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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 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 1.2.4 Car Drive 1.2.5 Omni Robot 1.3 Choosing WMR three wheels Part 2: Modeling the Moblie Robot Three Wheels .3 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 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 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 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: Where: 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 Om Xm axis The model is placed in a general coordinate system Xg ,Yg, and the coordinate system of motion associated with WMR Xm ,Ym The state vector of the vehicle in the general coordinate system is: Because the movement of the vehicle through transmission of rear wheels that moniting the WMR direction; therefore, the vehicle's longitudinal velocity is determined by: 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 vvT , we have a matrix S being vector fields representing the possible travel directions of the WMR: 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: Where: x2 , y2: font wheel coordinates The relationship between (x2,y2) with (x,y) as following: Therefore; Subtituting 2.10 into 2.8 we have : Phần 5: Mô hệ thống điều khiển Matlab Simulink Choosing controller: Where: and Choosing: 4.2 Designing The Dynamic Controller when t-> ꝏ Control purpose: We have: Where: 33 Phần 5: Mô hệ thống điều khiển Matlab Simulink Velocity deviation is : Derivative of deviation: Choosing: Where matrix C is a positive define 2x2 control matrix Then: 34 Phần 5: Mô hệ thống điều khiển Matlab Simulink Choosing: [ Part 5: Control System On Matlab Simulink 5.1 Knematic Model 35 Phần 5: Mô hệ thống điều khiển Matlab Simulink 36 Phần 5: Mô hệ thống điều khiển Matlab Simulink 5.2 Dynamic Model 37 Phần 5: Mô hệ thống điều khiển Matlab Simulink 38 Phần 5: Mô hệ thống điều khiển Matlab Simulink 5.3 Bộ điều khiển vịng ngồi Kynematic Controller 39 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: { = + 1.7 ∗ sin( ∗ ) The result of robot’s trajectory: 40 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 Phần 5: Mô hệ thống điều khiển Matlab Simulink 42 5.5.3 Third Case This situation changing matrix C becomes: [500 5] We get the result as following: Comparing with part 1: 43 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 valuesang g= 300 Thus, we get the result: 44 Comparing with part 1: 45 Comment: So, changing the kinematic controller affect a lot of to the system, the WMR’s trajectory will changes very much comparing with effect of dynamic controller Reference [1] WHEELED MOBILE ROBOTICS, Gregor Klancar, Andrej Zdešar, Sašo Blažic, Igor Škrjanc [2] Mobile robot, 2016, https://en.wikipedia.org/wiki/Mobile_robot (accessed 18.07.16) [3] “Design and implementation of an adaptive sliding-mode dynamic controller for wheeled mobile robots”, Chih-Yang Chen, Tzuu-Hseng S Li *, Ying-Chieh Yeh, Cha-Cheng Chang [4] [5] Wheeled Mobile Robot - an overview | ScienceDirect Topics 46 ... 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. .. ,Ym The state vector of the vehicle in the general coordinate system is: Because the movement of the vehicle through transmission of rear wheels that moniting the WMR direction; therefore, the. .. described by the Lagrange formula as follows: Where: : 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
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