1. Biped Robot Walking using Particle Swarm Optimization
Behzad Nikbin, Mohammad Reza Ranjbar, Behrooz Shafiee Sarjaz, Hamed Shah-Hosseini
Faculty of Electrical and Computer Engineering, Shahid Beheshti University, G.C., Tehran, Iran

2. Table of Contents Introduction to NAO Parameters of Walking Algorithm
Optimization
Results
Future Works
References

3. NAO, a Humanoid Robot

4. NAO’s technical information
Clock rate 50 Hz (T=0.02s)
Image processing tools
Height: 57 cm
Pressure sensors
Gravity sensor
Gyroscope
23 DOFs
Each joint moves with a given angular velocity

5. Simulated NAO
Optimization algorithms can run it again and again easily, and without wasting too much time
No cost
Standard simulated NAO is used in RoboCup Soccer 3D Simulation league

6. Parameters of Walking Algorithm
Parameter1: Hip_Height
the height of the hip joint during the walk process

7. Parameters of Walking Algorithm(2)
Parameter2: Hip_Offset
the distance along X-axis between left hip and left ankle.

8. Parameters of Walking Algorithm(3)
Parameter3: Max_Ankle_Height
the height of ankle joint at the highest point.

9. Parameters of Walking Algorithm(4)
Parameter4: Num_of_Steps
the number of cycles (hardware’s clock cycle) necessary to complete a Half-Loop.

10. Parameters of Walking Algorithm(5)
Parameter5: Gait_Length
the distance traversed during a Half-Loop

11. Walking Algorithm
NAO needs the angular velocity of each joint at each cycle
The position of each joint at each cycle, can be calculated inverse kinematics
The angular velocity of each joint at each cycle, would be calculated according to the joint’s position

12. Optimization
An optimization algorithm needed to optimize the five introduced parameters
Proper initial values
A visual toolkit is developed to manipulate the parameters and test them
Particle Swarm Optimization algorithm
Open source PSO library (jSwarm) is utilized

13. Initial Values for Particles

14. Particle Swarm Optimization (PSO)
PSO is a robust stochastic optimization technique based on the movement and intelligence of swarms.
PSO applies the concept of social interaction to problem solving.
It was developed in 1995 by James Kennedy (social-psychologist) and Russell Eberhart (electrical engineer).
It uses a number of agents (particles) that constitute a swarm moving around in the search space looking for the best solution.
Each particle is treated as a point in a N-dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles.

15. Particle Swarm Optimization
jSwarm
Open source java library for PSO
No. of Iterations
No. of Particles
Inertia
Particle Increment
Global Increment 30 20
0.98
0.01

16. Limiting the Sample Space
By limiting the parameters, an optimization algorithm such as PSO, will converge much faster
Joint name
Lower bound
Upper bound
Hip_Height
11 cm
25 cm
Hip_Offset
1 cm
10 cm
Max_Ankle_Height
1 mm
4 cm
Steps 3 14
Gait_Length
1 cm
30 cm

17. Fitness function
Support Area: the area between the two legs

18. Fitness Function (2) 𝑓=𝑤 𝑖=1 𝑛 𝑍 𝑖 − 𝐶 𝑖 2 + 1−𝑤 𝑖=1 𝑛−1 𝐶 𝑖 − 𝐶 𝑖+1 2
Zero Momentum Point
a point at which sum of all momentums around it is zero
If the projection of this point on the ground is inside the support area, the robot will be stable
𝑓=𝑤 𝑖=1 𝑛 𝑍 𝑖 − 𝐶 𝑖 −𝑤 𝑖=1 𝑛−1 𝐶 𝑖 − 𝐶 𝑖
Zi: ZMP at cycle i
Ci: Center of support area
w: a constant weight (0.6)
through manipulating the “w”, higher speed can achieve, but there is a tradeoff between stability and speed.

19. Simulation

20. Simulation

21. Results
Best and Average fitness of 10 run, at each iteration

22. Results (2)
Positions of left and right leg during the walk

23. Results (3)
Angles of each joint

24. Results (4) The best particle: Speed: 0.62 m/s Gait_Length
No. of steps
Max_Ankle_Height
Hip_Offset
Hip_Height
19.3 cm 8
3.0 cm
8.3 cm
17.9 cm

25. Future works Omni-directional walking
Using more DOFs (Degree of Freedom) of NAO to have more stable and faster walking

26. References
W. T. Miller III: Real-time neural network control of a biped walking robot. IEEE Control Systems Magazine. 14(1): (1994)
C. L. Shih: Ascending and descending stairs for a biped robot. IEEE Transactions on Systems, Man, andCybernetics. 29(3): (1999)
J. Yamaguchi, E. Soga, S. Inoue, A. Takanishi: Development of a bipedal humanoid robot control method of whole body cooperative dynamic biped walking. Paper presented at the IEEE international conference on robotics and automation, Detroit, Michigan, May 1999
K. Hirai, M. Hirose, T. Takenaka: The development of Honda humanoid robot. Paper presented at the IEEE international conference on robotics and automation, Leuven, Belgium, May 1998
S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa: Biped walking pattern generation by using preview control of Zero-Moment Point. Paper presented at the IEEE international conference on robotics and automation, Taipei, Taiwan, Sep. 2003
M.Vukobratovic, B. Borovac, D. Surla, D. Stokic: Biped locomotion. Springer-Verlag (1990)

27. References (2)
K. Nishiwaki, S. Kagami, Y. Kuniyoshi, M. Inaba, H. Inoue: Online generation of humanoid walking motion based on fast generation method of motion pattern that follows desired ZMP. Paper presented at the IEEE/RSJ international conference on intelligent robots and systems, Lausanne, Switzerland, 30 Sep. 5 Oct. 2002
J. Mrozowski, J. Awrejcewicz, P. Bamberski: Analysis of stability of the human gait, Journal of Theoretical and Applied Mechanics, vol. 45, no. 1, pp , 2007
L. Yang, C. Chew, T. Zielinska, A. Poo:A uniform biped gait generator with offline optimization and online adjustable parameters, Robotica (2007) volume 25, pp , March 19, 2007
JSwarm, Last Access Oct
N. Shafii, S. Aslani, S.Mohammad, H.S.Javadi,V. Azizi, O. M. Nezami: Robust Humanoid walking using Truncated Fourier Series gait generator,Iran Open Symposium, April. 2009
N. Shafii, L.P. Reis, N. Lau: Biped Walking using Coronal and Sagittal Movements based on Truncated Fourier Series, RoboCup-2010: Robot Soccer World Cup XIII, Springer LNAI / LNCS, Vol. 6556, pp , Berlin, 2011.