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MINISTRY OF EDUCATION AND TRAINING VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY - HA THI KIM DUYEN ADAPTIVE DYNAMIC SURFACE TRAJECTORY TRACKING CONTROL FOR THE FOUR-WHEELED OMNIDIRECTIONAL MOBILE ROBOT Majors: Control and Automation Engineering Code: 52 02 16 ELECTRICAL, ELECTRONIC AND TELECOMMUICATION ENGINEERING Hanoi – 2020 Publications at: Graduate University of Science and Technology – Vietnam Academy of Science anf Technology Advisor 1: Prof Phan Xuan Minh Advisor 2: Dr Pham Van Bach Ngoc Reviewer 1: Reviewer 2: Reviewer 3: The thesis is defended at the PhD dissertation committee, which meets at Graduate University of Science and Technology – Vietnam Academy of Science and Technology at…………,2020 Thesis can be found at: - Library of Graduate University of Science and Technology - National Library of Vietnam LIST OF AUTHOR’S PUBLICATIONS SCIENTIFIC JOURNAL Duyen Ha Thi Kim, Tien Ngo Manh, Cuong Nguyen Manh, Nhan Duc Nguyen, Manh Tran Van, Dung Pham Tien, Minh Phan Xuan “Adaptive Control for Uncertain Model of Omni-directional Mobile Robot Based on Radial Basis Function Neural Network” International Journal of Control, Automation, and Systems (SCI-E Q2, Impact Factor: 2.7) (Accepted 2020) Ha Thi Kim Duyen, Ngo Manh Tien, Pham Ngoc Minh, Quang Vinh Thai, Phan Xuan Minh, Pham Tien Dung, Nguyen Duc Dinh, Hiep Do Quang, “Fuzzy Adaptive Dynamic Surface Control for Omnidirectional Robot”, the Springer-Verlag book series “Computational Intelligence” indexed in Scopus and Compendex (Ei) ISSN 1860-9503 (electronic), ISBN 978-3-030-49536-7 (eBook) https://doi.org/10.1007/978-3-03049536-7 (2020) Hà Thị Kim Duyên, Phạm Thị Thanh Huyền, Trương Bích Liên, Ngô Mạnh Tiến, Lê Việt Anh, Nguyễn Mạnh Cường, “Điều khiển bám quỹ đạo đối thượng Robot tự hành thuật toán điều khiển trượt theo hàm mũ”, Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san ACMEC, 07 – 2017 ISSN 1859 - 1043 H T ị D , Ngô Mạnh Tiến, Phan Xuân, Minh Lê Xuân Hải, Vũ Đức Thuận, Nguyễn Minh Huy, “Điều khiển bám quỹ đạo Omni robot bốn bánh phương pháp thích nghi mờ trượt” Tạp chí Nghiên cứu Khoa học Công nghệ quân Số đặc san ACMEC 07-2017 ISSN 1859 - 1043 Ngo Manh Tien, Nguyen Nhu Chien, Do Hoang Viet, Ha Thi Kim Duyen “Research And Development Artificial Intelligence To Track Trajectory And Automatically Path Planning For Auto Car” Journal of Military Science and Technology; ISSN 1859 – 1043 11/2018 Duyen – Ha Thi Kim, Tien – Ngo Manh, Chien – Nguyen Nhu, Viet – Do Hoang, Huong-Nguyen Thi Thu Kien-Phung Chi, “Tracking Control For Electro-Optical System In Vibration Enviroment Based On Self-Tuning Fuzzy Sliding Mode Control”, Journal of Computer Science and Cybernetics, Vol 02, 6.2019 SCIENTIFIC CONFERENCE Ngô Mạnh Tiến, Nguyễn Như Chiến, Đỗ Hoàng Việt, H T ị D , Nguyễn Tuấn Nghĩa, “Trajectory Tracking Control for Four Wheeled Omnidirectional Mobile Robots using Adaptive Fuzzy Dynamic Surface Control Algorithm”, Proceedings the 4th Vietnam International Conference and Exhibition on Control and Automation VCCA2017; ISBN 978-604-73-5569-3 Duyen Ha Thi Kim, Tien Ngo Manh, Tuan Pham Duc and Ngoc Pham Van Bach, “Trajectory Tracking Control for Omnidirectional Mobile Robots Using Direct Adaptive Neural Network Dynamic Surface Controller” The 2019 First International Symposium on Instrumentation, Control, Artificial Intelligence, and Robotics 1/2019 NSPEC Accession Number: 18473513, DOI: 10.1109/ICA-SYMP.2019.8646146 Ha Thi Kim Duyen, Cuong Nguyen Manh, Hoang Thuat Vo, Manh Tran Van, Dinh Nguyen Duc, Anh Dung Bui, “Trajectory tracking control for four wheeled Omnidirectional mobile Robot using backstepping technique aggregated with sliding mode control”, The 2019 First International Symposium on Instrumentation, Control, Artificial Intelligence, and Robotics 1/2019 INSPEC Accession Number: 18473501, DOI: 10.1109/ICA-SYMP.2019.8646041 10 Ngô Mạnh Tiến, Nguyễn Mạnh Cường, H T ị D , Phan Sỹ Thuần, Nguyễn Ngọc Hải, Trần Văn Hoàng, Nguyễn Văn Dũng, “Giám sát định vị, đồ hóa điều hướng cho robot tự hành đa hướng sử dụng hệ điều hành lập trình ROS”, Hội nghị Quốc gia lần thứ XXII Điện tử, Truyền thông Công nghệ Thông tin lần thứ 22, 2019 INTRODUCTION Rasionale of the thesis Omni-directional mobile robot (OMR) is a holonomic robot using Omni or Mecanum wheel, which can move in any direction without changing the robot’s position and rotation angle Due to the outstandingly moving in narrow environmental conditions when using the particular wheel structure and wheel layout, OMR is being widely applied and developed not only in research but has quickly become widely used in production and life fields In robot control, the problem of trajectory tracking control, dealing with external disturbance, and the uncertain part existing in the robot model, including mass, moment, and friction,… is the content which is significantly focused in research The task which is to guarantee the high accuracy in the robot motion is commonly difficult because of the nonlinear and uncertain parts typically existing in the robot model Research Objective - Research and propose a novel adaptive trajectory tracking algorithm for FWOMR ‘s nonlinear uncertain model which is influenced by the change of robot parameters and the effect of noise when operating on another plane - Construct the physical model of FWOMR and the controller based on the microchip and embedded programming technique to experiment with the proposed algorithms Object and scope The object of the study: a four-wheeled omnidirectional mobile robot The thesis puts