**5. Conclusion**

In this chapter, we first introduced the Matsuoka and Van der Pol Oscillators. Then we presented our proposed oscillator, which was inspired by the solution of the Van der Pol that leads to stable limit cycle. The oscillator was designed using linear piecewise linear functions and the design parameters were obtained based on the equation of motion of inverted pendulum. Moreover, sensory feedback namely gyro and force sensors feedbacks were considered by adding neural controller to the oscillator's neural network. Therefore, the neural network was augmented by neural controllers with sensory connections to maintain the stability of the system. In addition, the rolling profile parameters were analytically obtained and the approximate solution was implemented giving much modularity to the motion pattern generator to include cuircuts of reflexes and task planning. The locomotion controller became so adaptive that the robot is enabled to walk on floor, carpet, and slope. In order to demonstrate the effectiveness of the proposed system, we conducted experiment using Fujitsu's humanoid robot HOAP-3. It was shown that the proposed pattern generator is robust in the presence of disturbance.

### **6. Acknowledgements**

The experimental work was conducted at Fujitsu Laboratories Limited, Japan.

### **7. References**

58 The Future of Humanoid Robots – Research and Applications

plant perturbations and disturbances, we conducted two experiments; one consists of making the robot walks on hard floor, which can be regarded as walking in the presence of small disturbance. The phase portrait in figure 18 demonstrates that the system exhibits stable limit cycle with three periods. The second experiment consists of locomotion in the presence of larger disturbance and plant perturbation by letting the robot walks on a carpet with surface irregularities. In this case, despite the high damping coefficient of the carpet, the proposed locomotion controller could robustly maintain the stability of the system as shown in figure 19. This result also demonstrates the efficiency of the proposed approach in designing a robust locomotion controller, which is simply based on few parameters, which

are the robot mass, COG height, and the distance between hip pitching joints.

Knee

Hip (pitch)

Angular position (deg)


Fig. 18. Outputs of the joints of right leg


**5. Conclusion** 

Fig. 19. Phase portrait of the ZMP in the lateral plane (Experiment)



0

Angular velocity

1

2

3

0

20

40

Hip (roll)

Ankle

0 1 3 4 5

Time (s)

"learnBest1.dat"using 8:9


In this chapter, we first introduced the Matsuoka and Van der Pol Oscillators. Then we presented our proposed oscillator, which was inspired by the solution of the Van der Pol

Position

2


**Part 2** 

**Grasping and Multi-Fingered Robot Hand** 

