Optimal path planning and adaptive sliding mode control of hexapod model

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  • Optimal path planning and adaptive sliding mode control of hexapod model

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VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY - LE HA ANH KHOA OPTIMAL PATH PLANNING AND ADAPTIVE SLIDING MODE CONTROL OF HEXAPOD MODEL HO NH QU OT U KHI T THÍCH NGHI MƠ HÌNH TAY MÁY SONG SONG HEXAPOD MAJOR: Control Engineering and Automation MAJOR CODE: 8520216 MASTER THESIS HO CHI MINH CITY, August 2021 THE RESEARCH IS COMPLETED AT: HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY VNU HCM Instructor: Dr Nguyen Vinh Hao Examiner 1: Assoc Prof Dr Nguyen Quoc Chi Examiner 2: Assoc Prof Dr Nguyen Tan Luy The master thesis is defended at Ho Chi Minh city University of Technology (HCMUT), VNU-HCM on Google Meet on August 19th, 2021 Thesis Defense Council includes: Prof Dr Ho Pham Huy Anh Dr Pham Viet Cuong Assoc Prof Dr Nguyen Quoc Chi Assoc Prof Dr Nguyen Tan Luy Assoc Prof Dr Nguy n Minh Tâm Chairman Secretary Reviewer Reviewer Member Verification and the Dean of faculty of Electrical & Electronics Engineering after the thesis being corrected (If any) CHAIRMAN OF THE COUNCIL DEAN OF FACULTY OF ELECTRICAL & (Full name & signature) ELECTRONICS ENGINEERING (Full name & signature) Prof Dr Ho Pham Huy Anh i VIET NAM NATIONAL UNIVERSITY SOCIALIST REPUBLIC OF VIETNAM HO CHI MINH CITY Independence Freedom - Happiness UNIVERSITY OF TECHNOLOGY Full name: LE HA ANH KHOA MSHV: 1870440 Date of birth: 24 02 1995 Place of birth: Ho Chi Minh City Major: Control Engineering and Automation Major code: 8520216 I THESIS TOPIC: Optimal Path Planning and Adaptive Sliding Mode Control of Hexapod model II NHI M V VÀ N I DUNG: Design multi-objective optimal path planning based on revolutionary swarm algorithm and then construct adaptive sliding mode control for parallel manipulator Hexapod to track the optimized path III TASKS STARTING DATE: February 24th, 2020 IV TASKS ENDING DATE: June 13th, 2021 V INSTRUCTOR: Dr Nguyen Vinh Hao Ho Chi Minh City, August 19th, 2021 INSTRUCTOR HEAD OF DEPARTMENT (Full name & signature) (Full name & signature) Dr Nguyen Vinh Hao Dr Nguyen Vinh Hao DEAN OF FACULTY OF ELECTRICAL & ELECTRONICS ENGINEERING (Full name & signature) ii THANK YOU I would like to say thank you to my mom who helps and gives me special care from the beginnings to endings Besides, I also give my honor to my professor, Dr Nguyen Vinh Hao who inspires and provides to me a lot of helpful advices and guidances for this project hich donated motors and controllers for building up my mechanical model Thank you to the Delta Technical Support team who trained and instructed me how to use their PLC and Servo system in this project Thank you to all my friends, my brothers, my colleagues who were beside and encouraged me to pass those most difficult moments iii ABSTRACT Researchers often think about the spider robot when hearing the term Hexapod However, in this Master of Science thesis, we talk about a special manipulator which has degrees of freedom in motion invented by Dr Stewart about a half-century ago Throughout the thesis, two problems that are examined are Multi-Objective Optimal Path Planning Algorithms and Adaptive Sliding Mode Controllers designing for the high complexity parallel manipulator with degrees of freedom (6-DOFs) in translation and orientation, the Rotary Parallel Manipulator Hexapod The optimal path planning algorithms are developed base on the formula of B-spline curves with the objectives to a minimum the motion times & path lengths and while satisfying the constraints of the Hexapod mechanical structures such as the limitation of active joint angles, joint angular velocities, joint accelerations, and a maximum of the joint torque outputs of the servo motors The scheme of solving these objective