SUBJECT REPORT designing tricycle with a trailer mobile robot

Hanoi University of Science and Technology -SEE ~~~~~~*~~~~~~ SUBJECT REPORT Designing Tricycle With A Trailer Mobile Robot Supervisor: Dr.Vu Thi Thuy Nga Members of Group 16: Khổng Trường Thịnh Nguyễn Thị Huyền Kiều Duy Phương Nghiêm Minh Tấn 20181927 20181894 20181914 20181923 ~~~~~~Ha Noi,2022~~~~~~ Gratitude And Acknowledgments Our team would like to express our sincere thanks to Dr Vu Thi Thuy Nga, previous classmates, and colleagues for their great support during the implementation of this project Currently, the group also has many shortcomings and the results have not reached the maximum set goals, but the work written in the report is the effort of all members We hope, this project will help with the implementation of our graduation thesis Introduction The world is more and more modern, the application of technology to life becomes inevitable Applications using mobile robots are researched and applied more and more In the medical field, robots are applied To monitor heart rate, body temperature , in the military field, the robot is used in unmanned combat aircraft, automatic minesweeping robot With a passion for making automatic robots with As university students, our team learned and decided to deploy the " Designing Tricycle With A Trailer Mobile Robot" model, which is a branch of autonomous robot cars, to satisfy our passion as well as meet the requirements of the subject.In this project, due to the limitation of specialized knowledge and working experience, we implement modules with modules With the first module, we are based on understanding the mathematical model of mobile robots wheels with freewheel and control wheels, then simulated on Matlab Simulink with the requirement to compare the error between the actual trajectory and the reference trajectory, combined with the compensation controller and related mathematical formulas that we will write in detail below, and at the same time design feedback hardware for the application of a digital PID controller, displayed on the LCD screen, no feedback yet position The second module is to simulate the line detection robot on Matlab Simulink, then design the hardware with modes: self-propelled line detector and manual control on the phone with communication method by communication module available Contents Gratitude And Acknowledgments .2 Introduction Chapter 1: Mathematical Formulas And Mobile Robot Modeling I Model of Mobile Robot (WMR) Kinematics Model Motion Constrains Dynamic Model Chapter Controller Design For The WMR And Simulation Results 12 I Ask for math problems 12 Kinematic Controller 16 Dynamic Controller .18 Chapter 3: Design a Robot Speed Control System Using PID Controller With DC Motor And Display On LCD .24 I Ideas and Hardware Implementations 24 II Common methods for determining controller parameters 25 2.1 Sample holder in closed loop control 27 2.2 Simulation of the PID in the discrete domain 27 Chapter Control System Design 29 I Building A General Block Diagram 29 II Hardware 32 2.1 Motor Drive 32 2.2 Encoder Motor 33 2.3 Power Supply .33 2.4 Microcontroller 34 2.5 LCD display .35 III Setting The Setpoint Value .37 3.1 Outline Algorithm 37 Chapter 5: Line Following Robot 40 I The problem posed 40 1.1 Understand Line Sensor 41 1.2 Line Creation Method 42 1.3 Line Following Algorithm 43 1.4 Design PID-based Line Following Algorithm 45 II Implemented on matlab Simulink 46 2.1 Step By Step of Desining 46 2.2 Simulation Result .48 Comment: 50 Reference: 50 Chapter 1: Mathematical Formulas And Mobile Robot Modeling I Model of Mobile Robot (WMR) Figure 1: Example of General Model of 3-wheeled Mobile Robot The most important thing for an engineer, especially an automation engineer, when designing controls for an object, is to thoroughly understand the formulas, methods of object modeling, and properties of that object because after all, to control an object, we need to define very clearly the controlled variables, manipulated variables and process variables That is very important for robot modeling by identifying the rather complicated way of working and the difficulty in converting from software simulation to hardware design Below is the modeling work that the team did during the learning process Kinematics Model Several types of kinematic models exist: • Internal kinematics: explains the relation between system internal variables • External kinematics: describes robot position and orientation