Diseño, modelado y control de antenas sensoras flexibles de dos grados de libertad

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(1)UNIVERSIDAD DE CASTILLA-LA MANCHA. DEPARTAMENTO DE INGENIERÍA ELÉCTRICA, ELECTRÓNICA, AUTOMÁTICA Y COMUNICACIONES. DISEÑO, MODELADO Y CONTROL DE ANTENAS SENSORAS FLEXIBLES DE DOS GRADOS DE LIBERTAD. TESIS DOCTORAL. AUTOR: CLAUDIA FERNANDA CASTILLO BERRIO. DIRECTOR: VICENTE FELIU BATLLE Ciudad Real, noviembre de 2015.

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(3) UNIVERSITY OF CASTILLA-LA MANCHA. DEPARTMENT OF ELECTRICAL ENGINEERING, ELECTRONICS, AUTOMATIC AND COMMUNICATIONS. DESIGN, MODELLING AND CONTROL OF TWO DEGREES OF FREEDOM FLEXIBLE ANTENNA SENSORS. PhD THESIS. AUTHOR: CLAUDIA FERNANDA CASTILLO BERRIO. SUPERVISOR: VICENTE FELIU BATLLE Ciudad Real, November 2015.

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(7) A mi familia. Por su apoyo incondicional y por tantas muestras de amor.. Ailem için. Ailemin destegi olmadan mumkun olmazdi, tesekkrler..

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(9) Preface. This thesis addresses the subject of the design of a two degree of freedom (2DOF) flexible-beam antenna sensor, along with its modelling and complete control for specific antenna performance. The experimental antenna is a lab scale flexible beam that attempts to mimic the function of natural tactile systems whose sensory capabilities predominantly depend on whiskers or antennae for various tasks, including short-range navigation and object exploration. Flexible-beam based sensors are interesting because of the unique physical process on which they are based, the fact that they are independent of illumination, and the potential to integrate this sensor with other sensory applications. Tactile sensation can be performed in complete darkness, in dusty or cloudy environments, and the sensor does not emit light or sound. Research into tactile flexible-beam sensors for both shape recognition and obstacle detection began in the mid 1980’s, and recent progress has been encouraged by the increased understanding of natural vibrissal systems and advances in engineering, microelectronics, transduction and actuation. However, most of the research carried out on artificial flexible-beam whisker and antenna sensors has not considered the controlled movements of the beam (before and after contact is made) as an important characteristic of the system and has concentrated only on the sensing task. Active touch should involve the active regulation of the position and movements in order to boost the quantity and quality of sensory information. Depending on the task to be performed, the sensor movements have to be actively controlled in order to maximise the amount of useful sensory information in the least amount of computational time. The exploration strategy should include precise free-air movements (repeated posterior-anterior sweep and speed regulation), in addition to contact reaction response. An artificial sensor system designed to operate in this way would differ from the passive binary collision-detection of many contemporary tactile systems. Many of the artificial sensor systems designed thus far have not been independently actuated since several degrees of freedom would be very challenging.

(10) ii with the use of existing motor technology. The flexible-beam must be lightweight and very flexible, and this flexibility leads to oscillatory tip behaviour, thus making precise positioning a difficult task that requires complex closedloop control. What is more, the controller for this application has to carry out two different tasks: motor positioning and tip oscillation suppression. The system has zero unstable dynamics and its model must be represented by means of high order dynamics. In order to overcome the difficulties described above, in this thesis we propose an experimental robotic platform designed and built to have a single vibration mode at the beam’s tip. It includes a two-axis robot with conventional DC motors that constitute the drive system in order to meet the need for wide range sensor movement and control. It additionally has a load-cell sensor and flexible beam, along with the software and hardware needed for real time applications. The platform has been designed as an experimental prototype for control purposes and could have various research possibilities. A reduced dynamic model of the system was obtained by using the Lagrange theory, and several experiments were performed to validate the accuracy of the model, along with the identification of motors and beam parameters. The flexible-beam dynamic model represented the system motion equations accurately and the model was sufficiently simple for a model based control method. In order to control the antenna system rapidly and precisely, and to reduce the tip vibration, the control design includes motor positioning regulators, the use of input state linearization and a closed-loop control law. These controllers have to be easily implemented and tuned, in addition to being robust to parameter uncertainties. The system makes use of 8th order Bezier polynomials as specially generated trajectories for precise control response, and to incorporate the smooth-path requirement when moving a flexible-beam structure (a soft trajectory with soft derivatives). The sensing task consists of attaining the contact point, which is obtained while controlling the beam when it touches an object, by processing the signals from force and torque measurements at the base of the beam. Finally, although the proposed methodology has several advantages, it is important to recall its limitations:.

(11) iii • The closed-loop control law based on input-state linearization along with the closed-loop motor regulators, which are proposed in this thesis, must be implemented using a digital computer that must allow for a faster sampling time. The fact that the platform requires real-time signal acquisition and processing (force/torque signals, generated trajectories, control signals, encoder acquisition, etc.) limits the digital implementation and bounds the system sampling time. • A future mechanism design could include a lighter and more compact structure if the antenna is to be located on the top of a mobile platform. • The provision of a specific antenna application whose size and parameters are fixed for a particular task, would permit larger or smaller servomotors (depending on the application) to be considered in the design, which might allow the use of larger maximum motor torques. The controllers speed is constrained by motor saturation or the control signal that is permitted. • In this thesis, we concentrate all our efforts on designing a control strategy phase that will allow the antenna tip to be placed in a precise manner, which is denominated as free-air motion. The movements of the mechanism are controlled and vibrations are prevented, and these factors could be used to ensure that each antenna movement takes place in the least possible amount of time. A second control phase is carried out and includes an algorithm with which to acquire the contact time, point and direction, while the damping control remains switched on. However, a third contact phase may be useful for contact tasks, which could stop the vibration suppression control and start a force controller. The force control has not been designed in this thesis but may be considered as further work. • A rigorous system calibration and a finite-state machine with all the possible states could enhance the full system performance. This must be thoroughly thought out for a particular antenna search and sensing task. The antenna system software has a basic calibration procedure which.

(12) iv was designed for the control tasks implemented. A switching logic of the antenna program could be described by means of a finite-state machine with the required states. However, it must be redesigned in order to include the sensing conditions for better contact tasks.. Each chapter is fairly independent but they all share the same mathematical notation.In Chapter 1, we provide an overview of the active sensing applications and a review of the existing literature related to this thesis. In Chapter 2, we describe the experimental platform, the mechanism designed, software and hardware requirements, the sensory system and general system characteristics. A description of the reduced dynamic model of the overall antenna system is provided in Chapter 3, in which the model’s dynamics is also validated. Two motion controllers with which to drive the flexible-beam fast and precisely are proposed in Chapter 4, while in Chapter 5, we present a complete control strategy that is used to reduce the flexible-beam tip vibration. In Chapter 6, we present an early stage study of a contact identification method in order to provide the capability to sense the 3D antenna work space by obtaining the contact time, point and the reaction forces generated. To conclude this thesis, a short summary, conclusions, contributions and some hints as to future research topics are shown in Chapter 7..

(13) v. Acknowledgments. This thesis would not have been possible without the financial support, the advice and guidance of many people. This study has been financially supported by the ‘Plan Nacional de Investigación’ (the Spanish Plan for Scientific Research). All of the component parts and the equipment needed for the platform were built thanks to the financial support of the following project: Title: Monitoring and Control of Vibrations in Flexible Mobile Structures. Extension to Impact Situations (2007-2009) Principal investigator: Vicente Feliu Batlle Funding institution: Science and Technology Department of the Spanish Government (C.I.C.Y.T., Ref.: DPI2006-13834). I was also employed for some time as a research assistant on the following project: Title: Design and Control of a Very Lightweight Flexible Robot Built With Composites Material. Application to an Inspection Robotic System (20102012) Principal investigator: Vicente Feliu Batlle Funding institution: Science and Technology Department of the Spanish Government (C.I.C.Y.T., Ref.: DPI2009-09956). I would like to express my most heartfelt gratitude to my supervisor, Professor Dr. Vicente Feliu Batlle, for his supervision, dedication, guidance and support over the past few years. I am also indebted to the Universidad de Castilla-La Mancha. I am additionally indebted to several relevant people whose suggestions have helped to add significant value to this thesis. They are not only relevant because of their suggestions, but also because of their hospitality and for the exceptional human and intellectual environment they have created. First of all,.