functions and constraints follows the theories of multi-objective optimization of Particle Swarm Optimization (MOPSO) The optimal solutions are chosen base on the objective weighting method from the distribution of the Pareto sets Then Adaptive Sliding Mode Controllers (ASMC) are constructed either to overcome the chattering phenomenon of the conventional sliding mode control technic and precisely track the end-effector of the mobile platform to the following optimal path planning process The Hexapod simulation model is exported from the mechanical CAD design software (SOLIDWORK) All the mathematical models and algorithms are realized using MATLAB/Simulink software with the help of SimScapes Libraries A lot of simulations have been conducted to proof of the optimal path planning and the asymptotical convergence stability of the control system iv TÓM T T LU Các nhà nghiên c u rô-bô nh n nh n c nh ng n thu t m t c bi t có th chuy ng theo b c t khác n Stewart vào kho ng gi a th k Xuyên su t lu u Khi c phát minh b i ti c hai n i dung s u a Bi n c kh o sát Ho ch t Thích Nghi t quay, c Hexapod Gi i thu t ho c phát tri n d nh t v n th a mãn ràng bu c v servo Trình t gi ng B u t Thích Nghi ng u v a kh c ng c xu t b n t MATLAB/Simulink v i s tr giúp c a b tính c xây d m cu i c a t m ph (SOLIDWORK) T t c mơ hình toán gi i thu c ti u c a (MOPSO) Các k t qu ng (chattering) v a ot ng tr ng s theo phân b c a Mơ hình mơ ph ph it c l a ch n d b bám theo qu dài c tiêu hàm ràng bu c tuân theo i n c a Gi i thu t T ph c tình tr ph c t p cao i h n góc quay c a kh p, v n t c góc c a kh p, gia t c t i kh p, moment xo n c t oT i u song song d ng tay quay cong B-spline v i m c tiêu c c ti u th i gian d ch chuy n c a gi i thu t nh Qu u song song v i b c t (6-DOFs) bao g m c lí thuy t t u c th c hi n ph n m m n SimScapes Nhi u thí nghi m mơ ch ng minh cho tính t nh ti m c n c a h th ph n m m thi t k u n a qu nh v DECLARATION The author confirms that all the contents used in this thesis are unique and are completely quoted and cited Ho Chi Minh City, August 19th, 2021 (Full name & signature) Le Ha Anh Khoa vi TABLE OF CONTENTS i THANK YOU ii ABSTRACT iii TÓM T T LU iv DECLARATION v TABLE OF CONTENTS vi LIST OF FIGURES vii LIST OF TABLES viii LIST OF ABBREVIATIONS ix Chapter INTRODUCTION 1.1 Hexapod and The Stewart Platform 1.2 Optimal Path Planning & Trajectory Planning algorithms 1.3 Adaptive control algorithms 1.4 The objectives of the thesis 1.5 Thesis organization Chapter 2.1 LITERATURE REVIEW Kinematic Analysis 2.1.1 Inverse Kinematic 2.1.2 Forward Kinematic 2.2 Dynamic Analysis 10 2.2.1 Velocity And Acceleration Analysis 10 2.2.2 Dynamic Modelling 14 Chapter MULTI-OBJECTIVE OPTIMAL PATH PLANNING SCHEME 16 3.1 WORKSPACE ANALYSIS 16 3.2 MULTI-OBJECTIVE OPTIMAL PATH PLANNING SCHEME 18 3.2.1 Singularity free path generation process 18 3.2.2 The path interpolation algorithm using B-spline curve 18 3.2.3 The Multi-objective path planning using Particle Swarm Optimization 20 vii Chapter ADAPTIVE SLIDING MODE CONTROLLER 25 4.1 Conventional Sliding Mode Controller 25 4.2 Adaptive Sliding Mode Controller 26 Chapter SIMULATION AND RESULT 32 5.1 Multi-objective Optimal Path Planning Test Plan 33 5.2 Adaptive Sliding Mode Control Test Plan 38 5.3 Result of simulation 42 5.3.1 Result of Multi-objective Optimal Path planning 42 5.3.2 Result of Adaptive Sliding Mode control 47 5.3.3 Discussion 67 Chapter CONCLUSION AND FUTURE WORK 68 6.1 Achievement 68 6.2 Limitation 68 6.3 Future work 69 LIST OF PUBLICATIONS 70 REFERENCES 71 viii LIST OF FIGURES Figure 2.1 Model Diagram of Hexapod Figure 2.2 The vector loop closure of one active link Figure 2.3 The coordinates of joints Ai & Bi Figure 2.4 The forward kinematic model using Simscape Simulink 10 Figure 2.5 The 6-DOF body sensor is used for tracking position, velocity, and acceleration of the end-effector of the mobile platform 10 Figure 3.1 