Dynamic Modeling, Design and Control of a Cheetah Inspired Robot Using Central Pattern Generators (CPG) Method A Thesis Submitted to the School of Mechanical Engineering For the Degree of Master of Science Author: Mohsen Azimi Director: Mohammad Reza Hairi Yazdi School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran 8/Sep/2014

2/23 Introduction Previous Works Driving Equations Results First Section: Second Section: Third Section: Forth Section: School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

3/23 Advantages of the Legged Robots: Applications of the Legged Robots: - A good vehicle in mountains and jungles - Running errand in dangerous places, like: space and volcanic area - Functioning as a rescuer in flood or earthquake area - Able to move on uneven surface کارهای گذشته استخراج معادلات نتیجه گیری School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Introduction

4/23 Legged Animals, The Best Model for Legged Robots - Studying the animals’ neural system for designing the robots’ controllers کارهای گذشته School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran - Studying the animals’ body for designing the robots’ body Introduction

5/23 Gait: the result of repeating a specific cycle Cycle: a combination of several phases Phase: 1.Single Support Phase 2. Double Support Phase 3. Impact Phase 4. Jump Off5. Flight Phase6. Touch Down کارهای گذشته استخراج معادلات نتیجه گیری School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Introduction

6/23 Inverted Pendulum model کارهای گذشته استخراج معادلات نتیجه گیری Methods based on inverse kinematic problem Passive dynamic walking Application of Inverted Pendulum Model [Arthur D. Kuo, University of Michigan, 2007] [Timothy M. Griffin, University of Colorado, 2004] School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Previous Works

7/23 Passive Dynamic Walking The most efficient approach Robot’s physical parameters Initial conditions The ground’s slope - The Disadvantages: - The Advantages: [Tda McGeer. Simin Fraster University, 1990, 1990] 1. Unable to control the robot’s position accurately 2. Sensitivity to School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Previous Works

8/23 Trajectory Generation Based on Passive Dynamic Walking 1. Energy Shaping Control Energy dissipated in previous IP = Energy injected in SSP Putting constrains on robot’s energy level during SSP 1. robot’s energy level is a function of robot’s both position and velocity 2. Unable to control the robot’s position during SSP Energy injected in previous SSP = Energy dissipated in IP Putting constrains on robot’s energy level during IP 1. robot’s energy level is just a function of robot’s velocity 2. Able to control the robot’s position during SSP Energy Dissipation Rate control [Mark W. Spong, University of Illinois at Urbana, 1999, 2003] [Matthew Todd Farrell] [Yuji Harata et al, Nagoya University,2007] [Fumihiko Asano, Tokyo Institute of Technology, 2001, 2004, 2005, 2006] School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran 2. Virtual Gravity Control 3. Parametric Excitation Control Previous Works

9/23 EDRC Demands an accurate Control of the Robot’s swing Limbs Quadruped robot’s Problem in Using Inverse Kinematic Problem - Under-actuation of the ankle joints Solutions 1. Considering each leg as a separate manipulator 2. Using inverse kinematic by considering three feet in contact with the ground criteria Establishing a Semi-Analytical Approach for designing the Robot’s Actuated Joints [Alexander Shkolnik et al. MIT, 2007] [Xuedong Chen et al. Saga University, 2000] School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Previous Works

10/23 2. Nonlinear Oscillator Model Using the Inverse Kinematic Problem and CPG Controllers Simultaneously Central Pattern Generator (CPG) Controllers 1. Neural Network Model 1. Unable to control the robot’s limbs accurately 2. The parameters must be redesigned for new environments The disadvantages [Fumiya Iida et al. University of Zurich] [WU QiDi et al. Tongji University, 2009] [Auke Ijspeert et al. EPFL, 2007] The advantages School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran The solution 1. Very simple and easy to design 2. Suitable for robots with high degrees of freedom Previous Works

11/23 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Deriving Equations

12/23 Limited just to robots with 3 DOF School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Deriving Equations

13/23 += - A galloping quadruped gait is a combination of a bouncing quadruped gait and a walking biped gait Robots with Higher Degrees of Freedom School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Previous Works

14/23 A New Approach for Using the Inverse Kinematic Problem and CPG Controllers Simultaneously School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Previous Works

15/23 Be considered as known parameters School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Deriving Equations

16/23 Limits for swing feet’s velocity School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

17/23 Analysis of the Biped Robot’s Dynamic Equations School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

18/23 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

19/23 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

20/23 Stick Diagrams School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

21/23 Mohsen Azimi, and M.R. Hairi Yazdi, “Energy Dissipation Rate control via a Semi Analytical Pattern Generation Approach for Planar Biped Walking Robot Based on the Property of Passive Dynamic Walking”, Transaction of the Institute of Measurement and Control, Submitted Mohsen Azimi, and M.R. Hairi Yazdi, “Energy Dissipation Rate Control Via a Semi Analytical Pattern Generation Approach for Planar Spined Quadruped Bouncing Robot Based on the Property of Passive Dynamic Walking”, Journal of Mechanical Science and Technology (JMST), Accepted & Revised Mohsen Azimi, and M.R. Hairi Yazdi, “Energy Dissipation Rate Control for Planar Quadruped Bouncing Robot Based on the Property of Passive Dynamic Walking”, the 2nd RSI International Conference on Robotics & Mechatronics (ICRoM), Tehran, October 15-17, 2014 Mohsen Azimi, and M.R. Hairi Yazdi - “Energy Dissipation Rate Control via a Semi-Analytical Pattern Generation Approach for Planar Three-Legged Galloping Robot based on the Property of Passive Dynamic Walking” Journal of Applied Mechanic (JAMECH) 46, no 1 (2015) Mohsen Azimi, and M.R. Hairi Yazdi, “Energy Dissipation Rate Control for Planar Biped Walking Robot Based on the Property of Passive Dynamic Walking”, IMECH ASME2014 International Mechanical Engineering Congress and Exposition, Montreal, November 14-20, 2014 Publications School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

22/23 Future works School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Results

23/23 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran