**1. Introduction**

12 Will-be-set-by-IN-TECH

40 The Future of Humanoid Robots – Research and Applications

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Standing and walking are very important activities for daily living, so that their absence or any abnormality in their performance causes difficulties in doing regular task independently. Analysis of human motion has traditionally been accomplished by subjectively through visual observations. By combining advanced measurement technology and biomechanical modeling, the human gait is today objectively quantified in what is known as Gait analysis. Gait analysis research and development is an ongoing activity. New models and methods continue to evolve. Recently, humanoid robotics becomes widely developing world-wide technology and currently represents one of the main tools not only to investigate and study human gaits but also to acquire knowledge on how to assist paraplegic walking of patient (Acosta-M´arquez and Bradley, 2000). Towards a better control of humanoid locomotion, much work can be found in the literature that has been focused on the dynamics of the robot using the Zero Moment Point (ZMP) approach (Vukobratovic and Borovac, 2004). More recently, biologically inspired control strategies such as Central Pattern Generators (CPG) have been proposed to generate autonomously adaptable rhythmic movement (Grillner, 1975, 1985; Taga, 1995; Taga *et. al*, 1991). Despite the extensive research focus in this area, suitable autonomous control system that can adapt and interact safely with the surrounding environment while delivering high robustness are yet to be discovered.

In this chapter, we deal with the design of oscillatory neural network for bipedal motion pattern generator and locomotion controller. The learning part of the system will be built based on the combination of simplified models of the system with an extensive and efficient use of sensory feedback (sensor fusion) as the main engine to stabilize and adapt the system against parameters changes. All motions including reflexes will be generated by a neural network (NN) that represents the lower layer of the system. Indeed, we believe that the NN would be the most appropriate code when dealing, to a certain limit, with the system behavior, which can be described by a set of ordinary differential equations (ODEs) (Zaier and Nagashima, 2002, 2004). The neural network will be augmented by neural controllers with sensory connections to maintain the stability of the system. Hence, the proposed learning method is expected to be much faster than the conventional ones. To validate the theoretical results, we used the humanoid robot "HOAP-3" of Fujitsu.

The structure of the chapter is as follows: the first section will present an introduction on the conventional CPG based locomotion control as well as the Van der Pol Based Oscillator;

Design of Oscillatory Neural Network for Locomotion Control of Humanoid Robots 43

Matsuoka proposed the neural oscillator shown in Figure 1 that consists of a flexor and extensor neuron (Matsuoka, 1985, 1987). Each neuron is presented by a nonlinear differential equation. Each neuron produces a periodic signal to inhabit the other neuron to control the limbs motion (i.e. extending and flexing the elbow). Compared to other models, Matsuoka model uses significantly less computational resources, has less parameters requiring tuning, and has no need for post-processing of the neural output signals (i.e., filtering of the spikes). The mathematical model of the Matsuoka neural oscillator can be expressed by equations (2- 7) and as quoted from Williamson (Williamson, 1999) and illustrated in Fig. 1 using the

(1)

(3)

(5)

(2)

(4)

max(0, ) *i i <sup>i</sup> <sup>y</sup> x x* (6)

max(0, ) *i i x x* (8)

*out* 1 2 12 *<sup>y</sup> x x y y* (7)

neuron model of equation 1 and as decribed in (Zaier and Nagashima, 2002):

1 1 *dx x inputs dt*

 <sup>1</sup> *r j* 1 1 21 2 *j dx xv x h <sup>g</sup> <sup>c</sup>*

*dv*

*dt* 

 <sup>2</sup> *r j* 2 2 12 1 *j dx x v x hg c dt*

*dv*

*dt* 

 

<sup>1</sup> *<sup>a</sup>* 1 1

<sup>2</sup> *<sup>a</sup>* 2 2

The extensor neuron 1 in Fig. 1 is governed by equations (2) and (3) and flexor neuron 2 by equations (4) and (5). The variable xi is the neuron potential or firing rate of the ith neuron, *v*<sup>i</sup> is the variable that represents the degree of adaptation or self-inhibition, c is the external tonic input with a constant rate, β specify the time constant for the adaptation, τa and τr are the adaptation and rising rates of the neuron potential, μij is the weight that represents the strength of inhibition connection between neurons, and gj is an external input which is usually the sensory feedback weighted by gain hj. Where the positive part of the input [gj ]+ is applied to one neuron and the negative part [gj]-=-min(gj,0) is applied to the other neuron. The positive part of the output of each neuron is denoted by yi=[x1 ]+ and the final output of the oscillator yout is the difference between the two neurons' outputs. However, the parameters should be adjusted correctly to suite the application the oscillator will be used

*v x*

*v x*

 

**2.1 Matsuoka based oscillator** 

where ε is the time delay of the neuron.

`

*dt* 

then the Piecewise Linear Function Based Oscillator as our proposed approach will be detailed. The fourth section will present the Experiment Results and Discussion, and finally the conclusion will highlight the possible of future developments of the method.