(14) vi I would like to thank Pedro Antonio Hungria Dı́az del Castillo for is valuable work in the experimental platform and his relevant suggestions. My sincere thanks to Dr. Fernando Jose Castillo for giving me the opportunity to work with him: his work and feedback have been essential in many steps of this thesis. He is also the co-author of some of the conference papers related to this thesis. I am also obliged to Dr. Seref Naci Engin for receiving me in his research group at Yildiz Teknik Universitesi, Istanbul, Turkey. I would like to acknowledge, Dr. Xavier del Toro Garcı́a, for his suggestions and feedback. It is also worth mentioning the contributions of Victor Hugo Jaramillo and Daniel Feliu Talegon as co-authors of some of the conference papers as regards the publication of collateral works. I wish to acknowledge all my colleagues and good friends I have made during these years at the Escuela Técnica Superior de Ingenieros Industriales in Ciudad Real. Choco, David, Xavi, Pedro, Victor, Agustı́n, Raul, Gonzalo, Juan Carlos, Eliza, Shlomi, Jesus López, Maria José, Daniel Cortazar and Alfonso. I thank them for their friendship.. I would like to thank my family for their unconditional support..

(15) Contents Contents. vii. List of Figures. xi. List of Tables. xvii. Notation and Acronyms. xxx. 1 Introduction. 1. 1.1. Flexible-beam based Sensor Applications . . . . . . . . . . . . .. 1. 1.2. Bio-mimetic Active Sensors . . . . . . . . . . . . . . . . . . . .. 3. 1.3. Other Tactile Sensors . . . . . . . . . . . . . . . . . . . . . . . .. 6. 1.4. Modelling and Control of Flexible-beams . . . . . . . . . . . . .. 9. 1.5. Our Solution Approach . . . . . . . . . . . . . . . . . . . . . . . 10. 1.6. Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 12. 1.7. 1.6.1. General Thesis Objectives . . . . . . . . . . . . . . . . . 12. 1.6.2. Specific Objectives of this Thesis . . . . . . . . . . . . . 13. Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 15. 2 Description of the Experimental Platform 2.1. 2.2. 17. Mechanism Characteristics . . . . . . . . . . . . . . . . . . . . . 17 2.1.1. Mechanism Construction Features . . . . . . . . . . . . . 17. 2.1.2. Mechanism Parameters and Specifications . . . . . . . . 19. Software and Hardware Requirements . . . . . . . . . . . . . . . 22 2.2.1. Software . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. 2.2.2. Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . 23 vii.

(16) viii. CONTENTS 2.3. Servo-motor System . . . . . . . . . . . . . . . . . . . . . . . . . 24. 2.4. Sensory System . . . . . . . . . . . . . . . . . . . . . . . . . . . 25. 2.5. Flexible-beam Parameters . . . . . . . . . . . . . . . . . . . . . 27. 3 Dynamic Model. 29. 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29. 3.2. Dynamics of the DC Motor . . . . . . . . . . . . . . . . . . . . 31. 3.3. 3.4. 3.5. 3.2.1. Coulomb Friction . . . . . . . . . . . . . . . . . . . . . . 32. 3.2.2. Servo-motor Parameter Identification . . . . . . . . . . . 33. Flexible-beam Dynamics . . . . . . . . . . . . . . . . . . . . . . 33 3.3.1. Beam Modelling Assumptions . . . . . . . . . . . . . . . 33. 3.3.2. Reduced Flexible-beam Model . . . . . . . . . . . . . . . 34. 3.3.3. Tip Energy Dissipation . . . . . . . . . . . . . . . . . . . 35. 3.3.4. Coupling Torque Equations . . . . . . . . . . . . . . . . 36. State Space Model of the Flexible-beam Dynamics . . . . . . . . 37 3.4.1. State Equations . . . . . . . . . . . . . . . . . . . . . . . 37. 3.4.2. A Tip Position Estimation . . . . . . . . . . . . . . . . . 38. Experimental and Simulated Results . . . . . . . . . . . . . . . 39 3.5.1. Bezier Curves as System Trajectories . . . . . . . . . . . 39. 3.5.2. Dynamic Model Validation . . . . . . . . . . . . . . . . . 40. 4 Motor Control. 47. 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47. 4.2. Inner loop: Motor Positioning . . . . . . . . . . . . . . . . . . . 48. 4.3. 4.2.1. PD Regulator and Compensation for the Static Friction . 50. 4.2.2. Algebraic PID Regulator . . . . . . . . . . . . . . . . . . 50. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 53. 5 Antenna Control. 55. 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55. 5.2. Control Method based on Input-state linearization . . . . . . . . 56. 5.3. 5.2.1. Multi-input Affine State Model . . . . . . . . . . . . . . 56. 5.2.2. Applying a linearization Method . . . . . . . . . . . . . . 57. A New Control Method for Vibration Reduction . . . . . . . . . 61.

(17) CONTENTS. ix. 5.3.1. Reducing the Closed-loop Motor Dynamics . . . . . . . . 61. 5.3.2. Defining an Affine Fictitious Input . . . . . . . . . . . . 62. 5.3.3. Fictitious Inputs and System Linearization . . . . . . . . 63. 5.4. Closed-loop Tip Positioning . . . . . . . . . . . . . . . . . . . . 65. 5.5. Simulation and Experimental Validation . . . . . . . . . . . . . 66 5.5.1. Simulation of the Developed Methods . . . . . . . . . . . 67. 5.5.2. Experimental Results . . . . . . . . . . . . . . . . . . . . 68 5.5.2.1. Validating the closed-loop motor dynamics . . . 68. 5.5.2.2. Fictitious inputs and system linearization validation (open-loop) . . . . . . . . . . . . . . . . 69. 5.5.2.3. Linearization based closed-loop control validation 70. 5.5.2.4. Control method comparison . . . . . . . . . . . 72. 5.5.2.5. Multiple trajectories and control performance . 75. 6 Contact Identification Method. 81. 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81. 6.2. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . 82. 6.3. Experimental Antenna . . . . . . . . . . . . . . . . . . . . . . . 84. 6.4. Collision Detection . . . . . . . . . . . . . . . . . . . . . . . . . 87. 6.5. Experimental Validation . . . . . . . . . . . . . . . . . . . . . . 89 6.5.1. Software . . . . . . . . . . . . . . . . . . . . . . . . . . . 89. 6.5.2. Contact Experiment: a Single Contact . . . . . . . . . . 90. 6.5.3. The Normal Force and the Collision Distance . . . . . . 93. 6.5.4. Contact Experiment: Several Distances . . . . . . . . . . 95. 6.5.5. Multiple Contacts: Searching for an Object. . . . . . . . 97. 7 Summary, Conclusions, Contributions and Future Research 103 7.1. Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 103. 7.2. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105. 7.3. Diffusion of Research Results . . . . . . . . . . . . . . . . . . . 111. 7.4. Future Research Suggestions . . . . . . . . . . . . . . . . . . . . 114. Appendix. 116.

(18) x A A Different Experimental Platform A.1 Flexible Antenna Prototype . . . . A.1.1 Mechanism Features . . . . A.1.2 Antenna Modelling . . . . . A.1.2.1 System kinematics A.1.2.2 System dynamics . Bibliography. CONTENTS. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 117 . 118 . 118 . 123 . 123 . 125 129.