emphasis on the construction of the mathematical robot model and the adaptive trajectory tracking control algorithms for FWOMR The study scope: Design an adaptive controller for FWOMR model which is influenced by the uncertain elements in the flat environment affected the surface friction and bounded abitrary noise Scientific significance and new contributions of the thesis Propose an adaptive fuzzy dynamic surface control (AFDSC) for the four-wheeled omnidirectional mobile robot The algorithm is constructed based on the DSC technique To take advantage of the DSC, AFDSC uses a fuzzy rule tuning the DSC parameters to guarantee the trajectory tracking quality when the FWOMR’s parameters are variable and are affected by the unknown disturbance Until now, the DSC tuned by the fuzzy rule has not ever been installed in any mobile robot platforms in domestic and overseas Propose an adaptive fuzzy neural network dynamic surface control (AFNNDSC) for FWOMR which contains uncertain parameters and its model is affected by the disturbance The algorithm is developed based on the DSC technique, its adaptive characteristic is created by the combination of the radial basis function neural network (RBFNN) and the fuzzy law The RBFNN is to approximate uncertain parameters of the FWOMR, while the fuzzy law simultaneously tunes the control parameter The system stability is verified by the Lyapunov standard Simulation results and experiments show the accuracy and effectiveness of the proposed method and its practical application ability The AFNNDSC has not ever been installed in any robot platforms in domestic and overseas Moreover, the AFNNDSC has highly flexible and adaptive characteristics when the robot is adversely influenced by the disturbance, and the model’s parameters are variable That leads to the expansion of the robot’s operation scope The algorithms are installed and successfully experimented in the four-wheeled omnidirectional mobile robot The constructed robot has the high-performance processor control circuit and the software built on ROS Thesis layout Chapter 1: “An overview of the four-wheeled omnidirectional mobile robot” An overview study of FWOMR, domestic and international research, detailed analysis of advantages and disadvantages of previously researched works according to the content of the subjects, the research scope of the thesis, from there draw appropriate research directions for the thesis Chương 2: “Modeling and trajectory control algorithms for the four-wheeled omnidirectional mobile robot” This chapter shows the construction of the dynamic model for FWOMR and a presentation of some typical trajectory control algorithms for FWOMR Moreover, the simulation, evaluation, and analysis the results of these algorithms are to evaluate and draw lessons learned in the proposed study of the new adaptive orbital control algorithm Chapter 3: “Design an adaptive trajectory tracking controller for the four-wheeled omnidirectional robot” The chapter is the main contribution of the thesis In this chapter, an adaptive trajectory tracking controller for the four-wheeled omnidirectional robot using a dynamic surface control is presented The DSC algorithm is the platform for the control quality improvement using the proposed adaptive trajectory tracking controller The DSC controller is combined with a radial basis function neural network (RBFNN) and fuzzy logic system (FLS) to design a novel adaptive DSC controller which is proposed in the thesis Chương 4: “Manufacture the four-wheeled omnidirectional mobile robot and experiment with the proposed control algorithm” This chapter shows the design and manufactures the four-wheeled omnidirectional mobile robot model, and programming and experiment of the proposed algorithms to verify and evaluate the practical applicability “Conclusion” presents the abstract of the main contributions and future works AN OVERVIEW OF THE FOUR-WHEELED OMNIDIRECTIONAL MOBILE ROBOT Omnidirectional mobile robots (OMR) are capable to move in any direction without the changing its direction and position With a particular wheel structure and the advantage of flexible movement in the environment which is narrow and difficult to change the position Nowadays, OMR is widespreadly applied not only in research but in the various production fields due to its ability to flexible and omnidirectional move 1.1 Autonomous mobile robot built with omnidirectional wheel In the thesis scope, a holonomic mobile robot is constructed using four Omni wheels with a consistent structure, which ensures that the robot can promptly move in horizontal direction 1.2 Trajectory tracking control problem The structure of the motion control system for OMR can be devided into three phases: - Set up the motion plan - Plan the reference trajectory - Control robot to track the reference trajectory 1.3 Overview of domestic and international research 1.3.1 Domestic research situation Institute of Information Technology and Institute of Mechanics, Vietnam Academy of Science and Technology Institute of Information Technology and Institute of Mechanics, Vietnam Academy of Science and Technology have a number of published research on autonomous robot research, such as [1] presenting new control methods to compensate the impact of the slip phenomena for mobile robots in the existence of wheel slip, uncertainties, and external noise for 3-wheel mobile robotics, [2] presenting the design and control of a nonholonomic mobile robot for warehouse applications Institute of Physics, Vietnam Academy of Science and Technology is also a research