Turning Robot Locomotion Using Truncated Fourier

Series and

Gravitational Search AlgorithmL.ZARBAN, S. JAFARIZADEH, S. JAFARI

Subjects:

History Walk Algorithm TFS Turn Algorithm GSA Algorithm GSA Flowchart Algorithm

How to use Implementation Environment Robot Structure Experimental RESULTS References Question

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

Walk Algorithm

Humanoid walk :

- Human gaits on flat-terrain recorded by VICON .

The below points can be modeled by Fourier Series

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.

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)

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.

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.

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

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:

Robot Structure

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

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):

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

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.

Question

Any Question?