Control of Legged Robotic Systems: Substantiation of Gait Design, Multi-Modal Behaviors, and Dynamic Scaling Theory in Practice Daniel J
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Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2018 Control of Legged Robotic Systems: Substantiation of Gait Design, Multi-Modal Behaviors, and Dynamic Scaling Theory in Practice Daniel J. Blackman Follow this and additional works at the DigiNole: FSU's Digital Repository. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING CONTROL OF LEGGED ROBOTIC SYSTEMS: SUBSTANTIATION OF GAIT DESIGN, MULTI-MODAL BEHAVIORS, AND DYNAMIC SCALING THEORY IN PRACTICE By DANIEL J. BLACKMAN A Thesis submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science 2018 Copyright c 2018 Daniel J. Blackman. All Rights Reserved. Daniel J. Blackman defended this thesis on July 13, 2018. The members of the supervisory committee were: Jonathan Clark Professor Directing Thesis William Oates Committee Member Carl A. Moore Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the thesis has been approved in accordance with university requirements. ii TABLE OF CONTENTS List of Tables.............................................v List of Figures............................................ vi Abstract................................................ ix 1 Introduction 1 2 Background 4 2.1 Natural Legged Locomotion................................4 2.2 Simulation and Robotics..................................4 2.2.1 Bioinspiration versus Biomimetics........................5 2.2.2 Gait Controller Design for Multi-legged Systems................6 2.2.3 Dynamic Scaling..................................7 3 Simulation and Experimental Design8 3.1 Introducing Minitaur....................................8 3.1.1 Initial Control Strategies.............................8 3.1.2 Isolating Sagittal Plane Dynamics........................ 10 3.2 Simulation Modeling.................................... 12 3.2.1 SLIP Modification................................. 12 3.2.2 Hopping....................................... 14 4 Gait Development on Minitaur 15 4.1 Experimental Setup for Gait Analysis.......................... 15 4.2 Minitaur Crawl Gait Results............................... 15 4.3 Controller Design Modification.............................. 16 4.4 Updated System Running................................. 17 4.5 Walk to Trot........................................ 18 5 Running and Jumping Behavior 20 5.1 Running........................................... 20 5.1.1 Simulation of 5-bar SLIP............................. 20 5.1.2 Experimental Validation of 5-bar SLIP...................... 22 5.2 Jumping........................................... 23 5.3 Running and Jumping................................... 25 6 A Physical Manifestation of Dynamic Similarity and Scaling 28 6.1 Designing at the Larger Scale............................... 29 6.2 Characterizing Limitations: System Identification.................... 29 iii 7 Conclusions 38 References............................................... 40 Biographical Sketch......................................... 44 iv LIST OF TABLES 3.1 Physical Parameters of the Minitaur Robotic Platform..................8 5.1 Single-leg Running Experimental Results of Stability Analysis (this table is reproduced from [9] c 2017 IEEE)................................... 22 6.1 Scaling Parameters Relating the UPenn Thumper and ARL Hopper.......... 34 v LIST OF FIGURES 1.1 The early stages of the quadrupedal robotic platform Minitaur (left; image taken by author) and a single Minitaur leg attached to a mechanical boom system for con- strained sagittal plane dynamic analysis (right). This image is reproduced from [9] c 2017 IEEE..........................................2 2.1 This figure shows demonstrative images for distinguishing the difference between bioin- spired and biomimetic engineering design..........................6 3.1 A single Minitaur leg (a) is depicted here with definitions of the angle parameters and link lengths used to determine leg length and touchdown angle. The trajectory is performed in the motor space (b) with the rotation of both motors together during stance and in opposition to provide toe liftoff and touchdown..............9 3.2 Robotic platforms designed to explore dynamic scaling with the larger UPenn Thumper (b) exhibiting the same kinematics but at a larger scale (αl = 1:5 and αm = 2:12)... 11 3.3 The dynamics and definitions of the SLIP model (a) and their translation to the 5-bar kinematic leg design (b, c). These figures are printed with permission [9] c 2017 IEEE. 12 4.1 Raw data from the motion capture system for velocity (a) was used filtered and differentiated (b) to calculate a window of steady system velocity (c). This image is reproduced from [10]..................................... 