Roboc locmotion

1. Turning Robot Locomotion Using
Truncated Fourier Series
and
Gravitational Search Algorithm
L.ZARBAN, S. JAFARIZADEH, S. JAFARI

2. Subjects:
 History
 Walk Algorithm
TFS
Turn Algorithm
 GSA Algorithm
GSA Flowchart Algorithm
How to use
 Implementation Environment
 Robot Structure
 Experimental RESULTS
 References
 Question

3. History
 Shinya Aoi and Kazuo Tsuchiya(2004) – controlled turning of a biped
locomotion robot using nonlinear oscillators.
 Nakanishi et al in 2004 and Yang et al in 2006, made use of
recorded human gaits as the reference for robot trajectory planning.
 Yang analyzed human locomotion and used TFS together with a
ZMP stability indicator to prove that; TFS can generate suitable
angular trajectories for controlling bipedal locomotion.
 Nima Shafii(2009) - Humanoid Clock-Turning Gait Synthesis based
on Fourier Series And Genetic Algorithms
 New at this work:
- Modeling
- Train Algorithm

4. Walk Algorithm
 Humanoid walk :
- Human gaits on flat-terrain recorded by VICON .
The below points can be modeled by Fourier Series

5. Truncated Fourier Series
 Truncated Fourier Series (TFS)
 An unique TFS is used for every body joints using its
Corresponding points value.
 The Fourier parameters must be changed to making a better
walk.
 We use the GSA algorithm to change and found a better
parameters for our own TFS.

6. Turn Algorithm
 As an experimental result , We found out that the turn action is
only based on the 3 joints(the hip-role, the hip-yaw and ankle)
 Every leg joints value has a phases distance with another leg. It's
shown below: (other joints is defined as a constant value)

7. GSA Algorithm
 Gravitational Search Algorithm (GSA) is a heuristic optimization
that is inspired of the law of gravity and mass interactions.
 The searcher agents are a collection of masses which interact with
each other based on the Newtonian gravity and the laws of
motion.
 In this algorithm, each agent has two characteristic, the position
which is a solution for the problem and the mass which
correspond to the performance of the solution.
 A heavy mass has a large effective attraction radius and hence a
great intensity of attraction. Therefore, agents with a higher
performance have a greater gravitational mass.
 As a result, the agents tend to move toward the best agent.

8. GSA Flowchart Algorithm
 (a) Search space identification.
 (b) Randomized initialization.
 (c) Fitness evaluation of agents.
 (d) Update G(t), best(t),
worst(t) and Mi(t) for i = 1,2,. . .,N.
 (e) Calculation of the total force
in different directions.
 (f) Calculation of acceleration
and velocity.
 (g) Updating agents’ position.
 (h) Repeat steps c to g until the
stop criteria is reached.
 (i) End.

9. How to Use
 As previous section, We know that only 2 equations has been
created by Fourier series, then every two equation has a below
parameters:
- A0 , A1, B1, A2, B2, A3, B3 (Of The Fourier Series Equation)
 Modeling: Every agent is modeled as above collection set.(For
every equation separately )
 Fitness Parameters: Constance distance from ball, Time to run
 Algorithm basic parameters:
- population size : 50
- Dimension : 11
- maximum iteration : 100

10. Implementation Environment
 The robot in this study is a simulated model of NAO
that is a real humanoid Robot with two arms, two legs
and a head.
 we have implemented and tested our new optimizing
approach on simulated NAO robot by an application
called rcssserver3D.
 The robot skeleton is shown at the figure:

11. Robot Structure

12. Experimental RESULTS
 The angular trajectories for hip-yaw-pitch and hip roll joints of left
leg is shown below. (Left leg is support in [t0,t1] and[t3,t4] and it is
turning in [t1,t2]. In [t2,t3] both of legs on floor and the time the
legs are switching.)
Hip-roll joint
Hip-yaw-pitch joint

13. Experimental RESULTS
 The robot can be turn and never falling if there is NOT external
force.
 The below data diagrams is taken from experimental environment
(Balance means usage of the Hip-Roll and Ankle-Roll joints only):

14. References
 S. Kajita, et al., Biped Walking Pattern Generation by using
Preview Control of Zero-Moment Point, In: Proceedings of the
2003 IEEE International Conference on Robotics & Automation
Taipei, Taiwan, September 2003, pp. 14-19.
 S. Kajita, F. Kanehiro, K. Kaneko, K. Yokoi, H. Hirukawa. The 3D
linear inverted pendulum mode A simple modeling for a biped
walking pattern generation, In: Proceedings of the 2001 IEEE/RSJ
International Conference on Intelligent Robots and Systems, 2001,
pp. 239–246.
 Nima Shafii, Humanoid Clock-Turning Gait Synthesis based on
Fourier Series And Genetic Algorithms , LIACC – Artificial
Intelligence and Computer Science Lab., Porto, Portugal

15. References
 C. L. Shih, W. A. Gruver, and T.T Lee, Inverse kinematics and
inverse dynamics for control of a biped walking machine, J. Robot.
Syst. Vol.10, 1993, pp. 531-555.
 N. Shafii1, L. Paulo Reis, N. Lau, Biped Walking using Coronal
and Sagittal Movements, based on Truncated Fourier Series,
Proceedings of the 5th Doctoral Symposium in Informatics
Engineering 2010
 G. Dip, V. Prahlad and P. Duc Kien, Genetic algorithm-based
optimal bipedal walking gait synthesis considering tradeoff
between stability margin and speed, Robotica, Vol. 27, 2009, pp.
355-365.
 All of the references is listed at the paper.

16. Question
 Any Question?