Target Trajectory Design of Parametrically Excited Inverted Pendulum for Efficient Bipedal Walking

For stable bipedal gait generation on the level floor, efficient restoring of mechanical energy lost by heel collision at the ground is necessary. Parametric excitation principle is one of the solutions. We dealt with the robot-s total center of mass as an inverted pendulum to consider the total dynamics of the robot. Parametrically excited walking requires the use of continuous target trajectory that is close to discontinuous optimal trajectory. In this paper, we proposed the new target trajectory based on a position in the walking direction. We surveyed relations between walking performance and the parameters that form the target trajectory via numerical simulations. As a result, it was found that our target trajectory has the similar characteristics of a parametrically excited inverted pendulum.

Authors:

• Toyoyuki Honjo
• Takeshi Hayashi
• Akinori Nagano
• Zhi-Wei Luo

Keywords:

• Dynamic Bipedal Walking
• Parametric Excitation
• Target Trajectory Design.

References:

[1] T. McGeer, "Passive Dynamic Walking," Int.J. of Robotics Research,
Vol.57, No.2, pp.62-82, 1990.
[2] A. Goswami, B. Espiau and A. Keramane, "Limit cycles in a passive
compass gait biped and passivity-mimicking control laws," J. of Autonomous
Robots, Vol.4, No. 3, pp.273-286 1997.
[3] F. Asano, M. Yamakita and K. Furuta, "Virtual passive dynamic walking
and energy-based control laws," IEEE/RSJ International Conference on
Intelligent Robotics and Systems, 2000.
[4] F. Asano and Z. W. Luo, "The effect of semicircular feet on energy dissipation
by heel-strike in dynamic biped locomotion," IEEE International
Conferance on Robotics and Automation, 2007.
[5] F. Asano and Z. W. Luo, "Efficient dynamic bipedal walking using
effects of semicircular feet," Robotica, Vol 29, pp.351-365, 2011.
[6] F. Asano, Z.W. Luo and S. Hyon, "Parametric excitation mechanisms for
dynamic bipedal walking," IEEE International Conference on Robotics
and Automation, 2005.
[7] F. Asano, T. Hayashi, Z. W. Luo, S. Hirano and A. Kato, "Parametric
excitation approaches to efficient bipedal walking," IEEE/RSJ International
Conference on Intelligent Robots and Systems, 2007.
[8] F. Asano and Z. W. Luo, "Energy-efficient and high-speed dynamic
biped locomotion based on principle of parametric excitation," IEEE
Transaction on Robotics. Vol.24, No.6, pp.1289-1301, 2008.
[9] Y. Harata, F. Asano, K. Taji and Y. Uno, "Biped gait generation based on
parametric excitation by knee-joint actuation," IEEE/RSJ International
Conference on Intelligent Robots and Systems, 2007.
[10] Y. Harata, F. Asano, K. Taji and Y. Uno, "Efficient parametric excitation
walking with delayed feedback control," IEEE/RSJ International
Conference on Intelligent Robots and Systems, 2009.
[11] Y. Harata, F. Asano, Z. W. Luo, K. Taji and Y. Uno, "Biped gait
generation based on parametric excitation by knee-joint actuation,"
Robotica, Vol. 27, pp.1063-1073, 2009.
[12] T. Honjo, A.Nagano and Z. W. Luo, "Parametric excitation of a biped
robot as an inverted pendulum," IEEE/RSJ International Conference on
Intelligent Robots and Systems, 2008.
[13] Y. Banno, Y. Harata, K. Taji and Y. Uno, "Optimal trajectory design for
parametric excitation walking," IEEE/RSJ International Conference on
Intelligent Robots and Systems, 2009.
[14] Y. Harata, Y. Banno and K. Taji, "Parametric excitation based bipedal
walking: Control method and optimization," Numerical Algebra, Control
and Optimization, Vol.1, No.1, pp.171-190, 2011.