Humanoid Robot Soccer Locomotion and Kick Dynamics Open Loop Walking, Kicking and Morphing into Special Motions on the Nao Robot Alexander Buckley B.Eng (Computer) (Hons.) In Partial Fulfillment of the Requirements for the Degree Master of Science Presented to the Faculty of Science and Engineering of the National University of Ireland Maynooth in June 2013 Department Head: Prof. Douglas Leith Supervisor: Prof. Richard Middleton Acknowledgements This work would not have been possible without the guidance, help and most of all the patience of my supervisor, Rick Middleton. I would like to thank the members of the RoboEireann team, and those I have worked with at the Hanilton institute. Their contribution to my work has been invaluable, and they have helped make my time here an enjoyable experience. Finally, RoboCup itself has been an exceptional experience. It has provided an environment that is both challenging and rewarding, allowing me the chance to fulfill one of my earliest goals in life, to work intimately with robots. Abstract Striker speed and accuracy in the RoboCup (SPL) international robot soccer league is becoming increasingly important as the level of play rises. Competition around the ball is now decided in a matter of seconds. Therefore, eliminating any wasted actions or motions is crucial when attempting to kick the ball. It is common to see a discontinuity between walking and kicking where a robot will return to an initial pose in preparation for the kick action. In this thesis we explore the removal of this behaviour by developing a transition gait that morphs the walk directly into the kick back swing pose. The solution presented here is targeted towards the use of the Aldebaran walk for the Nao robot. The solution we develop involves the design of a central pattern generator to allow for controlled steps with realtime accuracy, and a phase locked loop method to synchronise with the Aldebaran walk so that precise step length control can be activated when required. An open loop trajectory mapping approach is taken to the walk that is stabilized statically through the use of a phase varying joint holding torque technique. We also examine the basic princples of open loop walking, focussing on the commonly overlooked frontal plane motion. The act of kicking itself is explored both analytically and empirically, and solutions are provided that are versatile and powerful. Included as an appendix, the broader matter of striker behaviour (process of goal scoring) is reviewed and we present a velocity control algorithm that is very accurate and efficient in terms of speed of execution. i Contents Abstract ..........................................................................................................................i 1. Introduction .....................................................................................................................1 1.1. Contributions of Thesis ..........................................................................................................2 1.2. Thesis Outline .........................................................................................................................3 2. Literature Review ............................................................................................................5 2.1. Humanoid Walking .................................................................................................................5 2.1.1. Properties of a Humanoid Gait ...................................................................................7 2.1.1.1. Walk Phases ................................................................................................7 2.1.1.2. Ground Reaction Forces .............................................................................7 2.1.1.3. Center Of Pressure (COP) ...........................................................................7 2.1.1.4. Zero Moment Point (ZMP) .........................................................................7 2.1.1.5. Humanoid Dimensions ................................................................................8 2.1.2. Degrees Of Freedom / Dimensions, Kinematics, Simplified Models ........................8 2.1.2.1. DOF / Dimensions ......................................................................................8 2.1.2.2. Kinematics ..................................................................................................9 2.1.2.2.1. Forwards Kinematics (FK) .......................................................9 2.1.2.2.2. Inverse Kinematics ...................................................................9 2.1.2.3. Modelling ..................................................................................................10 2.1.3. Actuation Type ..........................................................................................................10 2.1.3.1. Electric motors .........................................................................................10 2.1.3.2. Pneumatics ................................................................................................11 2.1.3.3. Hydraulics .................................................................................................11 2.1.4. Control Type .............................................................................................................11 2.1.4.1. Position Controlled ....................................................................................11 2.1.4.2. Force Controlled ........................................................................................11 2.1.5. Locomotion .............................................................................................................11 2.1.5.1. Static Locomotion .....................................................................................11 2.1.5.2. Dynamic Locomotion ...............................................................................12 2.1.5.2.1. Passive ....................................................................................12 2.1.5.2.2. Active ....................................................................................12 2.1.5.2.3. Minimally Active or 'Virtual Passive Dynamics' ...................12 2.1.6. Problem Space ..........................................................................................................13 2.1.6.1. Joint Space Trajectories ............................................................................13 2.1.6.2. Cartesian limb trajectories ........................................................................13 iii 2.1.7. Popular Models and Methods ...................................................................................14 2.1.7.1. Compass Gait - 'Simplest Model' ..............................................................14 2.1.7.2. Six Determinants of Gait Theory ..............................................................14 2.1.7.3. Inverted Pendulum ....................................................................................15 2.1.7.4. 3D Linear Inverted Pendulum / Cart-on-a-Table ......................................16 2.1.7.5. Spring Mass Model ...................................................................................17 2.1.7.6. Zero Moment Point Based Methods .........................................................19 2.1.7.6.1. Zero Moment Point Criterion ................................................19 2.1.7.6.2. ZMP Preview Control ............................................................19 2.1.7.6.3. Theory of Capture Points .......................................................20 2.1.7.7. Foot Placement Estimator .........................................................................21 2.1.7.8. Limit Cycle Walking .................................................................................21 2.1.7.9. Central Pattern Generators ........................................................................22 2.1.7.10. Models Conclusion ................................................................................22 2.1.8. Lateral Motion ..........................................................................................................22 2.1.9. Walk Cycle Frequency ..............................................................................................27 2.1.10. Stiffness on the Nao Robot (Holding Torque) ........................................................27 2.1.11. Turning ....................................................................................................................28 2.1.12. Stability ..................................................................................................................28 2.1.13. Assessment .............................................................................................................28 2.1.13.1. Froude Number .......................................................................................29 2.1.13.2. Efficiency ................................................................................................29 2.1.13.3. Poincare Return Maps .............................................................................29 2.1.13.4. ZMP Stability Margin .............................................................................29 2.1.14. Proposed walk design .............................................................................................30 2.1.15. Conclusion ..............................................................................................................30