The process of workspace analysis 16 Figure 3.2 The result of the workspace analysis process in 3D View XYZ 17 Figure 3.3 The result of the workspace analysis process in 2D View XY 17 Figure 3.4 The Multi-objective optimal Path planning 22 Figure 4.1 The conventional sliding mode controller 26 Figure 4.2 Adaptive Sliding Mode Controller 26 Figure 5.1 Hexapod CAD model designed on SOLIDWORK software 32 Figure 5.2 Optimal path planning test plan 35 35 36 - ck 36 37 37 38 Figure 5.9 Adaptive Sliding Mode Control Test Plans 38 39 40 40 41 42 Figure 5.15 The Pareto distribution of the three objective function costs 42 61 Case 4: Testing with results of the optimal path planning with disturbance Figure 5.39 Space view of the platform position and orientation with disturbancefree Figure 5.40 Space view of the platform position and orientation with disturbance From the result, we found that there are small errors in the position and orientation of the platform when testing the controller in a disturbance affect environment 62 Figure 5.41 The sensitive response of the system with the disturbance-free (X-Y-Z axis) The position of the platform remains the planned path when the system served in the disturbances 63 Figure 5.42 The sensitive response of the system with the disturbance-free angles) - - Some small oscillates occur from the beginning and end of the simulation in the yaw orientation tracking 64 Figure 5.43 The joint-space coordinate response in the disturbance-free test Figure 5.44 The joint-space coordinate response in the disturbance test 65 Figure 5.45 The performance of Servo in the disturbance-free test Figure 5.46 The performance of Servo in the disturbance test In the disturbance test, the torque output of the ASMC controller remains the smooth shapes However, it has some small oscillations that lead to some interferences in velocity and acceleration 66 Table 5-7 Task space error compare for Case Simulation Case Tracking Error Disturbance-free Disturbance RMSE X 0.0323 0.0443 Max E X 0.0622 0.1284 RMSE Y 0.0767 0.0881 Max E Y 0.0950 0.1785 RMSE Z 0.2954 0.2951 Max E Z 0.5218 0.5218 RMSE Roll 0.0072 0.0073 Max E Roll 0.0156 0.0156 RMSE Pitch 0.0224 0.0224 Max E Pich 0.0310 0.0360 RMSE Yaw 0.0066 0.1119 Max E Yaw 0.0099 0.1707 In this test, we reduce the switching gain of the SMC by 10 times control, and the result is the tracking errors are smaller in the Disturbance-free test case in comparison with Case but there are more oscillates in the Disturbance test case The system is less sensitive to disturbances 67 5.3.3 Discussion About the Multi-objective optimal planning scheme, we found that the solution generated from the process meets the requirement goals with smooth path curves in task space and also in joint space and both the constraint conditions in kinematic and dynamic and the limitation in actuator mechanic The computation time of the algorithm depends on the number of population particles, the maximum iteration, and also the sample time resolution used in the kinematic & dynamic evaluation of each particle at both the beginning and the process of updating the new position of the particles in the operation About the Adaptive control, in these test cases, we can see that the proposed ASMC still tracks the desired motions of the mobile platform in the condition of the effect of the disturbances in the torque output of controllers Table 5-5 showed that tracking errors in task space are variant slightly in small value while the large change in model uncertainties Thus the ASMC can compensate unknown time-varying nonlinear tness In addition, Figure 5.38 showed that the robustness of the controller has improved thanks to the adaptively varied gain of the PD control, which allows the ASMC to obtain high control performance without any precise knowledge of the external disturbance bound This is useful to achieve the high precision of Stewart platforms