(19) List of Figures 2.1. 2DOF Antenna Sensor: Solidworks drawing 1. . . . . . . . . . . 19. 2.2. 2DOF Antenna Sensor: Solidworks drawing 2. . . . . . . . . . . 20. 2.3. 2DOF flexible-beam sensor: (a) mechanism design and (b) schematic diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21. 2.4. Photograph of the experimental antenna platform. . . . . . . . . 21. 2.5. Data acquisition and control algorithms programmed using LabV IEW T M 7.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. 2.6. Experimental platform: System setup. . . . . . . . . . . . . . . 23. 2.7. Electronic interface, diagram of the components. . . . . . . . . . 24. 2.8. Experimental antenna platform: 3 infra-red cameras that measure the 3D flexible-beam position. . . . . . . . . . . . . . . . . 26. 3.1. DC servo-motor model and compensation. . . . . . . . . . . . . 32. 3.2. Dynamic model and state estimation. . . . . . . . . . . . . . . . 40. 3.3. Dynamic model validation: tip position, azimuthal movement φ1 . 41. 3.4. Dynamic model validation: tip position, elevation movement φ2 . 41. 3.5. Single-Sided Amplitude Spectrum of φ1 . . . . . . . . . . . . . . 42. 3.6. Single-Sided Amplitude Spectrum of φ2 . . . . . . . . . . . . . . 43. 3.7. Torque measurements Γs = [Γx , Γy , Γz ], elevation movement of the beam φ1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43. 3.8. Torque measurements Γs = [Γx , Γy , Γz ], elevation movement of the beam φ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44. 3.9. Absolute error of the tip positioning, azimuthal movement. Error obtained by comparing the tip position (F-T) sensor to an external sensor. φ1 . . . . . . . . . . . . . . . . . . . . . . . . . . 44 xi.

(20) xii. LIST OF FIGURES 3.10 Absolute error of the tip positioning, elevation movement. Error obtained by comparing the tip position (F-T) sensor to an external sensor. φ2 . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1. Inner loop: PD Regulator + compensation (PD+C). . . . . . . 50. 4.2. Inner loop: Algebraic PID Regulator. . . . . . . . . . . . . . . . 52. 4.3. Algebraic PID and PD+C Regulator comparison, closed-loop motor responses to a Bezier curve, θ1 . . . . . . . . . . . . . . . . 53. 4.4. Algebraic PID and PD+C Regulator comparison, closed-loop motor responses to a Bezier curve, θ2 . . . . . . . . . . . . . . . . 54. 5.1. State model: closed-loop motor dynamics, inversion filters and beam dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62. 5.2. System linearization. . . . . . . . . . . . . . . . . . . . . . . . . 64. 5.3. System linearization and state estimation. . . . . . . . . . . . . 65. 5.4. System control: inner-loop, outer-loop and tip estimation. . . . 66. 5.5. Simulations of the closed-loop motor controllers, motor response to a Bezier curve: (a) azimuthal movement and (b) elevation movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68. 5.6. Comparison of control methods: (a) azimuthal movement and (b) elevation movement. Data obtained by means of Simulations. 69. 5.7. Closed-loop control, motor response to a Bezier curve, azimuthal movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70. 5.8. Closed-loop control, motor response to a Bezier curve, elevation movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70. 5.9. Tip damping results obtained by means of a system linearization, azimuthal movement. Tip measurements obtained by means of (F-T) and Ext. sensor. . . . . . . . . . . . . . . . . . . . . . . 71. 5.10 Tip damping results obtained by means of a system linearization, elevation movement. Tip measurements obtained by means of (F-T) and Ext. sensor. . . . . . . . . . . . . . . . . . . . . . . 71 5.11 Tip damping results of the complete control method, azimuthal movement. Tip measurements obtained by means of (F-T) and Ext. external sensors. . . . . . . . . . . . . . . . . . . . . . . . . 72.

(21) LIST OF FIGURES. xiii. 5.12 Tip damping results of the complete control method: elevation movement. Tip measurements obtained by means of (F-T) and Ext. external sensors. . . . . . . . . . . . . . . . . . . . . . . . . 73 5.13 Control method comparison: azimuthal movement. Tip measurements obtained by means of the external sensor. . . . . . . . 73 5.14 Control method comparison: elevation movement. Tip measurements obtained by means of the external sensor. . . . . . . . 74 5.15 3D tip position representation, tip reference and tip position of a system driven by only closed-loop motor controllers. Tip measurements obtained by means of the external sensor. The initial tip position (0), the final tip position and the movement direction are also illustrated. . . . . . . . . . . . . . . . . . . . . 74 5.16 3D tip position representation, tip reference and tip position of the complete control. Tip measurements obtained by means of the external sensor. The initial tip position (0), the final tip position and the movement direction are also illustrated. . . . . 75 5.17 Tip positioning for a long multiple trajectory using the complete control method: azimuthal movement. Tip measurements obtained by means of (F-T) and (Ext.) external sensors. . . . . 76 5.18 Tip positioning for a long multiple trajectory using the complete control method: elevation movement. Tip measurements obtained by means of (F-T) and (Ext.) external sensors. . . . . 76 5.19 Control method comparison: azimuthal movement. Tip measurements obtained by means of the (F-T) sensor. . . . . . . . . 77 5.20 Control method comparison: elevation movement. Tip measurements obtained by means of the (F-T) sensor. . . . . . . . . 77 5.21 Absolute error of the tip positioning for a long multiple trajectory using the complete control method: (a) azimuthal movement and (b) elevation movement. Error obtained by comparing the tip position (F-T sensor) to tip references. . . . . . . . . . . 78 5.22 Control method comparison after a contact disturbance: azimuthal movement. Tip measurements obtained by means of the (F-T) sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . 79.

(22) xiv. LIST OF FIGURES 5.23 Control method comparison after a contact disturbance: elevation movement. Tip measurements obtained by means of the (F-T) sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.1. The experimental antenna platform which comes into contact with an object. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85. 6.2. Two-dimensional drawing (XY axes), torque and forces measured by means of an (F-T) sensor. . . . . . . . . . . . . . . . . 86. 6.3. Two-dimensional drawing (XZ axes), torque and forces measured by means of a (F-T) sensor. . . . . . . . . . . . . . . . . . 86. 6.4. Complete scheme: data acquisition and control algorithms were programmed using LabV IEW T M 7.1. . . . . . . . . . . . . . . . 90. 6.5. A multiple long trajectory, 3D representation. . . . . . . . . . . 91. 6.6. Monitor and control interface using LabV IEW T M 7.1 . . . . . . 91. 6.7. Torque value of the most representative torque in the collision Γ1 . 93. 6.8. Absolute value of the torque derivative Γ̇1 ≥ Γ̇c1 , the most representative torque in the collision. . . . . . . . . . . . . . . . 93. 6.9. Absolute error of the tip trajectory |φ1 − φr1 | ≥ χ1 , collision detection experiment. The tip position is measured by means of the (F-T) sensor and calculated using the state estimator. . 94. 6.10 Tip speed φ̇1 ≤ ξ1 , collision detection experiment. . . . . . . . . 94 6.11 Fourth condition as a threshold φ̇1 − φ̇r1 ≥ ζ1 , collision detection experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.12 3D force at the collision time, obtained by means of a (F-T) sensor measurements. . . . . . . . . . . . . . . . . . . . . . . . . 95 6.13 3D torque at the collision time, obtained by means of a (F-T) sensor measurements. . . . . . . . . . . . . . . . . . . . . . . . . 96 6.14 An object contacted by the flexible-beam’s tip, photo of the experimental platform. . . . . . . . . . . . . . . . . . . . . . . . 97 6.15 Contact experiments: system references, estimation of the tip position by using the state estimator, and the measurement of the tip position by means of the external optotrack sensor. . . . 99.

(23) LIST OF FIGURES. xv. 6.16 Contact experiments: 3D presentation of the contacted object, contact points and normal forces. . . . . . . . . . . . . . . . . . 100 A.1 Antenna prototype with a flexible-beam and a rigid-beam: (a) 3D Solidworks drawing and (b) Schematic diagram. . . . . . . A.2 Antenna prototype with a flexible-beam: (a) 3D Solidworks drawing and (b) Schematic diagram. . . . . . . . . . . . . . . A.3 Solidworks drawings: (a) first and (b) second design. . . . . . A.4 Schematic diagrams: (a) first and (b) second design. . . . . . . A.5 3D representation of the antenna scheme and the coordinate frames, a Schematic diagram. . . . . . . . . . . . . . . . . . . A.6 Experimental platform, first design. . . . . . . . . . . . . . . .. . 119 . 119 . 120 . 120 . 122 . 122.

