付根平, 陈建平, 杨宜民. 基于双臂摆动的仿人机器人偏摆力矩矫正方法[J]. 机器人, 2012, 34(4): 498-504..
FU Genping, CHEN Jianping, YANG Yimin. A Yaw Moment Counteracting Method for Humanoid Robot Based on Arms Swinging. ROBOT, 2012, 34(4): 498-504..
In view of the problems of unstable walking and even falling down caused by the yaw moment around zero moment point (ZMP) when the humanoid robot walks, a method for counteracting the yaw moment based on arms swinging is proposed. The cause of the yaw moment and its effect on the robot walking stability are analyzed. According to the link model of humanoid robot and the single pendulum model of arm swinging, the expression of moment generated by arms swinging is deduced, and the principle of counteracting yaw moment with the arms swinging moment is formulated by using the illustration of arms swinging. With the adoption of cubic spline interpolation, the parametric angle trajectories of arms swinging are planned. Through the exhaustive search algorithm, the angle parameters are traversed to guarantee the yaw moment to be mostly counteracted by the arms swinging moment. The simulation result verifies that the method can not only counteract the yaw moment greatly to ensure walking stability of the humanoid robot, but also guarantee the monotonicity, the smoothness and the periodicity of the angle trajectories of arms swinging.
 Vukobratovic M, Borovac B. Zero-moment point -- Thirty five years of its life[J]. International Journal of Humanoid Robotics, 2004, 1(1): 157-173.
 Kim J Y, Park I W, Oh J Y. Walking control algorithm of biped humanoid robot on uneven and inclined floor[J]. Journal of Intelligent and Robotic Systems, 2007, 48(4): 457-484.
 Chestnutt J, Lau M, Cheung G, et al. Footstep planning for the Honda ASIMO humanoid[C]//IEEE International Conference on Robotics and Automation. Piscataway, NJ, USA: IEEE, 2005: 629-634.
 Akachi K, Kaneko K, Kanehira N, et al. Development of humanoid robot HRP-3P[C]//IEEE/RAS International Conference on Humanoid Robots. Piscataway, NJ, USA: IEEE, 2005: 50-55.
 Smolar P, Tuhársky J, Fedor Z, et al. Development of cognitive capabilities for robot Nao in Center for Intelligent Technologies in Kosice[C]//2nd International Conference on Cognitive Infocommunications. Piscataway, NJ, USA: IEEE, 2011: 1-5.
 Kim S, Kim C H, You B, et al. Stable whole-body motion generation for humanoid robots to imitate human motions[C]// IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, NJ, USA: IEEE, 2009: 2518-2524.
 梶田秀司.仿人机器人[M].北京:清华大学出版社,2007. Kajita S. Humanoid robots[M]. Beijing: Tsinghua University Press, 2007.
 Xing D P, Su J B. Arm/trunk motion generation for humanoid robot[J]. Science in China, Series F: Information Sciences, 2010, 53(8): 1603-1612.
 蔚伟,包钢,王祖温,等.基于腰关节力矩补偿的仿人机器人快速步行模式生成[J].机器人,2010,32(2):219-225. Yu W, Bao G, Wang Z W, et al. Fast walking pattern generation for humanoid robot using waist joint moment compensation[J]. Robot, 2010, 32(2): 219-225.
 Hirabayashi T, Ugurlu B, Kawamura A, et al. Yaw moment compensation of biped fast walking using 3D inverted pendulum[C]//International Workshop on Advanced Motion Control. Piscataway, NJ, USA: IEEE, 2008: 296-300.
 Hanamiya D, Kawamura A. 3D fast walking simulation of biped robot by yaw axis moment compensation[C]//IEEE International Workshop on Advanced Motion Control. Piscataway, NJ, USA: IEEE, 2004: 403-407.
 Peterka R J. Comparison of human and humanoid robot control of upright stance[J]. Journal of Physiology -- Paris, 2009, 103(3-5): 149-158.
 Shafii N, Khorsandian A, Abdolmaleki A, et al. An optimized gait generator based on Fourier series towards fast and robust biped locomotion involving arms swing[C]//IEEE International Conference on Automation and Logistics. Piscataway, NJ, USA: IEEE, 2009: 2018-2023.
 Aoustin Y, Formal'skii A M. On optimal swinging of the biped arms[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, NJ, USA: IEEE, 2008: 2922-2927.
 Huang Q, Yokoi K, Kajita S, et al. Planning walking patterns for a biped robot[J]. IEEE Transactions on Robotics and Automation, 2001, 17(3): 280-289.
 付根平,杨宜民,黄春林.基于粒子群优化算法的双足机器人步态优化[J].华中科技大学学报:自然科学版,2011, 39(S2): 355-358. Fu G P, Yang Y M, Huang C L. Walking pattern optimization based on particle swarm optimization for biped robot[J]. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2011, 39(S2): 355-358.