Glocal Control for Mecanum-Wheeled Vehicle with Slip Compensation
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GLOCAL CONTROL FOR MECANUM-WHEELED VEHICLE WITH SLIP COMPENSATION BY JIRAYU UDOMSAKSENEE A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING (INFORMATION AND COMMUNICATION TECHNOLOGY FOR EMBEDDED SYSTEMS) SIRINDHORN INTERNATIONAL INSTITUTE OF TECHNOLOGY THAMMASAT UNIVERSITY ACADEMIC YEAR 2018 Ref. code: 25615922040554LTX GLOCAL CONTROL FOR MECANUM-WHEELED VEHICLE WITH SLIP COMPENSATION BY JIRAYU UDOMSAKSENEE A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING (INFORMATION AND COMMUNICATION TECHNOLOGY FOR EMBEDDED SYSTEMS) SIRINDHORN INTERNATIONAL INSTITUTE OF TECHNOLOGY THAMMASAT UNIVERSITY ACADEMIC YEAR 2018 Ref. code: 25615922040554LTX Acknowledgements This research is financially supported by Thailand Advanced Institute of Science and Technology (TAIST), National Science and Technology Development Agency (NSTDA), Tokyo Institute of Technology and Sirindhorn International Institute of Technology (SIIT) under the Excellent Thai Students (ETS) program, and Thammasat University (TU). I am gratefully indebted to my thesis advisor, Asst. Prof. Dr. Itthisek Nilkhamhang of SIIT at TU, for his helpful advice and consistency support along this thesis. We worked hard together during day and night on my thesis. He is very kind to let Mr. Hendi Wicaksono brief me on the fundamental concept of the glocal control system at the beginning of my thesis. In addition to that, he also introduced me to Prof. Shinji Hara of Tokyo University, the expert of glocal control concept that I have an opportunity to learn more and obtain his advice on my thesis. I also would like to thank Assoc. Prof. Masaki Yamakita and Yamakita lab members, especially Mr. Rin Takano, for their lectures, helpful advice, and kind hospitality during my ten-week stay at Tokyo Institute of Technology. I would like to gratefully thank Assoc. Prof. Dr. Waree Kongprawechnon. With her kind advice and support, I have a chance to be a part of TAIST program. In addition, I have also got her continuing support and valuable advice on this thesis. I also would like to acknowledge valuable comments from Dr. Pished Bunnun, the Chairperson of Examination Committee. Last but not least, I would also like to thank my friends namely Mr. Apisit Pinitnanthakorn, Mr. Peammawat Chantevee, and Ms. Panatda Nalinnopphakhun for providing additional information. ii Ref. code: 25615922040554LTX Abstract GLOCAL CONTROL FOR MECANUM-WHEELED VEHICLE WITH SLIP COMPENSATION by JIRAYU UDOMSAKSENEE Bachelor of Engineering, Sirindhorn International Institute of Tecnology, Thailand, 2015 Master of Engineering, Sirindhorn International Institute of Tecnology, Thailand, 2018 This thesis proposes a hierarchical decentralized controller for a mecanum- wheeled vehicle represented as a homogenous multi-agent system. The equations of motion for each individual mecanum wheel and the entire vehicle with slip are analyzed to construct a linear time-varying interconnected model. The global objective is the position trajectory tracking of the vehicle as a result of the effective forces produced by each wheel. The local objective is the driving force and slip controls of each wheel, with consideration of the interconnection between all agents. The proposed hierarchical linear quadratic regulator (LQR) control ensures satisfaction of both global and local objectives, according to the concepts of glocal control. Simulation results of a mecanum-wheel vehicle are shown that verify the performance and validity of the method. Keywords: Mecanum wheel, glocal control, decentralized hierarchical control, slip control iii Ref. code: 25615922040554LTX Table of Contents Chapter Title Page Signature Page i Acknowledgements ii Abstract iii Table of Contents iv List of Figures vi List of Tables viii 1 Introduction 1 1.1 Motivation 1 1.1.1 Practical Applications 2 1.1.2 Problems of Mecanum-Wheeled Vehicle 5 1.1.3 Anti-Slip Control System for Conventional-Wheeled Vehicles 5 1.1.4 Anti-Slip Control System for Mecanum-Wheeled Vehicles 6 1.2 Objective 7 1.3 Thesis Scope 7 1.4 Thesis Structure 8 2 Literature Review 9 2.1 Mecanum-wheel Vehicle 9 2.1.1 Fundamental Vehicle Dynamics. 12 2.2 Anti-Slip Control Techniques 14 2.2.1 Slip Ratio 11 2.2.2 Anti-Slip Control via Kinematic Control 15 2.2.3 Anti-SlipControl via Driving Force Control 15 2.3 Hierarchically Decentralized Optimal Control 14 iv Ref. code: 25615922040554LTX 2.3.1 Homogeneous Multi-Agent Dynamical Systems 17 2.3.2 Multi-Agent Dynamical Systems with physical interconnection 21 3 Dynamical Modelling of Mecanum-Wheel Vehicle 24 3.1 Fundamental Vehicle Dynamics 24 3.2 Slip Ratio 26 3.3 Driving Force Dynamics 26 3.4 Group and Layering 28 3.4.1 Upper Layer: Position Control 29 3.4.2 Lower Layer: Driving Force Control 29 3.5 Hierarchical Decentralized Structure 29 4 Hierarchically Decentralized Optimal Control 31 4.1 Trajectory Tracking Controller 32 4.2 Hierarchically Decentralized Optimal Control 32 4.3 Performance Index 34 4.4 Hierarchical State Feedback LQR design 36 4.5 Numerical Simulation 37 4.5.1 Linear Translation along x-y Axis 40 4.5.2 Trajectory with Diagonal Cornering 53 5 Conclusions and Recommendations 58 References 60 v Ref. code: 25615922040554LTX List of Figures Figures Page 1.1 Omnidirectional robots: (a) mecanum drive (b) omni drive (c) swerve drive. 