group with many published works on autonomous robots, including [3] presenting research orientation for trajectory tracking control for nonholonomic mobile robots with the integration of the image processing technology to identify some parameters and track the target Moreover, [4] conducted research on applying the trajectory tracking control algorithm for the nonholonomic mobile robot using the ideal function adaptation Nowadays, there are a few domestic studies on OMR, in which, [5] is an obstacle avoidance control for OMR using Kinect image processing technology In addition, this work focuses more on image processing than the field of robot control for OMR There are not many publications about the trajectory tracking control algorithm for the four-wheeled robots using Ommi wheels in Vietnam 1.3.2 International research situation The robot was modeled using kinematic and dynamic models Robot modelling was researched based on Euler-Lagrange equations, which used theoretical and experimental methods [31], [32], [33], [34], [35], [36], [37], [38], [39], [40] A mount of research focused on the navigation system and motion control based on the robot kinematic model of OMR [43], [44], [45], and [46] The PID algorithm was applied for trajectory tracking control of the four-wheeled OMR in [43] and [44] However, recent research has considered both kinematic and dynamic models to enhance the accuracy in robot movement [42] and [43] The design of the trajectory tracking control algorithm for OMR taking into account all the kinematic and dynamic models has been considered in [39] The dynamic model is constructed in [47] and [48], followed by a number of trajectory tracking control algorithms for this full model in [49] and [50] Studies have used PI controllers to optimize orbital adhesion [52], [57], and [79] On the other hand, the algorithm using the predictive model has also been mentioned in [51] More and more research is focused on feedback control methods for the nonlinear model 52], [53], [54], [55], [56], and [57] The Backstepping feedback method is a viable solution to solve affined models [58] and [59] However, with high order nonlinear systems, the computational volume is large, complicated, and takes too many computation time due to the need to calculate the derivative in each iteration step Sliding mode control (SMC) has also been used [60], [61], [62] and [63 for its superior properties in the case of the system affected by noise However, the limitation of the SMC algorithm is chattering, and reducing this phenomenon requires an accurate object model It goes against the properties of the robot model, which is the parameter uncertainty In order to improve the quality of control as well as to limit some of the disadvantages of the Backstepping and SMC controllers, a dynamic surface control (DSC) technique is introduced in [64] and [65] The design steps are similar to those of the Backstepping, but to avoid derivative steps for the DSC virtual control signal, a low pass filter is added, just to get information about the lead medium function to filter the high-frequency internal noises occurring in the control object [65] For OMR, it is challenging to build an accurate mathematical model because factors such as friction, load change, and environmental conditions are not known Therefore, the effective modern design methods, in this case, are to use adaptive algorithms to tune controller parameters using Fuzzy logic or approximate the uncertainties using neural networks This adaptive controller significantly improves the quality of the nonlinear dynamics [60], [61], [62], [66], [68], [69], [70], [71] and [72] With the above reference and analysis, a new adaptive control structure based on a radial basis function neural network (RBFNN) and fuzzy logic system for the trajectory tracking controller is researched and developed based on the Dynamic Surface Control (DSC) technique A novel adaptive controller with RBFNN for the approximation of the nonlinear uncertain parameters of the FWOMR and fuzzy logic to tune the controller's parameter is proposed in the thesis 1.4 Conclusion Chapter presented an overview of mobile robot classification and autonomous mobile robots, which focuses on an autonomous mobile four-wheeled robot (FWOMR) being the main research object of the thesis Chapter also focused on a research overview of domestic and international research on OMR modeling and trajectory tracking control algorithms for OMR published and analyzed the advantages and disadvantages of these methods from which to draw appropriate research directions for the thesis MODELING AND TRAJECTORY CONTROL ALGORITHMS FOR THE FOUR-WHEELED OMNIDIRECTIONAL MOBILE ROBOT Building the system of kinematic and dynamic equations for OMR is the very first problem needed for the synthesis of the trajectory tracking control In the thesis, the research object considered is an autonomous four-wheeled robot using Omni-type wheels, which moves on the plane is affected by friction 2.1 Building the kinematic and dynamic models of the four-wheeled omnidirectional mobile robot 2.1.1 The Omni wheel Omni wheels are arranged perpendicular to the axis of the motor, the wheels are spaced 3600 / n apart Omni wheels are widely used in autonomous robots because it allows the robot to move immediately to a position on a plane without having to rotate before Furthermore, the translational movement along a straight trajectory can be combined with rotational movement that causes the robot to move to the desired position with the accuracy orientational angle 2.1.2 