in applications frequently subjected to time-varying external disturbances such as tool machining, flight, or tank driving simulations 68 Chapter CONCLUSION AND FUTURE WORK 6.1 Achievement This thesis achieved some new things: A new structure of the Hexapod based on the Stewart mechanism was designed and implemented in real-time Improvement of single objective Particle Swarm Optimization to deal with Multi-objective optimal path planning in many degrees of freedom parallel robot The new ASMC algorithms showed that the performance quality control can be maintained in the system with large disturbance and upper bound uncertainty Comparing with the conventional SMC method, the torque control of the new ASMC controllers is smoother and more efficient with the lower maximum values in all the domain controls Besides, with the new control method, the current chattering phenomenons generated by traditional switching functions are reduced significantly which makes the system more stables and saves the mechanical structure from overload or damage 6.2 Limitation Because of the limitation of project time in a short period of the academic year, the Simulate all the workspace zones of the parallel robots Finding the optimal parameter in interpolating the kinematic and dynamic model used in motion planning and controller design, so there will be some small errors in the tracking Establish an evaluation system that can measure the position and orientation of the platform in real-time of the real model The MOPSO works quite slow with a computation time of nearly hours 69 6.3 Future work This work is not terminated in just this thesis, some works continue then such that: Upgrade the MOPSO algorithms to faster computing Study and implement new evolutionary algorithms in optimal path planning thm Design a new redundant structure that can reduce singularity points in the workspace of the rotary parallel manipulator Design a measurement system that can track errors motion in all 6-DOF based on the high accurate inertial sensors or high-resolution vision systems 70 LIST OF PUBLICATIONS Le Ha Anh Khoa, and Parallel Manipulator Hexapod, in The 6th Vietnam International Conference and Exhibition on Control and Automation (VCCA), Ho Chi Minh City, Vietnam, 2021 71 REFERENCES [1] Aircr Eng Aerosp Technol., vol 38, no 4, pp 30 35, 1965 [2] -mode controller design for a 6DOF 10th IEEE 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Robotica, vol 36, no 4, pp 588 606, 2018, doi: 10.1017/S0263574717000662 75 PROFILE Full name: Le Ha Anh Khoa Date of birth: 24 02 1995 Place of birth: Ho Chi Minh City, Viet Nam Address: 58/55/4 Thong Nhat Street, Ward 10, Go Vap District, HCMC, VN Education: Program Time School name Bachelor of Engineering in 2013- Ho Chi Minh City University of Control Engineering and 2018 Technology Master in Control Engineering 2018- Ho Chi Minh City University of and Automation 2022 Technology Automation Work experience: Time 2018-2019 Company New Ocean Manufacturing Solutions Position Automation Engineering Co., Ltd 2019-2020 New Ocean Manufacturing Solutions Project Engineering Co., Ltd 2020-2021 New Ocean Manufacturing Solutions IoT Team Leader Co., Ltd 2022-now HEINEKEN Vietnam Brewery Limited Company Digital Specialist ... birth: Ho Chi Minh City Major: Control Engineering and Automation Major code: 8520216 I THESIS TOPIC: Optimal Path Planning and Adaptive Sliding Mode Control of Hexapod model II NHI M V VÀ N I DUNG:... Trajectory qd e SMC Controller -q d/dt eq SMC Hexapod Model edot Disturbance Figure 4.1 The conventional sliding mode controller 4.2 Adaptive Sliding Mode Controller Adaptive Law Adaptive Controller Adap... Multi-objective optimal Path planning 22 Figure 4.1 The conventional sliding mode controller 26 Figure 4.2 Adaptive Sliding Mode Controller 26 Figure 5.1 Hexapod CAD model designed
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