A Model-Based Control Approach for Locomotion of Biped cga/tmp-public/ robot inside this optimizer...

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Transcript of A Model-Based Control Approach for Locomotion of Biped cga/tmp-public/ robot inside this optimizer...

  • Projet de Master, (2013), Section de microtechnique

    A Model-Based Control Approach for Locomotion of Biped Robots

    Program:

    Robotics and Autonomous Systems

    Student:

    Salman Faraji

    Supervisor:

    Professor Auke Jan Ijspeert

    Assistant:

    Soha Pouya

    2.8.2013

    Lausanne, Switzerland

  • text

    This project was started on 8.4.2013

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  • Abstract

    In this research we aim at proposing a general novel walking method for locomotion of torque controlled robots. The method should be able to produce a wide range of speeds without requiring off-line optimizations and re-tuning of parameters. It should be capable of tolerating internal errors, noises and control delays as well as external disturbances such as pushes or roughness in the environment. We have a quadratic whole-body optimization which generates joint toques, given desired Cartesian accelerations of center of mass and feet. Using dynamics model of the robot inside this optimizer ensures compliance and better tracking, required for fast locomotion. We have simplified the model of robot to linear inverted pendulum and proposed different planners which are other quadratic convex problems opti- mizing future behavior of the robot. These planners are in fact model predictive control which optimize the system either in continuous or discrete time domains. Fast libraries help us performing these calculations per time step and producing desired motion. With very few parameters to tune and no perception, our method shows notable robustness against strong external pushes, large terrain variations, internal noises, model errors and also delayed communication. Evident by various simulations in different conditions, we can suggest our general method for walking control of a wide range of humanoid robots 1.

    1Watch all movies for different simulations in this work at http://biorob.epfl.ch/ page-96274.html.

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    http://biorob.epfl.ch/page-96274.html http://biorob.epfl.ch/page-96274.html

  • Contents

    List of figures viii

    List of tables ix

    1 Introduction 1 1.1 Main questions to answer . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.1.1 Energy efficiency . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Mechanical power . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Compliance . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.4 Agility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.2 Contributions of this work . . . . . . . . . . . . . . . . . . . . . . . 7

    2 Literature review 9 2.1 Model-Free Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.1.1 Central Pattern Generators (CPG) . . . . . . . . . . . . . . 10 2.1.2 Reflex based control . . . . . . . . . . . . . . . . . . . . . . 11

    2.2 Kinematic-model based methods . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Inverse kinematics . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Zero Moment Point (ZMP) . . . . . . . . . . . . . . . . . . . 14 2.2.3 Potential fields . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.4 Virtual Model Control (VMC) . . . . . . . . . . . . . . . . . 17

    2.3 Dynamic-model based methods . . . . . . . . . . . . . . . . . . . . 19 2.3.1 Inverse dynamics . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.2 Projected inverse dynamics . . . . . . . . . . . . . . . . . . 20 2.3.3 Trajectory optimization . . . . . . . . . . . . . . . . . . . . 23 2.3.4 Hybrid zero dynamics . . . . . . . . . . . . . . . . . . . . . 24 2.3.5 Operational space control . . . . . . . . . . . . . . . . . . . 27 2.3.6 Whole body optimization . . . . . . . . . . . . . . . . . . . 29

    2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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  • 3 Simulation platform 31 3.1 Atlas robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Simulation software . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    3.2.1 Gazebo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.2 DRCSim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.3 ROS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.4 CloudSim . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    3.3 Control packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.1 SD/FAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.2 CVXGEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    3.4 Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4.1 Constraint consistent local position . . . . . . . . . . . . . . 37 3.4.2 Incremental odometry . . . . . . . . . . . . . . . . . . . . . 38

    4 Whole body optimization, generating joint torques 40 4.1 Designing low level controller . . . . . . . . . . . . . . . . . . . . . 41

    4.1.1 On-board joint controller in simulator . . . . . . . . . . . . . 41 4.1.2 Robot states, combined position/force control . . . . . . . . 42 4.1.3 Abstracting the model to center of mass . . . . . . . . . . . 43 4.1.4 Swing foot accelerations . . . . . . . . . . . . . . . . . . . . 44 4.1.5 CoP, friction and joint torque constraints . . . . . . . . . . . 45

