and research, showcasing their versatility and adaptability Overall, the study aims to provide insights into improving robotic systems through effective modeling and simulation strategies.

Formula (3.3) calculates reference inputs aligned with a specific reference trajectory, serving as an open-loop controller for the kinematic model This approach ensures that the robot accurately follows the designated path.

The method involves transforming the input to the system to achieve linearity between the new input and the output, enabling the design of linear controllers The feedback linearization design process requires selecting appropriate flat outputs, ensuring that the number of outputs matches the number of inputs.

- Selecting the appropriate flat outputs, the number of outputs should be equal to the number of inputs

- Differentiate the outputs and check for the occurrence of the inputs, repeating until all inputs appear

- The system of equations is solved for the highest derivative of each input.

The 3-wheel mobile robot operates as a planar differential system, with its flat outputs represented by x(t) and y(t) The system's flat inputs are characterized by their first derivatives.

From the above equation, just only the appearance of v s , we continue to take second derivative:

This report focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles, kinematics, and dynamics that govern their movement The study emphasizes the importance of accurate simulations in predicting the robot's behavior in various environments Additionally, it discusses the applications of three-wheeled mobile robots in industries such as logistics and healthcare By leveraging advanced modeling techniques, the report aims to enhance the efficiency and functionality of these robots in real-world scenarios.

The equation has sufficient input v s and The equation is rewriten as follows:

So with this transformation, the input of the system becomes

 u 1 u 2  T   x y  T and state model z   x x y y  T is described as :

This article focuses on the modeling and simulation of three-wheeled mobile robots, exploring their design, functionality, and applications It emphasizes the importance of accurate modeling techniques to enhance the performance and efficiency of these robots in various environments By simulating different scenarios, researchers can predict the robot's behavior, optimize its movements, and improve navigation strategies The study aims to provide insights that can lead to advancements in robotics technology, making three-wheeled mobile robots more effective for tasks ranging from industrial automation to personal assistance.

Modeling and simulating a three-wheeled mobile robot involves creating a detailed representation of its mechanics and dynamics This process is essential for understanding the robot's movement and control strategies By utilizing advanced simulation tools, engineers can analyze performance metrics and optimize design parameters The three-wheeled configuration offers unique advantages in maneuverability and stability, making it suitable for various applications Effective modeling techniques enable the prediction of the robot's behavior in real-world scenarios, facilitating improvements in navigation and task execution Ultimately, comprehensive simulations contribute to the development of more efficient and reliable mobile robotic systems.

Then weed need to design the controller for this new linear system The reference trajectory is given by , then the reference trajectory can be determined as : We have:

The difference between the actual system state and the reference state is Then:

Using the pole setting method, we define the controller K:

3.3.4 Development of tracking kinetic trajectory

The position deviation of the robot in general coordiante system with the reference position is:

The position deviation of the robot in the coordinate system of motion associated with WMR is: z  z  z ref

This article focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles, control strategies, and applications of these robots in various fields By utilizing advanced simulation techniques, the study aims to enhance the understanding of robot dynamics and improve performance in real-world scenarios The significance of accurate modeling is emphasized, as it directly impacts the efficiency and reliability of robotic systems Overall, this research contributes valuable insights into the development and optimization of three-wheeled mobile robots for practical applications.

Where v ref and w ref are linear reference velocity: v fb and w fb are signals that are determined depending on the control law we choose The error equation is rewritten

Realize zero-error ( e x = e y = e  =0) is an equilibrium when both components respond

From the nonlinear error model in 3.3.4, we linearize around the zero- error point:

Thanks to special structure in equation (3.39), we can use a simple static feedback

This report focuses on the modeling and simulation of a three-wheeled mobile robot, highlighting its design, functionality, and potential applications The three-wheeled configuration offers enhanced maneuverability and stability, making it suitable for various tasks Through detailed simulations, we analyze the robot's performance in different environments and scenarios, providing insights into its operational capabilities The findings aim to contribute to the development of efficient robotic systems for practical use in fields such as automation, logistics, and research.

This article discusses the modeling and simulation of a three-wheeled mobile robot, focusing on how deviations in steering direction and angle can be corrected using feedback control mechanisms, specifically through the variables v_fb and ω_fb.

The control coefficients \( k_x \), \( k_y \), and \( k_\phi \) are selected to position the system's poles appropriately in the s-domain The system features three poles: one real pole and two conjugate complex poles, all strategically placed at a fixed location This arrangement is determined by the characteristic polynomial of the closed-loop system.

We have the control coefficient:

Designing Controller for Three Wheel Robot

Designing Kynametic Controller

Based on the content presented in part 3, we design an outer loop controller for

Mobile robot based on the candidate function Lyapunov

Robot reference coordinate is : (x ref (t), y ref (t))

This article focuses on the modeling and simulation of three-wheeled mobile robots, emphasizing their design, functionality, and applications It explores various methodologies for accurately representing the dynamics and control systems of these robots Additionally, the report highlights the significance of simulation in optimizing performance and enhancing navigation capabilities By examining case studies and practical implementations, the article provides insights into the future development of three-wheeled mobile robotics.

Phần 5: Mô phỏng hệ thống điều khiển trên Matlab Simulink

Thus, the reference velocity of the robot when moving on the reference trjectory is:

The position deviation on the coordinate system of motion associated with WMR is:

This report focuses on the modeling and simulation of three-wheeled mobile robots, exploring their design, functionality, and applications By utilizing advanced simulation techniques, we can analyze the performance and dynamics of these robots in various environments The study emphasizes the importance of precise modeling to enhance navigation and control systems, ensuring efficient operation Additionally, it addresses the challenges faced in real-world scenarios and proposes solutions to improve the reliability and effectiveness of three-wheeled mobile robots Overall, this research contributes valuable insights into the development of autonomous robotic systems.

This report focuses on modeling and simulating a three-wheeled mobile robot The study explores the design, functionality, and control mechanisms of the robot, highlighting its applications in various fields By utilizing advanced simulation techniques, the report demonstrates how the robot can navigate and perform tasks efficiently The findings provide valuable insights into the optimization of robotic systems, paving the way for future innovations in mobile robotics.

Designing the Dynamic Controller

This report focuses on the modeling and simulation of three-wheeled mobile robots It explores the dynamics and control mechanisms essential for optimizing their performance By utilizing advanced simulation techniques, the study aims to enhance the design and functionality of these robots in various applications The findings contribute to a deeper understanding of three-wheeled mobile robotics, paving the way for future innovations in the field.

Velocity deviation is : Derivative of deviation:

Where matrix C is a positive define 2x2 control matrix Then:

This article focuses on the modeling and simulation of three-wheeled mobile robots, exploring their design, functionality, and applications It emphasizes the importance of accurate modeling techniques to predict the robot's behavior in various environments Simulation tools are highlighted as essential for testing and refining the performance of three-wheeled robots before real-world implementation The study aims to enhance the understanding of mobile robotics, facilitating advancements in automation and robotics technology.

Control System On Matlab Simulink

Knematic Model

This article focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications By utilizing advanced simulation techniques, the performance and behavior of these robots can be accurately predicted in various environments The study emphasizes the importance of modeling in optimizing robot navigation and control systems, ensuring efficient movement and task execution Additionally, it explores the challenges faced in the development of three-wheeled mobile robots and proposes solutions to enhance their operational capabilities Overall, this research contributes to the growing field of robotics by providing valuable insights into the effective simulation of mobile robotic systems.

The article appears to be repetitive and unclear However, based on the provided content, here's a rewritten paragraph:"Modeling and simulating a three-wheeled mobile robot is a complex task that requires a deep understanding of robotics, mechanics, and computer science This report aims to provide a comprehensive overview of the modeling and simulation process for a three-wheeled mobile robot, highlighting the key challenges and solutions By using advanced simulation tools and techniques, researchers and engineers can design, test, and optimize the performance of three-wheeled mobile robots, paving the way for their widespread adoption in various industries and applications."

Dynamic Model

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control algorithms, and dynamic behavior essential for effective navigation and operation By utilizing advanced simulation techniques, the study aims to enhance the robot's performance in various environments The findings provide valuable insights into optimizing movement strategies and improving the overall functionality of three-wheeled mobile robots.

This article focuses on the modeling and simulation of three-wheeled mobile robots, emphasizing their design, functionality, and applications It explores various techniques for accurately representing the dynamics and kinematics of these robots, which are crucial for optimizing their performance in real-world scenarios The report also discusses the significance of simulation tools in predicting robot behavior and enhancing control strategies, ultimately contributing to advancements in robotics technology.

5.3 Bộ điều khiển vòng ngoài Kynematic Controller

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study aims to explore the dynamics and control mechanisms that enable efficient navigation and operation By utilizing advanced modeling techniques, the research seeks to enhance the performance and reliability of three-wheeled robots in various applications The simulation results provide valuable insights into the robot's behavior under different conditions, facilitating improvements in design and functionality Overall, this work contributes to the ongoing development of mobile robotics technology.

Getting the initial position of WMR is [x(0);y(0);  (0) ]= [2; 2; pi/4]

In other hands, the reference trajectory:

𝑦𝑟𝑒𝑓 = 5 + 1.7 ∗ cos⁡(𝑤 ∗ 𝑡) The result of robot’s trajectory:

This article focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles and operational mechanics that govern their functionality The study emphasizes the importance of accurate modeling techniques to enhance performance and reliability Additionally, it discusses various simulation tools that can be utilized to analyze robot behavior in different environments By integrating theoretical models with practical simulations, researchers can optimize the development of three-wheeled mobile robots for various applications.

At this time, the initial values stay the same as case one but increasing the frequency 6 times:

This report focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It explores the dynamics and kinematics involved in the movement of these robots, providing insights into their control mechanisms Additionally, the report discusses various simulation techniques used to analyze performance and optimize design, making it a valuable resource for researchers and engineers in the field of robotics Overall, the study emphasizes the significance of accurate modeling and simulation in enhancing the efficiency and reliability of three-wheeled mobile robots.

This report focuses on the modeling and simulation of a three-wheeled mobile robot The study explores the design principles, control mechanisms, and performance evaluation of the robot By utilizing advanced simulation techniques, we aim to enhance the robot's navigation and operational efficiency in various environments The findings will contribute to the development of more sophisticated robotic systems, improving their adaptability and functionality in real-world applications.

This situation changing matrix C becomes:

We get the result as following:

This article explores the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It delves into the mathematical frameworks and algorithms used to accurately represent the robot's movement and behavior in various environments The importance of simulation in testing and optimizing robot performance before real-world deployment is emphasized Additionally, the report discusses the challenges faced in the modeling process and potential solutions to enhance the efficiency and reliability of three-wheeled mobile robots Overall, this comprehensive analysis aims to contribute to the advancement of robotics technology and its practical uses.

In this section, the changes in matrix C are significant, leading to slight variations in trajectory However, the robot's ability to adapt using a dynamic controller is effective, and the impact of the kinematic controller on the system is minimal.

In final situation, we change the values  ang g= 300

Thus, we get the result:

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control strategies, and performance metrics essential for optimizing the robot's functionality By utilizing advanced simulation techniques, the report aims to enhance the understanding of the robot's dynamics and improve its operational efficiency in various environments The findings will provide valuable insights for future developments in mobile robotics technology.