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(25) List of Tables 1.1. Tactile Sensing Technologies . . . . . . . . . . . . . . . . . . . .. 2.1. Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . . 27. 3.1. Servo-motor parameters . . . . . . . . . . . . . . . . . . . . . . 33. 4.1. Control Parameters. . . . . . . . . . . . . . . . . . . . . . . . . 53. 5.1. System tip vibration damping. . . . . . . . . . . . . . . . . . . . 75. 6.1 6.2 6.3 6.4. Setup parameters . . . . . . . . . . . . . . . . . Contact Experiments: single movements . . . . Setup Parameters . . . . . . . . . . . . . . . . . Contact experiments: a long multiple trajectory. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 8. 92 96 98 99. A.1 Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . . 121. xvii.

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(27) Acronyms DC. Direct Current.. DOF. Degree of Freedom.. 3D. Three Dimension.. F-T. Force-Torque.. LabV IEW T M Laboratory Virtual Instrumentation Engineering Workbench NI. National Instruments. PCI. Peripheral Component Interface. Matlab. Matrix Laboratory. ATI. Industrial Automation Technologies. QTM. Qualisys Track Manager. LSC. Linear Servo Controller. 4-Q. 4 Quadrant. PID. proportional (P), integral (I) and derivative (D) gains. PD+C. proportional (P), derivative (D) gains and Coulomb friction compensation. LabVIEW Laboratory Virtual Instrumentation Engineering Workbench DSP. Digital Signal Processors xix.

(28) xx. Notation and Acronyms DAQ. Data Acquisition.

(29) Notation · denotes differentiation with regard to time ˆdenotes magnitudes seen from the motor side of the gear i a particular degree of freedom Pt the tip of the flexible-beam Pr the tip when the beam is considered as a rigid-beam. ∆P a 3D vector that describes the beam deflection E the beam Young module I the inertial moment resulting from the flexible-beam cross section g the gravity constant M the tip mass l the beam length CS the beam cross section ω the beam natural frequency r the beam radius the damping radius coefficient of the beam X axis along the Cartesian plane (X,Y ,Z) xxi.

(30) xxii. Notation and Acronyms Y axis along the Cartesian plane (X,Y ,Z) Z axis along the Cartesian plane (X,Y ,Z) φi the tip position, angle position φ1 tip position in spherical coordinates with regard to the absolute Cartesian plane φ2 tip position in spherical coordinates with regard to the absolute Cartesian plane θi the motor outputs, motor angle position θ1 motor angle position (azimuthal movement) θ2 motor angle position (elevation movement) Fs the Cartesian coupled force along the Cartesian plane (X 0 ,Y 0 ,Z 0 ) Fx the Cartesian coupled force along the Cartesian plane, axis X0 Fy the Cartesian coupled force along the Cartesian plane, axis Y0 Fz the Cartesian coupled force along the Cartesian plane, axis Z0 Γs the Cartesian coupled torque along the Cartesian plane (X 0 ,Y 0 ,Z 0 ) Γx the Cartesian coupled torque along the Cartesian plane, axis X0 Γy the Cartesian coupled torque along the Cartesian plane, axis Y0 Γz the Cartesian coupled torque along the Cartesian plane, axis Z0.

(31) Notation and Acronyms. xxiii. (X 0 , Y 0 , Z 0 ) the frame that results from the rigid mechanism rotations Ts platform sample time 0 0. n the gear reduction rate. ϑi motor control signals K̂i the motor constants Jˆi the motor inertias υ̂i the viscous friction coefficients Γ̂i the motor torques Γ̂nlf the motor torques caused by the static friction i ϑ̂mi the motor saturation as a control signal Γ̂coup the coupled torques i ϑi nlf voltage signal due to the Coulomb friction compensation ϑie nlf the static Coulomb friction which is identified in terms of the voltage ϑi coup voltage signal due to the coupled torques compensation Gi (s) transfer function of the DC servo-motor model Γ̂nlf ie the static Coulomb friction values which are obtained by a identification procedure Γt = 0 axial torques at the beam tip L the Lagrange equation Ec kinetic energy of the beam Eg the potential gravitational energy of the beam.

(32) xxiv. Notation and Acronyms Ee the elastic potential energy of the beam Qj variables of the generalised Lagrange equation Γj the generalised Lagrange equation In a matrix of the dynamic model C e a matrix of the dynamic model C c a matrix of the dynamic model G a matrix of the dynamic model E l a matrix of the dynamic model Γj the generalised non-conservative force vector Kg =. g l. Ka =. 3EI M l3. a defined constant a defined constant. κ1 = cos(θ2 )sin(θ1 − x1 ) κ2 = cos(θ2 )cos(θ1 − x1 ) Θ = [θ1 , θ2 ]T the state space model inputs Y = [φ1 , φ2 ]T the state space model outputs Y = g (X) state equation of the non-linear system h iT X = φ1 , φ̇1 , φ2 , φ̇2 the state space vector u = [θ1 ∗ , θ2 ∗ ]T the input to state space model Ẋ = f (X, θ) state equation of the non-linear system Y = g (X) state equation of the non-linear system C=. 3EI l. the flexible-beam stiffness.

(33) Notation and Acronyms. xxv. X e = [x1 e , x2 e , x3 e , x4 e ]T the estimated state space vector θi∗ References which are introduced to the controllers as input signals Si the system poles of the closed-loop motor controller αi = −Si−1 represents the motor speed response of the closedloop motor dynamics Mi (s) the closed-loop transfer function of a critically damped system that consist of motor dynamics and regulators Kp proportional gain of the PD regulator Kd derivative constant of the PD regulator Ĝi (s) PID transfer function from the input control signal to the motor angular position Gi (s) is the motor transfer function on the beam side of the gear which is equivalent to Ĝi (s) ĝn,i the numerator of Ĝi (s) at the motor side of the gear ĝd,i the denominator of Ĝi (s) at the motor side of the gear n1,i (s) = a2,i s2 + a1,i s + a0,i a polynomial of the PID controller transfer functions n2,i (s) = b2,i s2 + b1,i s + b0,i a polynomial of the PID controller transfer functions di (s) = s(s + ca,i ) a polynomial of the PID controller transfer functions a0,i , a1,i , a2,i , b0,i , b1,i , b2,i and ca,i are controller parameters pi pole position of the closed-loop motor controller (PID).

(34) xxvi. Notation and Acronyms f (X) a vector of the state space model h (X) a matrix of the state space model g (X) a matrix of the state space model Lkf repeated Lie derivative Lkh repeated Lie derivative k a particular value of the Lie derivative Y1 a system output Y2 a system output Φ1 (X) a function Φ2 (X) a function χ a function γ1 (X) a function γ2 (X) a function Υ a vector of four derivatives of the outputs Y1 and Y2 .... Υ1 = Y 1 four derivatives of the output Y1 .... Υ2 = Y 2 four derivatives of the output Y2 Fi (s) filters Fi (s) = Mi−1 (s) δi a time constant Θr = [θ1r , θ2r ]T the state inputs as references u1 a fictitious input u1 a fictitious input U = [u1 , u2 ]T fictitious input.

(35) Notation and Acronyms. xxvii. Ψi a function fX (X) a state matrix fU (X) a state matrix V = [ν1 , ν2 ]T a vector of fictitious control signals ν1 a fictitious control signal ν1 a fictitious control signal X r = [x1 r , x2 r , x3 r , x4 r ] the desired tip position and its first derivative values V r = [ẍr1 , ẍr3 ]T the fictitious input reference Θr the reference for the motor position λi the closed-loop poles of the system Fn = [Fnx , Fny , Fnz ] denotes the normal force or the reaction force at the contact point r = [rx , ry , rz ] represents the distance from the sensor reference, at the F-T sensor initial point, to the contact point (in the frame X 0, Y 0, Z 0) χi a threshold value ξi a threshold value ζi a threshold value Γci a threshold value Γsi a measured torque bias vector, initial conditions Fsi a measured force bias vector, initial conditions |rm | a measured distance.