16 4.2 Manipulations of the triangular trajectory include the height of toe lift (a) and the position of the apex height with respect to commanded touchdown (b). The results from an experimental analysis of the effects of parameter sweep (c) of the updated control used on Minitaur demonstrate greater velocities than seen previously (Fig. 4.1d). This image is reproduced from [10]......................... 18 4.3 Definitions and experimental results for walk-to-trot gait development (a) as well as a time-lapse of Minitaur performing a trot on the plywood surface (b) used through this gait study. These images are reproduced from [10].................. 19 5.1 Stability regions of running are shown here for a range of different postures (rows) and linkage ratios (columns) of the 5-bar kinematic SLIP model. The images in the left most column depict half of the symmetric linkage to demonstrate the posture of the leg with the different nominal linkage configuration angles. For the plots, the axes are non-dimensional stiffness versus angle of attack (α0 = 90 + ), with a secondary y-axis on the right demonstrating the torsional stiffness constant of the resultant hip ◦ ◦ ◦ spring (from Eq. 3.9). The three posture angles (θ0 = 45 , θ0 = 75 , and θ0 = 105 ) were chosen based on the physical limitations of the robot (linkage collision occurs at angles less than θ = 45o) and previous work regarding knee springs with a ratio R = 1=1. Reproduced with permission from [9] c 2017 IEEE.............. 21 vi 5.2 (a) The 1D hopping model performs a single jump, starting near full compression, extending until liftoff is achieved through force balancing between the actuator output and gravity. (b) For a range of different ratios at three designated control efforts (% voltage to motors), the hop height displacement demonstrated optimal ratios of 0.54, 0.60, and 0.62 (for 50%, 75%, and 100% effort, respectively). This figure is reproduced with permission from [9] c 2017 IEEE........................... 24 5.3 A single, powerful jump with the FSU MiniBoom platform begins with the leg at full compression (a) with output torque to both motors until full extension (b). The results of the hop height measured from maximum height of the boom arm are normalized for comparison between R = 1=1 and R = 1=2 (c). Reproduced with permission from [9] c 2017 IEEE........................................ 25 5.4 Experimental data depicting the run-to-jump results for the R = 1=2 and R = 1=1 legs. Reproduced with permission from [9] c 2017 IEEE................. 26 5.5 Photographic timelapse demonstrating the configuration of the R = 1=2 compressing and subsequently clearing the obstacle with its jumping capability. Reproduced with permission from [9] c 2017 IEEE.............................. 27 6.1 Sketch design for Thumper platform produced by Wei-hsi Chen of the Kod*lab at University of Pennsylvania.................................. 29 6.2 Analysis of 1D hopping on the ARL Hopper with variation in controller damping for two distinct system masses.................................. 30 6.3 Multiple leg drops are performed on the ARL Boom (a) then individual drop events are isolated (b). The necessary output values are extracted including the first two minimum peaks, the maximum peak, the period of oscillation, and the steady-state leg length............................................ 32 6.4 Calibration curves for stiffness (a) and damping (b) determined using the described fsolve method for the ARL Hopper system........................ 32 6.5 A Comparison of the ARL Hopper with added increments of +0:1kg and +0:2kg demonstrates similar steady-state hop heights when scaling is applied to the one di- mensional AER controller.................................. 33 6.6 Calibration curves for stiffness (a) and damping (b) determined using the described fsolve method for UPenn Thumper............................. 34 6.7 Theoretical motor speed/torque curves for the T-motor U10 Plus, DYS BE8108-16, and scaled down version of the U10 Plus.......................... 36 6.8 Experimental analysis of a range of different control parameters for AER control scaled steady-state hopping between the UPenn Thumper and ARL Hopper.......... 37 vii 6.9 Scaled matching of two dimensional, steady-state running between the UPenn Thumper and ARL Hopper comparing apex of flight phase, minimum compressed leg length, frequency of running, forward system velocity, touchdown angle, and stance angle swept. 37 viii ABSTRACT Through limb structure and neuromuscular control, animals have demonstrated the ability to nav- igate obstacles and uneven terrain using a variety of different mechanisms and behaviors. 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