Dr Changjiu Zhou School of Electrical & Electronic Engineering Singapore Polytechnic zhoucj@sp.edu.sg www.robo-erect

1. Learning and Control of Biped Locomotion Dr Changjiu Zhou School of Electrical & Electronic Engineering Singapore Polytechnic zhoucj@sp.edu.sg www.robo-erectus.org Development of Humanoid Soccer Robots

2. Outline • Introduction • Biped Walking Cycles • How to Control Biped Locomotion • How to Plan/Learn Biped Gaits • Biped learning by reinforcement • Some Research Topics Development of Humanoid Soccer Robots

3. Single Support Double Support Single Support Time Biped Gait (Frontal Plane) Biped Gait (Frontal View) Development of Humanoid Soccer Robots

4. Biped Gait (Sagittal Plane) Development of Humanoid Soccer Robots

5. Right Support Swing time completed Right foot touches down Right-to-Left Transition Left-to-Right Transition Left Support Left foot touches down Swing time completed Finite State Machine for Biped Walking Control Development of Humanoid Soccer Robots

6. Single Support Double Support Static Walking • In static walking, the biped has to move very slowly so that the dynamics can be ignored. • The biped’s projected center of gravity (PCOG) must be within the supporting area. Development of Humanoid Soccer Robots

7. Dynamic Walking • In dynamic walking, the motion is fast and hence the dynamics cannot be negligible. • In dynamic walking, we should look at the zero moment point (ZMP) rather than PCOG. • The stability margin of dynamic walking is much harder to quantify. Development of Humanoid Soccer Robots

8. Why is Biped Robotics Hard? • Unpowered DOF between the foot and ground • This constraint limits the trajectory tracking approaches used commonly in manipulators research. Development of Humanoid Soccer Robots

9. Biped Control:Model-based Feet position and ZMP (PCOG) Inverse kinematics model Desired joint angles Biped Robot Development of Humanoid Soccer Robots

10. Biped Control:Model-based • Except for certain massless leg models, most biped models are nonlinear and do not have analytical solutions. • Massless leg model is the simplest model. The body of the robot is usually assumed to be point mass and can be viewed to be an inverted pendulum. • When the leg inertia and other dynamics like that of the actuator, joint friction, etc. are included, the overall dynamic equations can be very nonlinear and complex. Development of Humanoid Soccer Robots

11. Example: Massless leg model • The simplest biped model • Some assumptions, e.g., • From D’Alembert’s principle Development of Humanoid Soccer Robots

12. Biped Control:Biologically Inspired • Since none of the humanoid robots match biological humanoids in terms of mobility, adaptability, and stability, many researchers try to examine biological bipeds so as to extract certain algorithms that are applicable to the robots. Reverse Engineering Development of Humanoid Soccer Robots

13. Biped Control:Biologically Inspired Two Main Research Areas • Central Pattern Generators (CPG) • Passive Walking Development of Humanoid Soccer Robots

14. ZMP-based Gait Planning • Plan the hip and ankle trajectories according to walking constraints and ground constraints. • Derive all joint trajectories by inverse kinematics. Development of Humanoid Soccer Robots

15. Example: Gait Planning for Walking on Slope - Plan gait using 3rd order Spine which guarantees the continuity of both 1st derivative and 2nd derivative. Development of Humanoid Soccer Robots

16. Example: Planning Results Consecutive walking gait along slope Joint angles Development of Humanoid Soccer Robots

17. v  L 2wf IP-based Gait Planning • The dynamic equation of the IP model • If the angle is small, it can be simplify as a linear homogeneous 2nd order differential equation Development of Humanoid Soccer Robots

18. 3D Linear Pendulum Model Development of Humanoid Soccer Robots

19. Example: IP-based Gait Planning Development of Humanoid Soccer Robots

20. Biped Kicking Kicking constraints: • Kicking range • Friction • … Development of Humanoid Soccer Robots

21. Kicking Pattern Development of Humanoid Soccer Robots

22. Supporting foot Stable r = 0 (reward) Unstable r = -1 (punishment) Biped Learning by Reinforcement (1) • A humanoid robot aims to select a good value for the swing leg parameters for each consecutive step so that it achieves stable walking. • A reward function that correctly defines this objective is critical for the reinforcement learning. Development of Humanoid Soccer Robots