Kinematic model of the four-wheeled omnidirectional mobile robot [41], [42] An equation presenting a relationship between the two coordinates is also the robot kinematic model cosθ -sinθ q Hv sinθ cosθ v 0 1 (2.1) cosθ -sinθ where: H = sinθ cosθ is a transition matrix 0 1 From (2.1), we calculate an equation presenting a relationship between the robot’s position and the velocity of wheels: 1 x y g ( ) 2 với g ( ) HH (2.4) 3 4 2.1.3 Dynamic model of the four-wheeled omnidirectional mobile robot [41], [42] The kinematic and dynamic models of FWOMR are constructed based on a robot model accompanied by the Omni wheels which are positioned 450 apart from the dynamic coordinate and 900 apart from the beside ones From which, the robot’s dynamic equation has the following formula M (q) v Cv Gsgn( v) τ d Bτ (2.8) with: v [ vx vy ]T is a velocity vector 2 2 2r 2r 2r 2r 2 2 B is a control parameter matrix r r r r d d d d r r r r m 0 M (q ) m is a matrix with m is the robot mass and J is the inertia moment 0 J 0 0 Bx C x C By and G C y are viscous friction parameter matrix and 0 B 0 C Coulomb friction matrix, respectively 2.2 Several existing trajectory tracking control algorithms for the four-wheeled omnidirectional mobile robot 2.2.1 PID controller for FWOMR The PID controller for FWOMR is proposed in [43] and [44] These studies have designed the PID controller based on the kinematic model of OMR Hence, the effects of external forces on the system in the robot's dynamic equation were not taken into account 1 x (t ) xd xd e1 y (t ) y d g ( ) y d (2.11) 3 (t ) d d 4 We need to find the angular velocity vector of the wheels for the closed-loop controller to be stable t x d e 1 0 x e t g T ( )( g ( ) g T ( ))1 K P ye K I ye d (2.12) 3 0 e t 4 d 0 e with K P and K I are diagonal positive definite matrices 2.2.2 Sliding mode control for FWOMR SMC in [60], [61], [62] and [63] is commonly used for robot systems in general and FWOMR in particular because of its robust characteristic with external noises x1 q From (2.1) and (2.8), let , we have state equations: x v x Hx (2.19) Mx Cx Gsgn(x ) τ d Bτ with τ d is uncertain and not accurately measured, and thus, this component will not exist during the calculation of SMC, MSSC controllers Define the sliding surface with conditions and assumptions e x1 x1d Define the errors with x1d is a reference trajectory and x 2d H 1x 1d is e x x 2d reference velocity Choose the sliding surface S e1 e1 with >0 is a sliding surface coefficient Take the sliding surface’s derivative He e H (M 1 (Bτ Cx Gsgn(x )) x ( H 1H )e ) S He 2 2 2d Choose a Lyapunov candidate function (2.20) (2.21) V S2 Take its derivative, we obtain )e ) V SS SH (M 1 (Bτ Cx Gsgn(x )) x d ( H -1H With the control signal is chosen as follows )e x ) Cx Gsgn(x ) K sgn(S)) τ BT (BBT ) 1 (M (( H 1H 2d 2 V SK sgn(S) , which satisfies the Lyapunov standard (2.22) (2.23) (2.24) The sliding controller (2.24) is designed for stability and durability when the system exists with model deviation and impact interference The function V in the formula (2.22) with control law (2.24) for the FWOMR system is the Lyapunov function of the closed system 2.2.3 Multiple sliding surface control for FWOMR - Consider the robot’s state equations x Hx (2.36) Mx Cx Gsgn(x ) τ d Bτ x vx with x1 y x v y - Consider the sliding surface S11 S1 S12 x1 x1d S13 (2.37) - Take derivative of S1 and use (2.37), we obtain S x x Hx x 1d 1d Choose a virtual control signal x d H 1 ( K1S1 x 1d ) - Choose the first Lyapunov candidate function V1 S1T S1 - Take derivative of V1 , and use (2.38) and (2.39) V ST S ST K S 1 1 (2.38) (2.39) (2.40) (2.41) - Consider S as the second sliding surface (2.42) S H(x x2 d ) Taking derivative of S (x x ) S H (x x d ) H 2d (2.43) (x x ) H (M 1 (Bτ Cx Gsgn(x )) x d ) H 2d Combine (2.39), (2.40), (2.43), and (2.44), we obtain: Lyapunov candidate function is proposed V1 e1T e1 Take derivative of V1 V1 e1T e1 e1T Hx x 1d e1T c1e1 e1T c1e1 Hx x 1d (3.7) (3.8) It can be seen that from (3.8) with the virtual control signal (3.5), V1 e1T c1e1 and that leads to the condition V e T c e is satisfied 1 1 Define the virtual signal error e2 x α f (3.9) Choose the sliding surface S e1 He2 (3.10) where is a coefficient Take derivative of S e He H M 1 Cx Gsgn x Bτ α S e1 He He 2 2 f The second Lyapunove candidate function is chosen as V2 ST S The control signal includes the two elements τ eq τ sw (3.11) (3.12) τ eq keeps the system states on the sliding surface τ eq is calculated from solving S x τ eq BT (BBT ) 1 M H 1 e1 He 2 d Cx Gsgn x (3.13) The equation of τ sw is chosen as follows: τ sw BT (BBT ) 1 MH 1 c2sgn S c3S c2 x c3 x with c2 c2 y and c3 c3 y 0 c2 matrixes Finally, the control signal is the sum of τ eq (3.14) are the diagonal positive definite c3 and τ sw : τ τ eq τ sw (3.15) Theorem 3.1: Consider the FWOMR model is described by (2.3), the controller (3.15) with τ eq in (3.13) and τ sw in (3.14) guarantees that the close-loop system is stable and the tracking error tends to Proof Taking derivative of V2 V2 ST S (3.16) From (3.11), V2 becomes 10 H M 1 Cx Gsgn x Bτ α V2 ST e1 He 2 f (3.17) With the control signal (3.13), the derivative of V2 can be rewritten as V ST c sgn S ST c S (3.18) By choosing appropriate values for c2 and c3 , we obtain V ST c sgn S ST c S (3.19) 2 2 3 That satisfies the Lyapunov standard, and the Theorem is proven! 