    CoP constraints . . . . . . . . . . . . . . . . . . . . . . . . . 45 Friction constraints . . . . . . . . . . . . . . . . . . . . . . . 46 Joint torque limits . . . . . . . . . . . . . . . . . . . . . . . 47 Existence of constraint . . . . . . . . . . . . . . . . . . . . . 47

    4.1.6 Formulating final quadratic problem . . . . . . . . . . . . . 48 4.1.7 Contact force distribution . . . . . . . . . . . . . . . . . . . 51 4.1.8 Imposed state of the low level controller . . . . . . . . . . . 51 4.1.9 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1.10 Posture control . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1.11 CoM acceleration regularization . . . . . . . . . . . . . . . . 54 4.1.12 Overall structure of low level controller . . . . . . . . . . . . 56

    4.2 Testing low level controller . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.1 Scenario 1: Squatting . . . . . . . . . . . . . . . . . . . . . . 57 4.2.2 Scenario 2: Sagittal motion . . . . . . . . . . . . . . . . . . 58 4.2.3 Scenario 3: Push recovery and compliance test . . . . . . . . 62 4.2.4 Scenario 4: Statically-Stable walking . . . . . . . . . . . . . 65

    4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

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  • 5 Control Method 1: Captured walking 72 5.1 3D Linear Inverted Pendulum Model (LIPM) . . . . . . . . . . . . . 72

    5.1.1 LIPM with point ground contact . . . . . . . . . . . . . . . 73 5.1.2 LIPM with support foot . . . . . . . . . . . . . . . . . . . . 74 5.1.3 LIPM with support foot and inertia mass . . . . . . . . . . . 75 5.1.4 Instantaneous capture point . . . . . . . . . . . . . . . . . . 76

    5.2 Captured walking using model predictive control . . . . . . . . . . . 79 5.2.1 Navigator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2.2 Stance planner, model predictive control . . . . . . . . . . . 83 5.2.3 Swing planner, LIPM accelerations . . . . . . . . . . . . . . 85 5.2.4 Parameter tuning . . . . . . . . . . . . . . . . . . . . . . . . 87

    5.3 Simulation of walking with different speeds . . . . . . . . . . . . . . 87 Changing parameters . . . . . . . . . . . . . . . . . . . . . . 92 Rapid speed change . . . . . . . . . . . . . . . . . . . . . . . 92 Push recovery . . . . . . . . . . . . . . . . . . . . . . . . . . 92

    5.4 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

    6 Control Method 2: Dynamic walking 96 6.1 Literature review on planning methods . . . . . . . . . . . . . . . . 97 6.2 Model predictive control: Step planning . . . . . . . . . . . . . . . . 99

    6.2.1 Navigator design . . . . . . . . . . . . . . . . . . . . . . . . 99 Solving LIPM differential equation . . . . . . . . . . . . . . 100 N-Step foot placement in future . . . . . . . . . . . . . . . . 101 Controllability . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Objective, constraints . . . . . . . . . . . . . . . . . . . . . 103 Quadratic Problem (QP) formulation . . . . . . . . . . . . . 103

    6.2.2 Planner design . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2.3 Parameter tuning . . . . . . . . . . . . . . . . . . . . . . . . 107

    6.3 Simulation of walking . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.3.1 Speed variations . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.3.2 External pushes . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.3.3 Delayed communication . . . . . . . . . . . . . . . . . . . . 119 6.3.4 System noises . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.3.5 Model errors in link masses . . . . . . . . . . . . . . . . . . 123 6.3.6 Model error in link lengths . . . . . . . . . . . . . . . . . . . 125 6.3.7 Walking on rough terrain . . . . . . . . . . . . . . . . . . . . 126 6.3.8 Walking on different slopes . . . . . . . . . . . . . . . . . . . 128

    6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

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  • 7 Conclusion and future works 131 7.1 Advantages, drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

    Bibliography 141

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  • List of Figures

    1.1 Different quadruped robots . . . . . . . . . . . . . . . . . . . . . . . 2