according to some reference coordinate frame • Direct kinematics and inverse kinematics: A direct kinematics describe robot states as a function of its inputs (wheel speeds, joints motion, wheel steering, etc.) From inverse kinematics one can design a motion planning, which means that the robot inputs can be calculated for a desired robot state sequence • Motion constraints: appear when a system has less input variables than degrees of freedom (DOFs) Holonomic constraints prohibit certain robot poses while a nonholonomic constraint prohibits certain robot velocities (the robot can drive only in the direction of the wheels’ rotation) Figure The Model of a Three Wheeled Mobile Robot (WMR) In the following, some examples of internal kinematics for wheeled mobile robots (WMR) will be given The robot pose in a plane is defined by its state vector: (1) in a global coordinate frame (Xg, Yg), as illustrated in Fig.2 A moving frame (Xm, Ym) is attached to the robot The relation between the global and moving frame (external kinematics) is defined by the translation vector [𝑋 𝑌]𝑇 and rotation matrix: (2) The relationship between the position 𝑞(𝑡) of the WMR with its velocity is: (3) Where control variables are wheels’ steering velocity ω, and forward speed 𝝑 We also have: (4) We will let α(t)= [ 𝑉(𝑡) ] 𝑊(𝑡) Where: +,r is the wheel radius +,L is the distance between the wheels +,R(t) is the instantaneous radius of the vehicle driving trajectory (the distance between the vehicle center (middle point between the wheels) and ICR point) +,ωL(t) and ωR(t) are left and right angular velocities of the wheels around their axes, respectively Motion Constrains Motion of WMR is constrained by dynamic and kinematic constraints Dynamic constraints have origin in the system dynamic model where the system’s response is limited due to its inertia or constraints of the actuators Kinematic constraints have origin in robot construction and its kinematic model Kinematic constraints can be holonomic or nonholonomic Nonholonomic constraints limit some driving directions of a mobile robot Holonomic constraints are related to the dimensionality of the system state description (generalized coordinates) For the robot of our group, it is subject to both types of constraints Holonomic constraint limits the robot's workspace at the ground level, i.e the XY axis, and Nonholonomic constraints limits the direction of the robot's movement., i.e the robot cannot move immediately to the left side According to the non-linear characteristics of the WMR, the motion constraint of the system is nonholonomic and can be represented as: (5) The constraint coefficient matrix is derived from the nonholonomic constraint above as: 𝐴 = [− sin(𝜑) cos(𝜑) 0] (6) Dynamic Model For systems with motion constraints the dynamic motion equations are given using Lagrange multipliers [15] as follows: (7) The kinematic model only describes static transformation of some robot velocities (pseudo velocities) to the velocities expressed in global coordinates However, the dynamic motion model of the mechanical system includes dynamic properties such as system motion caused by external forces and system inertia Using Lagrange formulation, which is especially suitable to describe mechanical systems, the dynamic model reads: (8) where unknown disturbance 𝜏𝑑𝑘 from Eq.7 relation is omitted Similarly, the forces and the torques due to the gravitation gk are not present because the vehicle drives on the plane where the potential energy is constant (without loss of generality 𝑊𝑃 = can be assumed) Overall, kinetic energy of the system reads: (9) The potential energy is WP = 0, so the Lagrangian is (10) Additionally damping and friction at the wheels rotation can be neglected (P = 0) Forces and torques in Eq (7) are (11) And (12) According to Lagrange formulation (7) the following differential equations are obtained: ... robot With a passion for making automatic robots with As university students, our team learned and decided to deploy the " Designing Tricycle With A Trailer Mobile Robot" model, which is a branch... kinematics one can design a motion planning, which means that the robot inputs can be calculated for a desired robot state sequence • Motion constraints: appear when a system has less input variables... suitable values for each parameter First, the team examines the performance of the controller with only parameter KP and adjusts its gradually until the mobile robot could grasped the set value At