3.2 An adaptive fuzzy dynamic surface control for trajectory tracking control for FWOMR 3.2.1 An adaptive fuzzy dynamic surface control The outstanding point of the DSC controller is its stability with variable system parameters (uncertainties vary in the limited range) However, this strength is only available when the system state is on the sliding surface or the vicinity of the sliding surface The schematic diagram of a fuzzy DSC system is shown in Figure 3.7 Figure 3.7 The structure of the adaptive fuzzy dynamic surface control system for FWOMR Based on the DSC simulation results for FWOMR, we found that the quality of the system significantly depends the determination of the DSC parameters (c1 , c2 , c3 ) c1 is a parameter directly affecting the tracking quality of the robot, while c2 and c3 take impact on the speed of approaching the sliding surface of the system states, as well as the ability to keep the system states on the sliding surface In each state, if the right set of parameters is selected, the system will achieve high-quality performance, especially when the system is affected by noise Thus, in this chapter, an adaptive fuzzy DSC is proposed for FWOMR The fuzzy inputs are the tracking error e1 and its derivative e1 Fuzzy sets for linguistic variables are described in Figure 3.8 and Figure 3.9 NB -10 -5 NS Z PS PB -0.01 0.01 NB 10 -25 -12 NS -0.06 Z PS PB 0.06 12 25 Figure 3.9 Fuzzy set for e1 Figure 3.8 Fuzzy set for e1 11 With the input and output data obtained when simulating the DSC controller, the fuzzy sets of the input language variable, as well as the output values and the constituent rules for the fuzzy tuner, are built based on the Sugeno fuzzy model The fuzzy sets for the input linguistic variables e1 e1 are triangle forms, while c1 , c2 , c3 are chosen through experiment Fuzzy linguistic variables and their meanings are shown in Table 3.1 The fuzzy output values are shown in Table 3.2 Table 3.1 Fuzzy sets of the input linguistic Bảng 3.2 Output values variable Output Meanin Output Output Linguistic Linguistic Meaning variabl g value of values of c2 e e1 e1 c1 and c NB NS Z PS PB NB NS Z PS PB Negative big Negative small Zero Positive small Positive big VS S M B VB Bảng 3.3 Fuzzy rule of c1 e1 e1 Very 1.5 20 small Small 4.25 25 Medium 6.5 30 Big 35 Very 10 40 big Bảng 3.4 Fuzzy rule of c2 ( c3 ) e1 NB NS Z PS PB NB M S VS S M N NB M B M S M B NS NS S VS B M B VS VB Z Z B M S M B PS PS S M S VS S M PB PB M 3.2.2 Simulation The external disturbance has the form in Figure 3.10 e1 NS B M S M B Z VB B M B VB PS B M S M M PB M S VB S M Figure 3.10 The external disturbance The reference trajectory is described by: xr r0 cos(t ) yr r0 sin(t ) r The paramters of the FWOMR model and the controller are chosen as in Table 3.5 12 Table 3.5 System parameters and control parameters m 10kg ; J=0.56 kgm ; d 0.3m; r 0.06m Dynamic parameters t 15, r0 10m Trajectory parameters Control parameters diag (10,10,10); b 25 Figure 3.13 angular motion Figure 3.12 y-axis motion Figure 3.11 x-axis motion It can be seen that the controllers ensured the tracking quality, but the AFDSC showed the most considerable performance The parameters (c1 , c2 , c3 ) of the AFDSC are in the Figures 3.14, 3.15, 3.16 Figure 3.14 c1 Figure 3.15 c2 Figure 3.16 c3 Figure 3.17 describes the motion of FWOMR in the Oxy coordinate It can be seen that the efficiency of the proposed algorithm when the robot’s trajectory tracks remarkably close to the reference Figure 3.17 Motion of FWOMR 13 3.3 Adaptive fuzzy neural network dynamic surface control for FWOMR AFDSC has been a suitable recommendation to improve the tracking quality for FWOMR in the case of model deviation and noise with a small amplitude But in the case of large model deviation, the control quality is no longer guaranteed Therefore, the estimation of model deviation and compensation in controller components will ensure to improve the quality of this controller Figure 3.18 The structure of AFNNDSC 3.3.1 Approximation of the uncertainty in FWOMR model using the radial basis function neural network The FWOMR model contains the uncertainties described by τ d in (2.8) Therefore, the calculated control signal τ in the previous chapter may not reach the good quality in many cases Besides, other uncertainties make the AFDSC difficult to perform The thesis proposes an estimator using RBF neural network for uncertain components in the AFDSC controller The uncertain elements are described by an equation: (3.20) Θ M 1 Cx Gsgn x τ d which is a (3x1) vector containing the uncertainties of FWOMR The equations describing FWOMR is rewritten as: x Hx (3.21) 1 x Θ M Bτ Conduct the calculation steps which are the same as previous chapter for control design, the sliding surface’s derivative has the form e He H Θ M 1Bτ x S e1 He He (3.22) 2 2d The system control signal is τ τ eq τ sw (3.23) with ˆ x Θ τ eq BT (BBT )1 M H 1 e1 He 2d τ sw BT (BBT ) 1 MH 1 c2sgn S c3S 14 (3.24) (3.25) ˆ is trained online to approximate the system The radial basis function neural where Θ network contains three layers, including input layer, hidden layer, and output layer Figure 3.19 Radial basis function neural network ˆ Lựa chọn giá trị để tính tốn luật thích nghi cho Θ Θ RT γ ε ˆ R ˆ Tγ Θ (3.26 (3.27) ˆ is the neural network output and it with Θ is idea value of the uncertainty While, Θ is also the value used for the controller R R ˆ is defined as the weight error The hidden layer output is calculated Next, R by a radial basis function x1 1i x 2i γ i exp (3.28) i where x1 and x are input vectors of the RBFNN 1i and 2i are the center vectorsn nơ-ron, and i indicates the standard deviation With the designed neural network structure, the updated law is chosen as ˆ ˆ R γST H S R (3.29) where is a square positive