(36) xxviii. Notation and Acronyms |rc | a calculated distance Tc time of contact µ ∼ = 0 friction coefficient between the contact surface and the beam A different antenna is explained in the appendix. The antenna kinematics and dynamics make use of some extra notation which are going to be written here l1 is the equivalent length of the rigid-beam l2 is the length of the flexible-beam 0. PR is the end-point of the rigid-beam and the flexible-beam attachment point 0. Pt is the end-point of the flexible-beam. 0. Pr is the same beam end-point position when it is considered as a rigid-beam ∆P is a 3D vector that describes the beam deflection (X0 , Y0 , Z0 ) the Cartesian origin of the system (X1 , Y1 , Z1 ) and (X2 , Y2 , Z2 ) are frames due to the mechanism rotation (X3 , Y3 , Z3 ) is a final frame due to the translation m is the rigid-beam mass cθ1 is shorthand for cos(θ1 ) sθ1 is shorthand for sin(θ1 ) cθ2 is shorthand for cos(θ2 ) sθ2 is shorthand for sin(θ2 ).

(37) Notation and Acronyms. xxix. cφ1 is shorthand for cos(φ1 ) sφ1 is shorthand for sin(φ1 ) cφ2 is shorthand for cos(φ2 ) sφ2 is shorthand for sin(φ2 ) 0 3T. the rigid-beam’s Cartesian position and orientation. 0 1R. and 12 R are the rotation matrices. 2 3T. is the translation matrix. 0 3R. the system rotation matrix. 0P ˙. t. the tip speed expressed in spherical coordinates. J The Jacobian which defines the connection between the joint and rigid-beam velocities v3 the linear velocity velocity at the rigid-beam w3 the angular velocity at the rigid tip qj = [φ2 , φ1 , θ2 θ1 ] variables of the system ρk a function where k = 1, 2, 3, ..., 8 Ix and Iz are inertia moments of slender rigid-beams J2 and J1 are the motor inertias φt the total position, both degrees of freedom φrt the total tip reference, both degrees of freedom Γt the total torque measured by means of the F-T sensor, both degrees of freedom. Γct a torque value at the contact time, as threshold condition.

(38) xxx. Notation and Acronyms rex , rey and rez contact point in Cartesian coordinates. rerror distance error of the collision point when compared to rm.

(39) Chapter 1 Introduction This chapter provides a general view of antenna-based sensors in order to show the state-of-the-art bibliography that motivated the solution approach described in this thesis. Section 1.1 outlines the use of integrated sensory systems and active sensing applications. Section 1.2 presents the main literature directly related to biomimetic based sensor applications. Section 1.3 provides some hints on the most frequently used contact sensors, along with their advantages and disadvantages. Section 1.4 presents a brief overview of flexible-beam modelling and its use to control certain beams. Section 1.5 summarises the main assumptions and the solution approach used in this thesis, while our main objectives are listed in Section 1.6. Finally, in Section 1.7, we outline the document structure.. 1.1. Flexible-beam based Sensor Applications. Many applications require integrated sensory systems, as is the case of robotic assemblies for accurate positioning, collision protection, navigation around obstacles, etc. The current trend when measuring stimuli is to use tactile sensors and compensate deficiencies by means of external vision systems. Although integrated sensory systems have produced remarkable results in certain applications, the complications entailed in electronic sensing and control systems might make them unfeasible for the performance of particular tasks, 1.

(40) 2. 1. Introduction. and some of these systems do not therefore work under certain work-space conditions. From an engineering point of view, flexible-beam based sensors have several advantages: they are mechanically very simple, they require very little energy to run, and can work in confined spaces [16]. These sensors are independent of the lighting conditions, do not rely on the surface properties of the objects to be sensed and they do not involve excessive contact with the environment. Moreover, they do not require a complex electronic interface and can be considered as cheap and robust sensors. In nature, many different animal species, and particularly rodents and some aquatic mammals, rely heavily on whiskers and antennas for varied tasks related to short-range navigation and object exploration [7, 16, 62]. Artificial flexible-beam based sensors have a great potential to be uniquely useful in a broad range of tasks, such as sorting items by texture and classification for quality control, during which touch sensing involves active regulation of the position and movement in order to boost quality and the amount of sensory information obtained [50, 59]. For autonomous off-road vehicles, climbing robots, rescue robots, and planetary explorers, the vibrissal sensing of ground and surface texture could aid in the control of a mobile automata when exploring rough terrain during, for example, search and rescue operations following the collapse of buildings or mines. They may provide a useful engineering solution to the problem of sensing and navigation in robotics in the absence of light. Similar systems might also find applications in aquatic environments, particularly in turbid water [66]. Inspection in enclosed environments, such as ducting systems, could use vibrissal sensors as an aid to search for and quantify blockages or damage. Sensor tasks that are concerned with detecting material properties, might also benefit from the use of vibrissal sensors which, in nature, are similar to the resolution of the human fingertip. Interest has also been shown in the area of minimally-invasive surgery, since surgeons are concerned about the loss of tactile information during operations, because they are no longer able to use their fingertips to assess tissue properties. A number of sensor types have been designed and tested but there is much scope as regards improving their design and sensitivity [71]..

(41) 1.2. Bio-mimetic Active Sensors. 3. Systems such as antennae and whiskers might provide a good deal of information by means of the integration of sensing and manipulation for active touch [1, 62]. Tactile sensing applications that make use of force or torque measurements, as is the case of this approach, have been investigated for surgery applications [55], micro-manipulation systems [15], rehabilitation and service robotics [37], in addition to sensing and control [40, 57], etc. Such an antenna system should have the capacity to sample a large area of 3D space, direct the beam towards unknown targets in order to reach special points in a precise manner, and control the velocity and duration of contacts with surfaces. This would involve important efforts for control objectives, such as tip-position accuracy and residual vibration suppression to permit the performance of precise tasks. Active sensing usually entails sensor movement, but more fundamentally involves the control of the sensor apparatus, in whatever manner best suits the task that may be used to maximize information gain, as reported in [49] [42]. Beyond this, the ability to employ alternative active sensing strategies in different contexts may constitute the principal gain. The independent control of flexible beams allows the system to select the position of both the shaft and tip, so as to provide the maximum amount of task-relevant information.. 1.2. Bio-mimetic Active Sensors. There have been multiple examples of bio-mimetic active sensory system applications, which are also known as vibrational systems, some of which will be explained in this section. Whisker and antenna based sensors were first explored in the early 1990s by, for example, Russell et al. [3] and Kaneko et al. [52]. In the work by Russell, a robotic arm that explored its environment made use of a tip contact sensor with a based angle sensor. An antenna sensor was proposed in the work by Kaneko as one of the first active sensing applications. In that work, a rigid spring steel antenna was attached to a one degree of freedom rotating axis, along with a joint angle and a torque sensor, which were used to asses any contacts encountered while sweeping the antenna back and forward..

(42) 4. 1. Introduction. Remarkable active sensory applications have been created, such as those of [80,83,88], in which measuring the size of an object by sliding the beam from one end to the other requires the accurate regulation of the contact force. Some designs similarly make use of (F-T) (force-torque) sensors that are capable of providing as much information as possible using sensory feedback followed by the integration of sensing and manipulation for active touch [1, 60]. Other studies, meanwhile, make use of computational neural systems and advanced artificial intelligence in robotic sensing with particular emphasis on biologically inspired neural networks and methods, as in the works of [30, 70]. Multiple forms of engineering applications based on mammal or insectinspired sensing have been researched, such as the work in [35]. This study developed an active whiskering array consisting of real rat whiskers glued in groups of four to condenser microphones which were constructed, mounted and moved together on a mobile robot. The signals obtained by using this mobile robot were used for texture discrimination. Solomon [46] used an array of four steel whiskers to measure whisker bending in two dimensions. The array was mounted on a pole, instrumented with strain gauges and, using a single servo-motor, the system was swept against a small sculpted head. The authors demonstrated that the bending moment at the base of the whisker could be used to calculate the radial distance from the whisker base to the point of contact which could then be used to iteratively map out a 3D shape. The work by Kim et al. [54] attached two arrays of steel whiskers with a Hall effect sensor onto a robot (Koala). Actuated metal plates rotated the whiskers until they were interrupted by a sensed contact. The whiskers were then moved towards the object to obtain a bending at the base of the whiskers in order to distinguish geometrical shapes by using the deflection angle and the whiskers’ velocity. The Whiskerbot [69] used a bilateral array of moulded glass fibre whiskers equipped with strain gauges to measure bending in two dimensions. The whisker actuation used shape-memory alloy material, and when a current passed through the material, heat produced a linear muscle-like contraction, thus generating the protraction of springs that brought the whiskers back to.

