REPORT TOPIC MODELING AND SIMULATING THE THREEWHEELED MOBILE ROBOT

HA NOI UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF ELECTRICAL - ELECTRONICS FACULTY OF AUTOMATON *** REPORT TOPIC: MODELING AND SIMULATING THE THREEWHEELED MOBILE ROBOT INSTRUCTOR: Ph.D Vũ Thị Thúy Nga Group: Phan Sỹ Nhật Tân Vũ Quang Khải Nguyễn Thành Hưng Tô Viết Hiếu Hà Nội, 2022 Group 15 20192247 20192218 20192211 20192206 Mục lục Table of Contents .i Part 1: Introduction 1.1 Wheeled Mobile Robot 1.2 Some typed of Wheeled Mobile Robot 1.2.1 Differential Drive 1.2.2 Bicycle Drive 1.2.3 Tricycle Drive .1 1.2.4 Car Drive .2 1.2.5 Omni Robot 1.3 Choosing WMR three wheels Part 2: Modeling the Moblie Robot Three Wheels 2.1 Kinetic Model 2.2 Dynamic Model Part 3:Controlling Methods Wheel Mobile Robot 16 3.1 Control Overview 16 3.2 Basic approaches 17 3.2.1 Directional and translational control 17 3.2.2 Basic approaches 19 3.3 Orbit Following Control 22 3.3.1 following the trajectory using basic approaches 22 3.3.2 Analysis feedforward and feedback elements 22 3.3.3 Linearization of feedback 23 3.3.4 Development of tracking kinetic trajectory 25 3.3.5 Linear Controller 27 Part 4: Designing Controller for Three Wheel Robot 29 4.1 Designing Kynametic Controller 29 4.2 Designing the Dynamic Controller 32 i Mục lục Part 5: Control System On Matlab Simulink 34 5.1 Knematic Model .34 5.2 Dynamic Model 36 5.3 Kynematic Controller 38 5.4 Dynamic Controller 39 5.5 Simulink Result 39 5.5.1 First Case 39 5.5.2 Second case 40 5.5.3 Third Case 42 5.5.4 Fouth case 43 Reference 45 ii REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Part 1: Introduction 1.1 Wheeled Mobile Robot Wheeled Mobile Robots (WMR) are dynamic systems where an appropriate torque needs to be applied to the wheels to obtain desired motion of platform Motion control algorithms therefore need to consider the system’s dynamic properties Usually this problem is tackled using cascade control schemas with the outer controller for velocity control and the inner torque(force, motor current,etc.) The outer controller determines the required system velocities for the system to navigate to the reference pose or to follow the reference trajectory While the inner faster controller calculates the required torques to achieve the system velocities determined from the outer controller 1.2 Some Typed Of Wheeled Mobile Robot 1.2.1 Differential Drive 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 1.2.2 Bicycle Drive Bicyce Drive also have wheels as Differential Drive, but its wheels are arrange in a straight line, and usually only one wheel is active and other can control the steering angle, similar like a bicycle This type of robot is rarely used cause of its backwardness in reality applications 1.2.3 Tricycle Drive REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.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 wheels: rear wheels are arranged coaxially and front wheel is steering one Two of three wheels are attached to the actuator to control and the remaining one is free or to control desired speed or angle 1.2.4 Car Drive WMR has a structure similar to a car with front wheels that can change the steering angle 1.2.5 Omni Robot The Omni Directional Wheel is a kind of wheel that can freely role in more than one direction.In addition to the types of WMR just mentioned above, there are many other types of WMR, these are just some typical examples of WMR REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT 1.3 Choosing WMR three wheels Two Drive Rear Wheel Robot nonholonomic Front Drive Wheel Omnirobot Independent Three Wheels In this topic, We choose a Tricycle Drive with rear wheels as active wheels attached with actuators to control and front wheel as free wheel Part 2: Modeling The Moblie Robot Three Wheels 2.1 Kinetic Model WMR is illustrates as in the figure H2.1: REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Phần 5: Mô hệ thống điều khiển Matlab Simulink 5.3 Bộ điều khiển vịng ngồi Kynematic Controller 39 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Phần 5: Mô hệ thống điều khiển Matlab Simulink 5.4 Dynamic Controller 5.5 Simulink result 5.5.1 First Case Getting the initial position of WMR is [x(0);y(0);  (0)]= [2; 2; pi/4] In other hands, the reference trajectory: 𝑥𝑟𝑒𝑓 = + 1.7 ∗ sin⁡(𝑤 ∗ 𝑡) { 𝑦𝑟𝑒𝑓 = + 1.7 ∗ cos⁡(𝑤 ∗ 𝑡) The result of robot’s trajectory: 40 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Phần 5: Mô hệ thống điều khiển Matlab Simulink 5.5.2 Second Case At this time, the initial values stay the same as case one but increasing the frequency times: 41 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Phần 5: Mô hệ thống điều khiển Matlab Simulink 42 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT 5.5.3 Third Case This situation changing matrix C becomes: 50 [ ] We get the result as following: Comparing with part 1: 43 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Comment: In this part, changing in matrix C is quite large, there is a little bit different of trajectory So, but the ability of robot adaptations of dynamic controller is good with kinematic controller that affect to system is trivial  5.5.4 Fouth Case In final situation, we change the values ang g= 300 Thus, we get the result: 44 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT Comparing with part 1: 45 REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MO DELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT REPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPOR T.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOTREPORT.TOPIC.MODELING.AND.SIMULATING.THE.THREEWHEELED.MOBILE.ROBOT