definite matrix with n dimension, in which n is a neural number is a learning rate, which is chosen in the range (0,1) Theorem 3.2: Consider the FWOMR model (3.2), with the controller (3.23) and the adaptive law (3.29), if the bounded condition N S R F (3.30) c3min is satisfied, then the system stability is validated according to the Lyapunov standard Proof Consider a Lyapunov candidate function: 1 T 1R V2 ST S tr R (3.31) 2 Take derivative of V2 ˆ T 1R V2 ST S tr R ) (3.32) 15 Combine (3.22) with the control signal (3.23), the derivative of V2 becomes ˆ ) tr R T 1R ˆ V2 ST c2sgn S ST c3S ST H (Θ Θ (3.33) Use (3.22), (3.24), and (3.25), we obtain ˆ T γ tr R T 1R V2 ST c2sgn S ST c3S ST Hε ST HΘ (3.34) (3.35) (3.36) After some calculation steps, the derivative of V2 becomes ˆ T 1R V2 ST c2sgn S ST c3S ST H tr R γST HM 1 With the adaptive law (3.29), V2 is rewritten as T R R V2 ST c2sgn S ST c3S ST Hε S tr R Apply the Cauchy-Schwarz inequality T R R R tr R F R F R (3.37) F We obtain V2 ST c2sgn S ST c3S S N S R F R F R F (3.38) With the bouned condition (3.30), V2 becomes V2 ST c2sgn S S R V2 and Theorem is proven! F R F (3.39) 3.3.2 Construct the fuzzy law for AFNNDSC The fuzzy law is described in the section 3.21 The fuzzy inputs are a vector containing e1x , e1 y , e1 and its derivative, which are shown in Table 3.6 The fuzzy sets for the input linguistic variables are described in Figure 3.20 In addtion, The fuzzy law outputs are given in Table bẳng 3.7 The first output is the tuned value for c1i i x, y, The other is the value for c2i i x, y, c3i i x, y, To simplify the paramters choosing for AFNNDSC, c2i is chosen so that it is equal c3i The fuzzy rule is given in Table 3.6 Figure 3.20 The fuzzy sets for the input 16 Figure 3.6 Fuzzy rules for c1i (c2i ) e1 Figure 3.7 Output values of c1i (c2i ) e1 VS S M B VB 3.0 (5) 4.15 (10) (20) 7.5 (25) 12 (30) NB NS Z PS PB NB M(M) S(B) VS(VB) S(B) M(M) NS B(S) M(M) S(B) M(M) B(S) Z VS(VB) B(S) M(M) B(S) VS(VB) B(S) M(M) S(B) M(M) B(S) PS PB M(M) S(B) VS(VB) S(B) M(M) 3.3.3 Simualtion results In this section, the simulations are performed in Matlab/Simulink environment 3.3.3.1 Robot model affected by the external disturbances The reference trajectory for FWOMR is a circular trajectory described by a equation with the radius r0 5m ; t 10 In addition, the robot parameters are: m=10kg, J=0.56kgm2, d=0.3m, r=0.06m The initial position of the robot is chosen as ( x; y ) (2; 2) In this case, the system is simulated and evaluted in the condition, which is directly influenced by the Gaussian-type moment noise affecting the motors Moreover, the impact of friction force is ignored The sliding surface coefficient is chosen as: diag 10,10,10 Figure 3.21 Moment noise (Nm) The simulation results are shown as the following figures The Figure 3.22, 3.23, and 3.24 compare the tracking error of FWOMR when using the three controllers, including DSC, adaptive neural network dynamic surface control (ANNDSC), and adaptive fuzzy neural network dynamic surface control (AFNNDSC) Figure 3.24 angular error Figure 3.23 y-axis error Figure 3.22 x-axis error From the figures 3.22, 3.23, 3.24, it can be seen that all the controllers can ensure the system tracking errors along with the three-axis when the robot is affected by the external 17 noise moments is not too large and kept within a permissible range However, there is still a quality difference between the controllers in the above results, when combining the DSC algorithm with the neural network and the controller fuzzy logic system shows much better quality than the controller using a conventional DSC algorithm Figure 3.26 Tuned value of c2 and c3 Figure 3.25 Tuned value of c1 Under the condition where the robot is affected by external noises, a conventional DSC controller is not appreciated because it is challenging to accurately determine the robot's parameters In this case, the DSC controller combines fuzzy logic with an RBF neural network (AFNNDSC), which helps to tune the coefficients of the controller with the fuzzy law and approximate the uncertainty components in the robot model using the neural network, improves the system response time, as well as significantly alleviate the tracking errors It can be seen from the above simulation results, the time for the robot to approach the set value is about 0.2 seconds when using the AFNNDSC controller Figure 3.25 and Figure 3.26 show the variations in control parameters when applying fuzzy law: Figure 3.27 Robot circular trajectory Tuned controller parameters based on fuzzy rules help the system state to progress faster to the sliding surface, and control parameters are constantly updated during robot movement At the initial time when the robot is not on the desired trajectory, the tracking error is large, thus the control parameters need to achieve values that are large enough to 18 ensure that the system states rapidly approach the sliding surface Then, when it is close to the set trajectory, the control parameters should be adjusted to reduce the "chattering" phenomenon, while ensuring the robot is closely track to the set trajectory Figure 3.27 depicts the motion of FWOMR compared to the reference trajectory when applying different control algorithms In general, the controllers ensure the robot's ability to track the trajectory However, AFNNDSC adaptive controller showed better quality than the others in reducing the overshot time as well as the static deviation of the system 3.3.3.2 Robot model affected by the variation of the friction forces One of the most common problems in the motion