(43) 1.2. Bio-mimetic Active Sensors. 5. their initial position. The use of shape memory alloy actuation made it difficult to mount and control multiple whiskers independently. The system also lacked degrees of freedom with which to position the robot head, which was fixed to the robot. The Whiskerbot was unable to explore vertical surfaces near ground level. A subsequent application was denominated as SCRATCHbot [68]: three whisker-carriers were mounted on either side of a plastic head with single actuators in order to rotate at 120 degrees on each side. A second actuated axis of rotation was also implemented. The design allowed the whiskers to be oriented towards surfaces at different vertical positions of ± 15 degrees. The whisker movement used DC motors equipped with shaft encoders to measure angular position. The whiskers used 3-axis magnetic Hall effect sensors to transduce whisker deflection signals. The platform included active touch sensing with the control of whisker movements during surface exploration [43]. The BIOTACT was a completely modular artificial whisker that incorporated actuation and control electronics. It made use of a miniature brush-less DC motor with a closed-loop PD control provided by an on-board micro controller. Deflection of the whisker shaft was detected using a Hall effect sensor. These modular whiskers were mounted onto a sensory cone and attached to a robotic arm. The complete design was used for experiments in artificial texture discrimination and radial distance detection. The system used a number of innovative classifiers for tactile pattern recognition [77]. SHREWBOT was a platform that consisted of a wheeled robot base called Robotino [67]. Its neck had three Degree of Freedom (3DOF), like that used on SCRATCHbot. The head was mounted as an end-effector on the neck and populated with 18 individually actuated macro-vibrissae and electronics similar to the BIOTACT sensor. The main innovation from a bio-mimetic point of view was therefore the morphology of the snout and its macro-vibrissal array. The main emphasis of the aforementioned bio-inspired works was on the extraction of object properties from contact measurements rather than on the control or the impact of this control on sensing. The authors supported the.

(44) 6. 1. Introduction. claim that feedback control can improve discrimination performance, but had not previously analysed the effects of feedback on signal metrics. In this thesis, we present an alternative work that focuses on the design and active control of the sensor apparatus in order to improve complete movement during a specific task which depends on a particular application. It would similarly be possible to discriminate among the signals originating from contact events, analyse the effects of the proposed control method, and enhance the quality and/or quantity of sensory information for our particular task. The sensor, antenna and mechanism are not intended to be bio-mimetic. The previously cited works are examples of similar important bio-mimetic works. However, this work does not attempt to replicate the physical characteristics of vibrational sensing systems in nature, but rather to attain the best from the natural sensor systems’ functionality and propose a modular robotic sensor designed for robustness and manoeuvrability. Most of the research carried out on both artificial active sensing and flexiblebeam sensors have, to date, focused on processing the information when the beam makes contact [43]. However, the beam trajectory, precision and the vibration damping have not been considered. In this study, the sensor free-air movement of the beam, the mechanism control, and the vibration damping for each manoeuvre are important, since the beam tip will be used to search for specific points, will follow particular trajectories, and will be pointed in a precise manner while recording the information before and after contact has been made.. 1.3. Other Tactile Sensors. In robotics, tactile sensing is important in manipulative tasks during which touch information can be used as a control parameter. The information required might include contact point estimation, normal surface force, curvature measurement and slip detection. The measurement of normal static forces is used for grasping force control, which is essential for maintaining stable grasps, as reported in [24]. The magnitude and the direction of force are also critical in dexterous manipulation since they regulate the balance between normal and.

(45) 1.3. Other Tactile Sensors. 7. tangential forces. When choosing an effective artificial tactile system, it is necessary to consider many criteria for a particular application, such as cost effectiveness, typical estimated range, spatial sensitivity, sensitivity to forces, response bandwidth, reasonable response linearity, negligible hysteresis and the capability to measure contact parameters such as hardness, temperature, etc. The tactile technologies reported have used sensors and sensing arrays with a large variety of transduction methods, some of which are listed in Table 1.1, in which some of their advantages and disadvantages are also reported. There are also miniaturise sensors based on polymers or organic substrate with high spatial resolution but the nature of these sensors makes it difficult for them to withstand large forces or, in the case of organic substrate based sensors, signifies that they have a slow time response.. The less frequent use of tactile sensing could be partly attributed to its complex and distributed nature. Some problems, such as placement, the robustness of sensors or wiring complexity, among others, make an effective utilisation difficult. The interaction of these tactile sensors with the environment has been limited to the measurement of static interaction forces whereas real world interaction also involves dynamic forces. To the best of our knowledge, few works on tactile sensing have mechanically actuated the tactile sensors and considered the system constraints, such as the servo-motor drivers, controllers, computer system, data processing, etc.. In this thesis, we have started from the transducer level, its mechanical design, and worked on every single system constraint in order to develop a system approach that may be helpful as regards filling in the gaps between tactile sensing, transduction and actuation. The antenna design can be considered to be sensitive owing to force and torque sensor resolution, with a fast dynamic response, high bandwidth, and physical robustness..

(46) 8. 1. Introduction. Table 1.1: Tactile Sensing Technologies Transduction Resistive Material Composites System structure Micro electromechanical Advantages Sensitive and low cost Disadvantages High power consumption, detect single contact point, lack of contact force Transduction Material System structure Advantages Disadvantages. Piezo electric Conductive gels Flexible printed circuit board Dynamic response and high bandwidth Temperature sensitive and not so robust electrical connection. Transduction Material System structure Advantages. Capacitive Carbon nano tubes Plastic MEMS Sensitive, low cost, availability of commercial A/D chips Cross-talk, hysteresis, complex electronics. Disadvantages Transduction Material System structure Advantages Disadvantages. Optical Conductive polymers POSFET Immunity to electromagnetic interference, physically flexible, sensitive, fast and no interconnections Bulky, loss of light by micro bending, chirping, power consumption and complex computations. Transduction Material System structure Advantages Disadvantages. Ultrasonic Pressure sensitive ink Organic field effect transistors OFET Fast dynamic response and good force resolution Limited utility at low frequency, complex electronics, temperature sensitive. Transduction Material System structure Advantages. Magnetic Force sensing resistors Extended gate transistors High sensitivity, good dynamic range, no mechanical hysteresis, physical robustness Sensitive to magnetic interference, complex computations, somewhat bulky and high power consumption. Disadvantages.

(47) 1.4. Modelling and Control of Flexible-beams. 9. Note: the information in this table was taken from the research work reported in [24] and [25], which highlights some of the advantages and disadvantages of certain current tactile sensing technologies and their use in robotics.. 1.4. Modelling and Control of Flexible-beams. In this thesis, we consider a two Degree of Freedom (2DOF) antenna with five basic components: a flexible-beam made of a composite material, a light mass attached to the tip of the beam, two DC motor sets that drive the system (one for each degree of freedom), and a multi-axis force/torque (F-T) sensor as a sensory system. An exact solution of the flexible-beam model is not practical or feasible since flexible beams are continuous dynamic systems with infinite dynamic modes and are governed by non-linear coupled differential equations which, in addition, impose multiple constraints on their control design. Most of the research carried out on flexible-beam dynamic modelling is devoted to single links, e.g. [45, 79, 86]. In the work of [12], the linear elastic material deflection is analysed under the effect of an external load at the tip. Flexible-beam dynamics is usually modelled with the assumption of distributed mass where the infinite high-order dynamics is truncated to obtain manageable models [13]. An alternative to this approach is to model the flexure using discrete models, such as finite elements [8] or to approximate the link dynamics by means of a set of lumped and linked masses, as in the works reported in [48, 63, 87]. However, the success of implementing these methods critically depends on the accuracy of the mathematical model and the efficiency of the computation algorithm. The flexible-beam multiple vibration modes and the beam deflection allowed, which causes a misalignment of the motor angle and the final beam angle, have to be studied for the antenna design. This first characteristic can be mechanically constrained to obtain a main vibrational mode (a single mode with maximum amplitude). The beam deflection was limited to 10% of the total beam length in order to obtain a linear beam deflection. Greater or nonlinear deflections are not studied herein. In this thesis, we proposed a reduced dynamic model of the 2DOF antenna system that consists of a flexible beam.

