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2011, 1(1): 171-190. doi: 10.3934/naco.2011.1.171

## Parametric excitation based bipedal walking: Control method and optimization

 1 Division of Mechanical Systems and Applied Mechanics, Faculty of Engineering, Hiroshima University, Japan 2 Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University, Japan, Japan

Received  August 2010 Revised  November 2010 Published  February 2011

In parametric excitation walking, energy lost by a heel strike is restored by bending and stretching a swing leg, and then a sustainable gait is generated with only knee torque. In this paper, we first propose the method that combines the parametric excitation method for a swing leg with that for a support leg to improve gait efficiency. Next, we improve gait efficiency of the combined parametric excitation walking by the optimization method for reference trajectories. Numerical results show that the specific resistance of the combined method is reduced to about one tenth of those of the previous results. In addition, the results of multi-objective optimization method are presented by reformulating a single-objective optimization problem.
Citation: Yuji Harata, Yoshihisa Banno, Kouichi Taji. Parametric excitation based bipedal walking: Control method and optimization. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 171-190. doi: 10.3934/naco.2011.1.171
##### References:
 [1] F. Asano and Z. W. Luo, Parametrically excited dynamic bipedal walking based on up-and-down hip motion, (Japanese), 6th SICE System Integration Division Annual Conference, (2005), 907-908. [2] F. Asano and Z. W. Luo, Energy-efficient and high-speed dynamic biped locomotion based on principle of parametric excitation, IEEE Transactions on Robotics, 24 (2008), 1289-1301. doi: 10.1109/TRO.2008.2006234. [3] F. Asano, Z. W. Luo and S. Hyon, Parametric excitation mechanisms for dynamic bipedal walking, Proceedings of the IEEE International Conference on Robotics and Automation, (2005), 611-617. doi: 10.1109/ROBOT.2005.1570185. [4] F. Asano, M. Yamakita and K. Furuta, Virtual passive dynamic walking and energy-based control Laws, Proceedings of the IEEE/RSJ International Conference on Intelligent Robotics and Systems, (2000), 1149-1154. [5] C. Chevallereau and Y. Aoustin, Optimal reference trajectories for walking and running of a biped robot, Robotica, 19 (2001), 557-569. doi: 10.1017/S0263574701003307. [6] G. Gabrielli and Th. von Karman, What price speed? Specific power required for propulsion of vehicles, Mechanical Engineering, 72 (1950), 775-781. [7] A. Goswami, B. Espiau and A. Keramane, Limit cycles in a passive compass gait biped and passivity-mimicking control laws, Journal of Autonomous Robots, 4 (1997), 273-286. doi: 10.1023/A:1008844026298. [8] J. W. Grizzle, G. Abba and F. Plestan, Asymptotically stable walking for biped robots: analysis via systems with impulse effects, IEEE Transaction on Automatic Control, 46 (2001), 51-64. doi: 10.1109/9.898695. [9] Y. Harata, F. Asano, K. Taji and Y. Uno, Parametric excitation based gait generation for ornithoid walking, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (2008), 2940-2945. [10] Y. Harata, F. Asano, K. Taji and Y. Uno, Ornithoid gait generation based on parametric excitation, (Japanese), Journal of Robotics Society of Japan, 27 (2009), 575-582. [11] Y. Harata, F. Asano, K. Taji and Y. Uno, Parametric excitation walking for four-linked bipedal robot, Preprint of the 9th IFAC Symposium on Robot Control, (2009), 589-594. [12] Y. Harata, F. Asano, Z. W. Luo, K. Taji and Y. Uno, Biped gait generation based on parametric excitation by knee-joint actuation, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (2007), 2198-2203. [13] Y. Harata, F. Asano, Z. W. Luo, K. Taji and Y. Uno, Biped gait generation based on parametric excitation by knee-joint actuation, Robotica, 27 (2009), 1063-1073. doi: 10.1017/S0263574709005487. [14] T. McGeer, Passive dynamic walking, International Journal of Robotics Research, 9 (1990), 62-82. doi: 10.1177/027836499000900206. [15] K. Taji, Y. Banno and Y. Harata, An optimizing method for a reference trajectory of parametric excitation walking,, Robotica., ().  doi: 10.1017/S0263574710000342.

show all references

##### References:
 [1] F. Asano and Z. W. Luo, Parametrically excited dynamic bipedal walking based on up-and-down hip motion, (Japanese), 6th SICE System Integration Division Annual Conference, (2005), 907-908. [2] F. Asano and Z. W. Luo, Energy-efficient and high-speed dynamic biped locomotion based on principle of parametric excitation, IEEE Transactions on Robotics, 24 (2008), 1289-1301. doi: 10.1109/TRO.2008.2006234. [3] F. Asano, Z. W. Luo and S. Hyon, Parametric excitation mechanisms for dynamic bipedal walking, Proceedings of the IEEE International Conference on Robotics and Automation, (2005), 611-617. doi: 10.1109/ROBOT.2005.1570185. [4] F. Asano, M. Yamakita and K. Furuta, Virtual passive dynamic walking and energy-based control Laws, Proceedings of the IEEE/RSJ International Conference on Intelligent Robotics and Systems, (2000), 1149-1154. [5] C. Chevallereau and Y. Aoustin, Optimal reference trajectories for walking and running of a biped robot, Robotica, 19 (2001), 557-569. doi: 10.1017/S0263574701003307. [6] G. Gabrielli and Th. von Karman, What price speed? Specific power required for propulsion of vehicles, Mechanical Engineering, 72 (1950), 775-781. [7] A. Goswami, B. Espiau and A. Keramane, Limit cycles in a passive compass gait biped and passivity-mimicking control laws, Journal of Autonomous Robots, 4 (1997), 273-286. doi: 10.1023/A:1008844026298. [8] J. W. Grizzle, G. Abba and F. Plestan, Asymptotically stable walking for biped robots: analysis via systems with impulse effects, IEEE Transaction on Automatic Control, 46 (2001), 51-64. doi: 10.1109/9.898695. [9] Y. Harata, F. Asano, K. Taji and Y. Uno, Parametric excitation based gait generation for ornithoid walking, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (2008), 2940-2945. [10] Y. Harata, F. Asano, K. Taji and Y. Uno, Ornithoid gait generation based on parametric excitation, (Japanese), Journal of Robotics Society of Japan, 27 (2009), 575-582. [11] Y. Harata, F. Asano, K. Taji and Y. Uno, Parametric excitation walking for four-linked bipedal robot, Preprint of the 9th IFAC Symposium on Robot Control, (2009), 589-594. [12] Y. Harata, F. Asano, Z. W. Luo, K. Taji and Y. Uno, Biped gait generation based on parametric excitation by knee-joint actuation, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (2007), 2198-2203. [13] Y. Harata, F. Asano, Z. W. Luo, K. Taji and Y. Uno, Biped gait generation based on parametric excitation by knee-joint actuation, Robotica, 27 (2009), 1063-1073. doi: 10.1017/S0263574709005487. [14] T. McGeer, Passive dynamic walking, International Journal of Robotics Research, 9 (1990), 62-82. doi: 10.1177/027836499000900206. [15] K. Taji, Y. Banno and Y. Harata, An optimizing method for a reference trajectory of parametric excitation walking,, Robotica., ().  doi: 10.1017/S0263574710000342.
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