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control mechanisms, and performance evaluation of the robot, highlighting its applications in various fields The study aims to provide insights into the dynamics and kinematics of the robot, enabling better understanding and optimization of its movement capabilities By utilizing advanced simulation techniques, the report demonstrates how to effectively predict and enhance the robot's operational efficiency in real-world scenarios.

Simulink Result

Getting the initial position of WMR is [x(0);y(0);  (0) ]= [2; 2; pi/4]

In other hands, the reference trajectory:

𝑦𝑟𝑒𝑓 = 5 + 1.7 ∗ cos⁡(𝑤 ∗ 𝑡) The result of robot’s trajectory:

This article focuses on the modeling and simulation of three-wheeled mobile robots, emphasizing their design, functionality, and applications It explores the mathematical models that govern their movement and behavior, providing insights into the dynamics of three-wheeled systems Additionally, the simulation techniques used to predict and analyze the performance of these robots are discussed, highlighting the importance of accurate modeling in robotics By understanding these concepts, researchers and engineers can enhance the efficiency and effectiveness of three-wheeled mobile robots in various fields.

At this time, the initial values stay the same as case one but increasing the frequency 6 times:

This article focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It discusses the importance of accurate modeling for effective simulation, which aids in understanding the robot's movement and behavior in various environments The paper emphasizes the role of simulations in testing algorithms and improving navigation strategies, ultimately enhancing the performance of three-wheeled mobile robots in real-world scenarios By integrating advanced modeling techniques, researchers can optimize the efficiency and reliability of these robots for diverse applications.

This report focuses on the modeling and simulation of a three-wheeled mobile robot It explores the design principles, control mechanisms, and performance metrics of the robot, highlighting its applications in various fields Through advanced simulation techniques, the report demonstrates how the robot can navigate and perform tasks efficiently The findings aim to enhance understanding of mobile robotics and contribute to future developments in autonomous systems.

This situation changing matrix C becomes:

We get the result as following:

This article focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It explores the dynamics and control mechanisms that enable these robots to navigate various environments effectively Additionally, the report delves into the software tools and methodologies used for simulating robot behavior, providing insights into performance optimization and real-world implementation By examining case studies and experimental results, the article underscores the significance of three-wheeled mobile robots in modern robotics and automation.

In this section, the changes in matrix C are significant, leading to a slightly altered trajectory However, the robot's ability to adapt using a dynamic controller is effective, and the impact of the kinematic controller on the system remains minimal.

In final situation, we change the values  ang g= 300

Thus, we get the result:

This article focuses on the modeling and simulation of three-wheeled mobile robots, highlighting their design, functionality, and applications It explores the mathematical models that govern their movement and the simulation techniques used to predict their behavior in various environments The importance of accurate modeling in enhancing the efficiency and performance of these robots is emphasized Additionally, the article discusses the challenges faced in the development process and how simulation tools can aid in overcoming these obstacles Ultimately, the insights provided aim to contribute to advancements in robotic technology and its practical implementations.

This article focuses on the modeling and simulation of three-wheeled mobile robots It explores the design principles and operational mechanics that enable these robots to navigate effectively The study emphasizes the importance of accurate modeling techniques for predicting robot behavior in various environments Additionally, it discusses simulation tools that facilitate the testing and optimization of robotic systems, ensuring enhanced performance and reliability Overall, the research aims to contribute to the advancement of mobile robotics by providing insights into the effective deployment of three-wheeled robots in real-world applications.

Tiêu đề	Modeling And Simulating The Threewheeled Mobile Robot
Tác giả	Phan Sỹ Nhật Tân, Vũ Quang Khải, Nguyễn Thành Hưng, Tô Viết Hiếu
Người hướng dẫn	Ph.D. Vũ Thị Thúy Nga
Trường học	Ha Noi University Of Science And Technology
Chuyên ngành	Electrical - Electronics
Thể loại	Report
Năm xuất bản	2022
Thành phố	Hà Nội

Định dạng
Số trang	95
Dung lượng	1,98 MB