(48) 10. 1. Introduction. and motor dynamics. The flexible-beam dynamics is based on a simple lumped model and the system performs azimuthal and elevation movements in which gravity is considered. Beam flexibility, which leads to oscillatory tip behaviour, high-order and non-linear dynamics, along with being non-minimum phase, makes precise positioning a difficult task that requires closed-loop control. The control system has to carry out motor positioning and tip oscillation suppression. Some examples of surveys concerning the applications and challenging problems related to the use of flexible-beams as flexible manipulators can be found in [14,29,53,81]. Several control methods have incorporated control designs in which beam dynamic modelling was improved under the assumption of small elastic displacements; however, most of these works were focused on flexible single-beam arms.. 1.5. Our Solution Approach. The proposed antenna is an example of an artificial multi-sensory application, designed and modelled to be operated along with robust sensory-motor control strategies. The system makes use of encoders to measure joint angles and a load-cell or force/torque sensor to obtain the flexible beam tip position. A optotrack camera system is used as an external sensor to track the beam tip, thus making it possible for the simulated and measured tip positions to be compared to those obtained by an external sensor. Most of the flexible-beam based sensors reported earlier in Section 1.2 focused on improving the algorithm performance when there was a contact between the beam and an object. Force control systems have been proposed in order to maintain the contact and guarantee accurate point measurements. However, the performance of an antenna for sensing tasks greatly depends on accurate and fast tip positioning for free movements (i.e. without contact). This could save time during the object recognition process and allow specific areas of an object to be addressed for detailed inspections. In fact, this issue has not been dealt with in depth in the investigations cited above. This work therefore aims to develop an antenna prototype in order to explore and improve.

(49) 1.5. Our Solution Approach. 11. the free motion control of flexible-beams. In this respect, this thesis presents the following innovative approaches: 1) A mechanical setup that can be modelled by means of a reduced dynamic model is proposed. This leads to a mechanism whose dynamics are slow and can be modelled as a simple flexible structure with only one oscillation mode. Moreover, the slow dynamics signify that fewer sensors are needed to measure the antenna deflection and hence less computational effort is required. 2) A simplified dynamic model for the antenna system is consequently proposed. Many of the works reviewed for this study considered distributed mass dynamic models that yielded high order dynamics, or ignored the dynamics completely and made use of a static elasticity equation. 3) However, the proposed reduced dynamic model is sufficiently accurate to capture the dominant flexural behaviour, while being sufficiently simple for controller design. In this model, it is possible to split the antenna dynamics into several subsystems which will facilitate analysis and control design. 4) The system has been equipped with PID motion controllers in order to drive the antenna. The system performs azimuthal and elevation movements during which gravity is considered. The PID controllers have proved to be precise, fast, and robust to friction (of a linear and non-linear nature) and other varying parameters. What is more, the control references designed allow the system to work under the system constraints (servo-motor and beam deflection in their linear zones). This thesis proposes an inverse dynamics-based control with which to control the final tip position of the antenna. The general framework is provided in order to compute a feed-forward input that can be used to move a flexiblebeam along a desired trajectory. The feed-forward computation depends on the closed-loop motor controller dynamics and a system input-state linearization. In order to successfully invert the beam dynamics, the beam was modelled by obtaining a reduced fourth order model and new fictitious inputs were designed, such that the state model of the previous reduced system was converted into a multi-input affine model. The inversion was accomplished in both an openloop controller and a closed-loop control, both of which were based on inputstate linearization. A simple control law based on input-state linearization was designed along with an observer of the full system states, and these were.

(50) 12. 1. Introduction. therefore used to control the final tip position, thus leading to a remarkable reduction in the vibration. Experimental results are reported which show the effects of the system output on the overall tracking performance.. 1.6 1.6.1. Thesis Objectives General Thesis Objectives. The purpose of the thesis is to design and obtain a dynamic model of the system and control the position of a lab scale 2DOF flexible antenna. It is a flexible-beam that may be similar in function to some sensory systems present in nature (e.g. antennae and whiskers). However, in this work no effort is made to attempt to mimic the physical appearance, shape or any other physical characteristic of natural sensory systems. It was considered that the experimental platform would be very useful as regards performing experiments with different flexible beams, several materials and types of antennas. Mathematical models of each of the subsystems that constitute the whole robotic system will be developed, tested and validated on this experimental platform. The experimental work will include model-based control strategies, which have been specifically developed for the system tip positioning, along with vibration cancellation techniques. However, many issues must be taken into account when addressing the system design, such as the facts that the flexible-beam must be light-weight, made of composite material, and hence very flexible. The antenna system is a non-minimum phase system whose model must be represented using high order dynamics. Moreover, the system is driven by two small Direct Current (DC) servo-motors for high precision, in which the limited maximum allowed torques, intermittent operation and the strong non-linearity owing to the static friction, limits the motor control design. The stability of the closed-loop control is additionally sensitive to non-modelled dynamics and parameter uncertainties. The objective of our work is, therefore, to design a first control strategy phase that will allow the tip to be placed in a precise manner, and which will be denominated as free-air motion. The movements of the entire mechanism will.

(51) 1.6. Thesis Objectives. 13. be controlled, while the vibrations caused by each and every movement will in turn be damped, and this could be used to ensure that each manoeuvre is performed in the least possible amount of time. A second control phase should, meanwhile, control the contact conditions. This contact phase is carried out in a type of early study and includes an algorithm with which to acquire the contact time, point and direction, while maintaining the damping control switched on, or switching it off for a specific amount of time while approaching the object again. A comprehensive study that includes the design of the mechanism, dynamics modelling and a control method has therefore been proposed for the entire strategy. An oscillatory movement of the beam tip with a single vibration frequency must therefore be settled, thus allowing a simple and invertible model to be obtained that will make it easier to design the controller. The beam dynamics should be slower than the motor dynamics which, when considering the motor reaction, represents an advantage. The beam’s lower dynamics additionally allows a real-time system with a less demanding sample time to be used, which could be implemented using a basic computer system. This computer will be in charge of controlling the overall antenna system, tracking the necessary trajectories, and recording the contact/impact events while processing the signals in order to study the vibrations.. 1.6.2. Specific Objectives of this Thesis. The specific objectives of the thesis are listed as follows: 1. To design an experimental platform (2DOF flexible antenna sensor). The mechanical design of the antenna, manufacture, installation and component parts. 2. To identify the mechanical platform parameters. 3. To select suitable software and hardware for the complete platform. The complete design has to be run using a basic computer system, which has to be considered in order to obtain a suitable sampling time for the entire system..

(52) 14. 1. Introduction. 4. To design a communication interface between software and hardware applications (platform algorithms, input/output signals and communications). 5. To model the antenna dynamics, which includes the load-cell as a force and torque sensor. 6. To perform simulations using Simulink/Matlab and carry out an experimental validation of the proposed model. 7. To design 2DOF controllers for servo-motor positioning in order to obtain fast and precise responses of the control system and the experimental validation of the proposed controllers. 8. To generate Bezier polynomials as specially generated references for the antenna precise control. 9. To design a model-based control strategy in order to cancel antenna tip vibrations. Experimental validation of the proposed controllers. 10. To perform signal processing in order to design a contact detection algorithm by means of force and torque measurements from the loadcell. The expected outcomes are listed as follows: 1. An optimised mechanical design of the antenna. 2. A dynamic model that properly considers the flexible behaviour of the system. 3. An accurate motor position control. 4. A reduction in the vibration at the antenna tip. 5. The tracking of Bezier trajectories for the antenna tip. 6. The performance of control techniques for antenna free movements. 7. Information about contacted points around 3D work space of the antenna..