control of the Omni robot as well as conventional mobile robots is the influence of the friction forces In the dynamic model of the robot, the friction coefficients are often considered as certain values or ignored since it is difficult to obtain the accurate value of these parameters Therefore, in this case, the simulation is conducted with the assumption that the friction coefficient matrixes C q, q diag Bx , By , B and G q diag C x , C y , C are unknown Then the nerual ˆ ˆ network approximates Θ x ˆ y ˆ T to ensure the system stablity as shown in Figure 3.28, Figure 3.29, and Figure 3.30 The uncertain values are approximated and they converge to the approximate value and improve the control quality of the system ˆ compared Figure 3.30 Θ ˆ compared Figure 3.29 Θ y ˆ Figure 3.28 Θ x compared to to Θ to Θ y Θx In this case, a quality difference between the controllers can be clearly seen in reducing the tracking error Figure 3.33 Angular error Figure 3.32 y-axis error Figure 3.31 x-axis error The system's tracking error, as well as the time it takes for the system to reach the set trajectory when using the DSC controller, is the greatest, while there is no significant 19 difference between the two controllers ANNDSC and AFNNDSC in Figure 3.31, figure 3.32, and figure 3.33 Furthermore, with the change in the coefficient of the friction of the medium, the DSC controller cannot completely eliminate system bias Table 3.8 compares the tracking errors of the system when applying the three controllers in case the system is affected by the impact of the environment Table 3.1 The maximum value of tracking errors when the robot is on the orbit Controller The maximum value of the tracking errors X-axis (m) Y-axis (m) Angular (rad) 0.1362 0.1426 0.005947 DSC 0.00224 0.00154 0.0003964 ANNDSC 0.000429 0.000301 0.0003953 AFNNDSC These controllers ensure that the Omni robot can track the required trajectory, while the control performance using RBFNN has the best control quality in reducing the settling time and eliminating the tracking errors There are obvious differences in the performance of decreasing the tracking errors between the presented methods The tracking errors of the classic DSC technique dramatically change and take the longest time to keep the error approximately back to zero Whereas, the DSCNN and DSCNNF control laws are not negligibly affected The tracking errors of these controllers are significantly smaller than one only using DSC technique In general, the results using the controller AFNNDSC show the most significant performance in reducing settling time and tracking errors 3.4 Conclusion Chapter is the main contribution of the thesis In this chapter, the DSC algorithm, and new adaptive algorithms such as AFDSC, AFNNDSC are proposed to solve the trajectory tracking control problem for FWOMR The steps to solve this problem is as follows: + Applying the DSC algorithm to solve the trajectory tracking control problem for FWOMR Simulating the DSC control system for FWOMR, analyzing and evaluating the advantage and disadvantage to propose AFDSC to improve the control quality FWOMR + Proposing AFDSC algorithm for FWOMR This algorithm is designed on the basis of DSC algorithm and fuzzy logic Because the quality of the controller majorly depends on the parameters of the DSC, the thesis has proposed a method of adjusting the parameters of the controller by Sugeno fuzzy model Sugano model fuzzy has the advantage of simple synthesis, and it is easily embeded into the microcontroller AFDSC system for FWOMR is investigated by numerical simulation The simulation results show that the quality of the control system is much better than the one using DSC However, with large deviation from the accurate model and many uncertainties also affecting FWOMR, the AFDSC no longer guarantees the quality Therefore, in order for the controller to be suitable for more complex conditions, the thesis has proposed a method to use the RBF network to approximate these uncertain components The result is published in the publications and in the section “Author’s Publications” + An AFNNDSC is proposed to solve the trajectory tracking control problem for FWOMR In this controller, the RBF neural network for the approximation of the 20 uncertainty in robot dynamic model, the fuzzy rule for the parameter tuning of DSC The numerical simulation results show that the quality of this controller ensures the quality of operation for FWOMR with the uncertain nonlinear model influenced by environmental noise The result is published in the publications and in the section “Author’s Publications” The novel contributions are also necessary to be experimented in the physical model to to verify the accuracy and the application ability of these algorithms This is the main content in the next chapter CHẾ TẠO ROBOT TỰ HÀNH BỐN BÁNH ĐA HƯỚNG VÀ CHẠY THỬ NGHIỆM THUẬT TOÁN ĐIỀU KHIỂN The new proposals in chapter will be verified by physical modeling In this chapter, an FWOMR and controller embedded algorithms proposed in Chapter are fabricated at the same time 4.1 Design and manufacture the four-wheeled omnidirectional mobile robot 4.1.1 Design the mechanic structure and construct the physical robot Figure 4.1 Mechanical design of FWOMR Figure 4.2 Physical model of the robot 4.1.2 Design the structure control system Figure 4.3 Hardware structure diagram of robot control system 4.1.3 Robot control software The algorithms are applied for embedded robot controller on operating system 21 platform for robot programming - ROS (Robot Operating System), with simulation