1Introduction To date,in model-based gait-planning methods,the dynamics of the center of mass(COM)of bipedal robots have been analyzed by establishing their linear inverted pendulum model(LIPM)or extended forms(Owaki ...1Introduction To date,in model-based gait-planning methods,the dynamics of the center of mass(COM)of bipedal robots have been analyzed by establishing their linear inverted pendulum model(LIPM)or extended forms(Owaki et al.,2010;Englsberger et al.,2015;Xie et al.,2020).With regard to model-based gait-generation methods for uphill and downhill terrain,Kuo(2007)simulated human gait using an inverted pendulum,which provided a circular trajectory for the COM rather than a horizontal trajectory.He found that a horizontal COM trajectory consumed more muscle energy.Massah et al.(2012)utilized a 3D LIPM and the concept of zero moment point(ZMP).They developed a trajectory planner using the semi-elliptical motion equations of an NAO humanoid robot and simulated walking on various sloped terrains using the Webots platform.展开更多
Gait planning based on linear inverted pendulum (LIPM) on structured road surface can be quickly generated because of the simple model and definite physical meaning. However, over-simplifi- cation of the model and dis...Gait planning based on linear inverted pendulum (LIPM) on structured road surface can be quickly generated because of the simple model and definite physical meaning. However, over-simplifi- cation of the model and discontents of zero velocity and acceleration boundary conditions when robot starts and stops walking lead to obvious difference between the model and the real robot. In this paper, parameterized gait is planned and trajectories’ smoothness of each joint angle and centroid are ensured using the 3-D LIPM theory. Static walking method is used to satisfy zero velocity and acceleration boundary conditions. Besides, a multi-link model is built to validate the stability. Simulation experiments show that: despite of some deviation from the theoretical solution, the actual zero-moment point (ZMP) is still within the support polygon, and the robot walks steadily. In consequence, the rationality and validity of model simplification of LIPM is demonstrated.展开更多
为了提高双足机器人步行运动的稳定性,将双腿支撑阶段的机器人简化为一个虚拟的线性倒立摆模型。该模型以机器人运动的ZMP(zero moment point)为虚拟支点,以机器人质心为模型的质点;在运动中保持质点高度不变。通过预先设定ZMP的轨迹,...为了提高双足机器人步行运动的稳定性,将双腿支撑阶段的机器人简化为一个虚拟的线性倒立摆模型。该模型以机器人运动的ZMP(zero moment point)为虚拟支点,以机器人质心为模型的质点;在运动中保持质点高度不变。通过预先设定ZMP的轨迹,即可获得机器人质心在双腿支撑阶段的运动轨迹。将该模型与机器人单腿支撑阶段的普通线性倒立摆模型综合运用,就能保证步行时机器人质心速度变化的连续性和步行运动的稳定性。该方法在实际机器人上进行了实验验证,结果表明该方法能够很好地适用于实际机器人的步行运动。展开更多
基金supported by the National Natural Science Foundation of China(No.12332023)the Zhejiang Provincial Natural Science Foundation of China(No.LY23E050010).
文摘1Introduction To date,in model-based gait-planning methods,the dynamics of the center of mass(COM)of bipedal robots have been analyzed by establishing their linear inverted pendulum model(LIPM)or extended forms(Owaki et al.,2010;Englsberger et al.,2015;Xie et al.,2020).With regard to model-based gait-generation methods for uphill and downhill terrain,Kuo(2007)simulated human gait using an inverted pendulum,which provided a circular trajectory for the COM rather than a horizontal trajectory.He found that a horizontal COM trajectory consumed more muscle energy.Massah et al.(2012)utilized a 3D LIPM and the concept of zero moment point(ZMP).They developed a trajectory planner using the semi-elliptical motion equations of an NAO humanoid robot and simulated walking on various sloped terrains using the Webots platform.
文摘Gait planning based on linear inverted pendulum (LIPM) on structured road surface can be quickly generated because of the simple model and definite physical meaning. However, over-simplifi- cation of the model and discontents of zero velocity and acceleration boundary conditions when robot starts and stops walking lead to obvious difference between the model and the real robot. In this paper, parameterized gait is planned and trajectories’ smoothness of each joint angle and centroid are ensured using the 3-D LIPM theory. Static walking method is used to satisfy zero velocity and acceleration boundary conditions. Besides, a multi-link model is built to validate the stability. Simulation experiments show that: despite of some deviation from the theoretical solution, the actual zero-moment point (ZMP) is still within the support polygon, and the robot walks steadily. In consequence, the rationality and validity of model simplification of LIPM is demonstrated.
文摘为了提高双足机器人步行运动的稳定性,将双腿支撑阶段的机器人简化为一个虚拟的线性倒立摆模型。该模型以机器人运动的ZMP(zero moment point)为虚拟支点,以机器人质心为模型的质点;在运动中保持质点高度不变。通过预先设定ZMP的轨迹,即可获得机器人质心在双腿支撑阶段的运动轨迹。将该模型与机器人单腿支撑阶段的普通线性倒立摆模型综合运用,就能保证步行时机器人质心速度变化的连续性和步行运动的稳定性。该方法在实际机器人上进行了实验验证,结果表明该方法能够很好地适用于实际机器人的步行运动。