(53) 1.7. Thesis Organization. 1.7. 15. Thesis Organization. This thesis consists of seven chapters that address the platform design, dynamic modelling and a control method for a robotic antenna with a 2DOF flexible beam. The Chapters are specifically related to the thesis framework, mathematical modelling and validation of the proposed methods based on solving the control issues of a flexible and very light beam made of a composite material.. Chapter 1 introduces the thesis framework, literature review, motivation and structure of the document. It starts with an overview of flexible-beam based sensor applications, describing some examples of applications and biomimetic active sensors. A short review of the modelling and control of flexiblebeams is provided in order to explain the aims of the thesis and our solution approaches. Finally, the general and specific objectives of the thesis are listed.. Chapter 2 presents the experimental platform design, which includes the mechanism characteristics and the parameter identification, software and hardware requirements, and the sensory system.. Chapter 3 provides explanations of a reduced dynamic model of the system, the design characteristics and model assumptions. The system is modelled as a series connection of two subsystems: the servo-motor dynamics and the flexible-beam dynamics.. Chapter 4 compares two position controllers for DC servo-motors which have been designed by considering the following requirements: the controller should track a desired trajectory (in both transient and permanent states) and compensate for static Coulomb friction effects. We describe a PD regulator with an additional term that compensates for the static friction. The performance of the PD regulator (and its compensation) is then compared to that of a PID regulator which was tuned using an algebraic method..

(54) 16. 1. Introduction. Chapter 5 explains a complete control method based on the design of two motor control loops and an outer-loop that are used to place the flexible-beam tip as precisely and fast as possible. It tests a control scheme that includes two nested loops: an inner-loop as a motor control and an outer-loop or tip position control. Chapter 6 introduces an early stage study carried out to provide contact identification. It includes signal processing and a contact detection algorithm obtained by means of force/torque measurements from the load-cell. Future research work is also suggested. Chapter 7 provides a summary of the thesis, relevant conclusions and contributions related to the procedures proposed herein. Future research work is also suggested. This document additionally includes an appendix: Appendix A provides detailed information on a different antenna that was designed, modelled and built at our laboratory. This second prototype is composed of a flexible beam to which a rigid beam is connected. The rigid beam represents a mechanical piece that holds a load-cell sensor which also displaces the flexible-beam initial point from the motor shaft. A dynamic model was obtained from the laws of mechanics, the system was identified and several experiments were performed with this antenna. The design proposed in this appendix has advantages and disadvantages. For example, the second antenna is compact and has advantages related to the volume since it is going to be located on a mobile platform. Moreover, it is symmetric, thus lessening the inertia when moving the motor and the system that moves with the azimuthal movement. The antenna prototype in this appendix therefore has mechanical advantages over that used in this thesis. However, the dynamics is by far more complex, which also makes the model based controllers more difficult to use..

(55) Chapter 2 Description of the Experimental Platform This section provides an explanation of the experimental platform. A two Degree of Freedom (2DOF) flexible-beam is used as an extension of a multi-axis force and torque (F-T) sensor. A simple mechanism was designed to join the flexible-beam and the (F-T) sensor in order to accomplish the desired motion and force transmission. This chapter shows the mechanism characteristics and provides an initial identification of the system. The basic platform software and hardware requirements, along with the sensory system, are also briefly explained.. 2.1 2.1.1. Mechanism Characteristics Mechanism Construction Features. Two drawings of the antenna mechanism are illustrated in Figure 2.1 and Figure 2.2. The structure was built and installed on a tripod structure to ensure that the component parts would be perfectly stable. The figures also illustrate some of the constitutive parts of the design as follows: 1. A tripod structure made of stainless steel to ensure perfect stability. The tripod is fixed to an anti-shake table by means of three fixation screws 17.

(56) 18. 2. Description of the Experimental Platform. that also allow the complete system slope to be adjusted. 2. A (F-T) sensor to measure the Cartesian coupling torques and forces. 3. A servo-motor that rotates the system (azimuthal movement). 4. A servo-motor that rotates the system (elevation movement). 5. A flexible-beam made of carbon fibre. In this case, the composite consists of two parts: a matrix and the reinforcement. A composite material was chosen owing to its remarkable properties such as being lightweight, strong and highly resistant to deformation in order to provide suitable component reliability throughout its service life. However, the beam can be easily changed, thus permitting the use of beams made of different materials and the possibility of changing the radius, length and mass at the tip (bearing in mind the structure’s mechanical limits and the system boundaries). 6. A mechanical part made of stainless steel, which transfers the rotation of the servo-motor shaft in 3 (azimuthal movement), and holds the mechanical part, as shown in 7, along with the motor for the elevation movement. 7. A mechanical part made of stainless steel, which transfers the rotation of the servo-motor shaft in 4 (elevation movement), and holds the (F-T) sensor. 8. A mechanical part made of stainless steel that allows the flexible-beam to be adjusted to one side of the (F-T) sensor tool sides. 9. Two adjustment discs that hold the magnetic limit switches. Each disc has two switches and allows the system work space to be altered by moving the limit switches around and setting them. The switches are known as cylindrical reed switches. A reed sensor is a conveniently packaged switch that acts as a proximity sensor when a suitable vane passes through the slot between the magnet and the switch..

(57) 2.1. Mechanism Characteristics. 19. 10. A fixation screw that corresponds with the key-way of the servo-motor shaft in 3, and transfers movement to the mechanical part, as shown in 6. 11. A small spherical mass made of lead that is placed at the tip. Its size depends on the beam physical features, the expected maximum deflection, etc. But it should not be less than 2.5 times the mass of the beam.. Figure 2.1: 2DOF Antenna Sensor: Solidworks drawing 1.. 2.1.2. Mechanism Parameters and Specifications. Figure 2.3(a) illustrates the mechanism that is used to hold the multi-axis (F-T) sensor. Two servo-motor sets (motor, gear-box, and encoder) are used to drive the sensor, and there is a flexible-beam on the top of the sensor whose initial point at the base of the beam coincides with both motor shafts. Throughout this section, the subscript “i” denotes a particular degree of freedom, while the angle subscript is i = 1 for the motor that drives the azimuthal angles and i = 2 for the motor in charge of the elevation angles..

(58) 20. 2. Description of the Experimental Platform. Figure 2.2: 2DOF Antenna Sensor: Solidworks drawing 2.. Figure 2.3(b) shows the schematic diagram in which the equivalent length of the beam is l. The beam deflection was limited to 10% of the total beam length in order to obtain a linear beam deflection. Larger or non-linear deflection are not studied in this thesis. Pt is the tip of the flexible-beam and Pr is the beam tip itself when the beam is considered to be a rigid-beam. ∆P is a 3D vector that describes the beam deflection, E is the Young module, I is the inertial moment resulting from the flexible-beam cross section, g is the gravity constant (9.81 sm2 ) and M is the tip mass. The tip positions is expressed in spherical coordinates φ1 and φ2 with regard to the absolute Cartesian frame (X,Y ,Z). The rigid part of the system, which rotates the motor angles θ1 , θ2 , holds the (F-T) sensor and the flexible-beam that is attached to one of its tool sides. This allows the Cartesian coupling force Fs =(Fx , Fy , Fz ) and the torques Γs =(Γx ,Γy ,Γz ) to be measured. In this work, the tip position is estimated using the measured torques at the base of the beam. The tip position is expressed in the frame (X, Y, Z) and the frame that eventually results from the rigid mechanism rotations is (X 0 , Y 0 , Z 0 ). The experimental antenna platform is shown in Figure 2.4..

(59) 21. 2.1. Mechanism Characteristics. Pr ∆P Pt, M. E,I,l Z. Pr. ∆P Pt, M X. 1. θ1. X. θ2. θ1 Z’. E,I,l. 2. Z. Y. X’ θ2. θ2. θ1. Y Y’. (b). (a). Figure 2.3: 2DOF flexible-beam sensor: (a) mechanism design and (b) schematic diagram.. Tip Z F-T sensor. Flexible-beam X Y. Figure 2.4: Photograph of the experimental antenna platform..