23. Biped Learning by Reinforcement (2) • The control objective of the gait synthesizing for biped dynamic balance can be described as • To evaluate biped dynamic balance in the frontal plane, a penalty signal should be given if the biped robot falls down in the frontal plane

24. Good Very Bad Bad Supporting foot Excellent OK Biped Learning by Reinforcement (3) Reinforcement Learning with Fuzzy Evaluative Feedback Development of Humanoid Soccer Robots

25. The RL Agent • AEN - the action-state evaluation network • ASN - the action selection network • SAM - the stochastic action modifier • Both the AEN and ASN are initialized randomly. • Learning starts from scratch. • It needs a large number of trials for learning. Development of Humanoid Soccer Robots

26. The FRL Agent • Neural fuzzy networks are used to replace the neuron-like adaptive elements. • The expert knowledge can be directly built into the FRL agent as a starting configuration. • The ASN and/or AEN could house available expert knowledge to speed up its learning. Development of Humanoid Soccer Robots

27. The FRL Agent with Fuzzy Evaluative Feedback • The numerical evaluative feedback is not the biological plausible. • The fuzzy evaluative feedback is much closer to the learning environment in the real world. • The fuzzy evaluative feedback is based on a form of continuous evaluation. Development of Humanoid Soccer Robots

28. Comparison of FRL Agents Development of Humanoid Soccer Robots

29. Information Available for Biped Gait Synthesizing Development of Humanoid Soccer Robots

30. The Gait Synthesizer Using Two Independent FRL Agents Development of Humanoid Soccer Robots

31. Before and After Learning Ankle joint Knee joint Development of Humanoid Soccer Robots

32. Results (1) The ZMP trajectory after FRL (type C) Development of Humanoid Soccer Robots

33. Results (2) Walk (Backward) Development of Humanoid Soccer Robots

34. Some Research Topics • Online gait generating • Online footprint planning • Constraints • ZMP constraint for stable walking • Friction constraint for stable walking • … • Current Challenges • Knee bending • Body shifting • … • … Development of Humanoid Soccer Robots

35. References • C. Zhou, “Robot learning with GA-based fuzzy reinforcement learning agents,” Information Sciences 145 (2002) 45-68. • C. Zhou, “Fuzzy-arithmetic-based Lyapunov synthesis to the design of stable fuzzy controllers: a computing with words approach,” Int. J. Applied Mathematics and Computer Science12(3) (2002) 101-111. • C. Zhou and Q. Meng, “Dynamic balance of a biped robot using fuzzy reinforcement learning agents,” Fuzzy Sets and Systems 134(1) (2003) 169-187. • C. Zhou, P.K. Yue, Z. Tang and Z. Sun, “Development of Robo-Erectus: A soccer-playing humanoid robot,” Proc. IEEE-RAS Intl. Conf. on Humanoid Robots, CD-ROM, 2003. • Z. Tang, C. Zhou and Z. Sun, “Gait synthesizing for humanoid penalty kicking,”  Dynamics of Continuous, Discrete and Impulsive Systems, Series B, (2003) 472-477. • D. Maravall, C. Zhou and J. Alonso, “Hybrid fuzzy control of inverted pendulum via vertical forces,” Int. J. of Intelligent Systems, 2004 (in press). Development of Humanoid Soccer Robots

36. Acknowledgements • Staff Member P.K. Yue, F.S. Choy, Nazeer Ahmed M.F. Ercan, Mike Wong, H. Li • Research Associate Z. Tang (Tsinghua U.), J. Ni (Shanghai Jiao Tong U.) • Technical Support Officer H.M. Tan, W. Ye • Students P.P. Khing, H. W. Yin, H.F. Lu, H.X. Tan, J.X. Teo, Stephen Quah, H.M. Tan, Y.T. Tan Development of Humanoid Soccer Robots

37. Thanks! Dr Changjiu Zhou School of Electrical and Electronic Engineering Singapore Polytechnic zhoucj@sp.edu.sg www.robo-erectus.org Development of Humanoid Soccer Robots