2 1.2 Mecanum wheel. 3 1.3 NASA OmniBot 2. 4 1.4 Industrial robots: (a) Airtrax ATX-3000 industrial forklifts (b) Mecanum- wheeled vehicle with container and trolley 2. 4 1.5 Medical mecanum-wheeled vehicle: OMNI 6, CIIPS wheelchair 7, iRW 8 (from left to right). 4 1.6 The interactive shopping trolley 9. 5 2.1 Mecanum wheel. 10 2.2 Mecanum-wheeled vehicle. 10 2.3 Single wheel model. 11 2.4 Mecanum-wheeled vehicle model. 12 2.5 Driving and slip forces developed on a roller of the i wheel. 12 2.6 Friction coefficient versus slip ratio 12. 14 2.7 Relaxation length versus slip ratio 22. 16 2.8 Block diagram of hierarchical networked control system. 19 2.9 Block diagram of state feedback controller. 19 3.1 Single wheel model. 25 3.2 Mecanum-wheeled vehicle model. 25 3.3 Driving and slip forces developed on a roller of the i wheel 25 3.4 Friction coefficient versus slip ratio 12. 27 3.5 Relaxation length versus slip ratio 22. 27 3.6 Hierarchical network system of the mecanum-wheeled vehicle. 29 4.1 Overall control system. 31 4.2 P-Controller. 32 4.3 Block diagram of hierarchical networked control system with physical interconnection. 33 4.4 Block diagram of state feedback controller with physical interconnection. 33 4.5 Friction coefficient versus slip ratio of rubber rollers on dry tarmac surface. 38 vi Ref. code: 25615922040554LTX 4.6 Relaxation length versus slip ratio 22. 38 4.7 Overall control system with state feedback controller. 39 4.8 Manually-tuned state feedback controller. 39 4.9 X-Y trajectory of manually-tuned state feedback controller. 40 4.10 Velocity and position responses of manually-tuned state feedback controller. 41 4.11 Driving force responses of manually-tuned state feedback controller. 41 4.12 Slip responses of manually-tuned state feedback controller. 42 4.13 Torques generated by manually-tuned state feedback controller. 42 4.14 Position error of manually-tuned state feedback controller. 43 4.15 Driving Force error of manually-tuned state feedback controller. 43 4.16 X-Y trajectory of HLQR controller with global gains. 44 4.17 Velocity and position responses of HLQR controller with global gains. 45 4.18 Driving force responses of HLQR controller with global gains. 45 4.19 Slip responses of HLQR controller with global gains. 46 4.20 Torques generated by HLQR controller with global gains. 46 4.21 Position error of HLQR controller with global gains. 47 4.22 Driving Force error of HLQR controller with global gains. 47 4.23 X-Y trajectory of HLQR controller without global gains. 48 4.24 Velocity and position responses of HLQR controller without global gains. 49 4.25 Driving force responses of HLQR controller without global gains. 49 4.26 Slip responses of HLQR controller without global gains. 50 4.27 Torques generated by HLQR controller without global gains. 50 4.28 Position error of HLQR controller without global gains. 51 4.29 Driving Force error of HLQR controller without global gains. 51 4.30 X-Y trajectory of diagonal cornering. 54 4.31 Velocity and position responses of diagonal cornering. 55 4.32 Driving force responses of diagonal cornering. 55 4.33 Slip responses of diagonal cornering. 56 4.34 Torques generated during diagonal cornering. 56 4.35 Position error during diagonal cornering. 57 4.36 Driving Force error during diagonal cornering. 57 vii Ref. code: 25615922040554LTX List of Tables Tables Page 2.1 Combination of wheel motion and resulting vehicle direction 19. 11 4.1 System parameters and description. 31 4.2 Vehicle ppecification. 37 4.3 Controller gains. 39 4.4 Weighting matrices. 44 4.5 Integral square error of the first path. 53 4.6 Control effort comparison. 53 4.7 Integral square error of diagonal cornering. 53 viii Ref. code: 25615922040554LTX Chapter 1 Introduction 1.1 Motivation Nowadays, autonomous mobile robots are widely used in many industrial and household applications. These robots are typically non-holonomic systems that have limited maneuverability in tight, confined workspaces due to the minimum steering angle. This may necessitate multiple readjustments of the orientation to navigate through narrow pathways and around corners. In these situations, holonomic or omni- directional wheeled robots would provide better performance and maneuverability 1. This includes mobile robots that employ mecanum wheels shown in Fig. 1.1(a) with the ability to move in any direction without changing the orientation of the vehicle. Other mechanisms that allow for omni-directional movements include omni wheels and swerve drives shown in Fig.