tool GAZEBO and visualization tool Rviz ROS is a dedicated operating system for programming and controlling robots researched and developed at Stantford University since 2007 ROS includes huge tools, libraries and allows for a wide variety of programming languages programs like C ++, python help users to easily deploy and build their products 4.2 Install the algorithm and experiment 4.2.1 Software programming of embedded microprocessors algorithms and controls Figure 4.5 Programming sofware structure 4.2.2 Experiment result The experimental run will be programmed and tested based on model in Figure 4.9 Experimental system included: Figure 4.9 Model robot experiment Experiment result: Figure 4.10 HMI interface and the results of trajectory tracking control experiment Experiment results with the circular trajectory: 22 Figure 4.11 Circular trajectory of FWOMR in experiment Figure 4.12 Different trajectories of FWOMR in experiment Comments: FWOMR move forward 4m in 10 seconds, and then rotates 90 degree and backs to the initial position after 10 seconds, the tracking quality is good and the tracking error is in acceptable range FWOMR tracks circular trajectory with the radius 3m in the period of 10 seconds, the tracking quality is good and the tracking error is in acceptable range FWOMR tracks zig-zag trajectory in the period of 20 seconds, tracking trajectory is not good, especially at sharp corner Moreover, there is a large error existing in the system in tracking process (because of the mechanical structure) 4.3 Conclusion With the aim of testing the proposed algorithms, the fabrication of a physical robot, programming and testing the performance is the content of this Chapter 4: + Successfully design, fabricate and test run omnidirectional mobile robots, robots with high-performance hardware and control circuitry and software to support programming on the ROS robot operating system + Design and manufacture of hardware and peripherals synchronously, fabricate electronic circuits, control and peripheral communication with the target of fast calculation, robust in the orientation that can be expanded and upgraded + Design the structure, program and install research algorithms for the robot, conduct the experiments and evaluate the results The experiment results show the correctness of theoretical analysis, the efficiency of the proposed controller and practical applicability CONCLUSION AND PROPOSAL The four-wheeled omnidirectional mobile robot is capable of moving in any direction without having to change position and orientation With a particular wheel structure and the advantage of outstanding mobility in conditions of narrow and difficult to change positions, this FWOMR model is being widely applied not only in research but also in the fields of production and life Problems of trajectory tracking control, handling of exogenous interference effects, changes of uncertain components such as mass, torque, friction are of 23 interest in the OMR field The results of the thesis are initial successes in this field The achieved results of the thesis The thesis has achieved the target of researching and proposing a new adaptive control algorithm for trajectory tracking control of the four-wheeled omnidirectional mobile robot on the basis of the nonlinear uncertain system, put special focus on tracking quality and the variation of robot parameters (because the application of the robot is to interact with different objects and environments) and is affected by noises when operating on different terrain Summary of main contributions of the thesis: Scientific significances - contributions of the thesis: The thesis proposed an adaptive fuzzy dynamic surface control algorithm for trajectory tracking control task of the four-wheeled omnidirectional mobile robot The thesis proposed an adaptive fuzzy neural network dynamic surface control algorithm for trajectory tracking control task of the four-wheeled omnidirectional mobile robot, in which the model is uncertain and affected by external disturbances These algorithms are successfully installed and experimented in the four-wheeled omnidirectional mobile robot The robot is fabricated and set up using the high-performance microchip and the software supporting the programming on ROS In addition, during the implementation of the thesis, the researches and applications have also been published at prestigious domestic and international scientific conferences and journals Future work of the thesis Research to improve adaptive algorithms when robots move on steep terrain (3D), as well as the robot movement on different types of complex terrain when operating in practical applications Synchronize the tasks in the overall control flowchart of the system, integrate new sensor technologies such as Lindar, camera, optimize real-time processing time and apply a programming operating system ROS to the robot to improve the system's tracking speed 24 ... Ngọc Hải, Trần Văn Hoàng, Nguyễn Văn Dũng, “Giám sát định vị, đồ hóa điều hướng cho robot tự hành đa hướng sử dụng hệ điều hành lập trình ROS”, Hội nghị Quốc gia lần thứ XXII Điện tử, Truyền thông... of these algorithms This is the main content in the next chapter CHẾ TẠO ROBOT TỰ HÀNH BỐN BÁNH ĐA HƯỚNG VÀ CHẠY THỬ NGHI? ??M THUẬT TOÁN ĐIỀU KHIỂN The new proposals in chapter will be verified... “Điều khiển bám quỹ đạo Omni robot bốn bánh phương pháp thích nghi mờ trượt” Tạp chí Nghi? ?n cứu Khoa học Công nghệ quân Số đặc san ACMEC 07-2017 ISSN 1859 - 1043 Ngo Manh Tien, Nguyen Nhu Chien,
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