表征被动双足行走的二维无边轮辐的动力学及稳定性分析  

Dynamics and stability analysis of 2D rimless wheel revealing passive bipedal walking

作　　者：奚如如[1] 王兴松[1] 韩亚丽[2] 

机构地区：[1]东南大学机械工程学院,南京211189 [2]南京工程学院机械工程学院,南京211167

出　　处：《东南大学学报（自然科学版）》2015年第6期1066-1074,共9页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金青年基金资助项目(51205182);江苏省普通高校研究生科研创新计划资助项目(CXZZ12_0092)

摘　　要：为验证具有被动行走特征的二维无边轮辐稳定极限环的存在,使静止于斜坡上的无边轮辐以不同的初始运动条件开始运动,对其进行运动学及动力学分析,建立表征被动双足行走理论的无边轮辐模型的无碰撞阶段运动方程及碰撞瞬间切换方程.利用庞加莱映射理论进行斜坡上滚动的无边轮辐运动稳定性分析,结果表明,不动点与极限环为轮辐运动稳定性的表征参数,且不动点与极限环的存在与轮辐的辐条数目、惯性矩参数、运动初始条件和斜坡角度有关.利用M ATLAB软件对不动点与极限环的存在进行仿真分析,验证了在一定的斜坡角度和初始运动条件下无边轮辐可实现稳定持续的下坡滚动.基于无边轮辐模型可建立斜坡上行走的无驱动被动双足行走模型,将下坡时由重力提供的驱动力等同于主动驱动力施加到平面上行走的无驱动被动双足行走模型,可以减少驱动能量损耗及简化行走控制理论.To verify the existence of the stable limit cycle of 2D rimless wheel revealing passive bi- pedal walking, different initial motion conditions are applied to the rimless wheel standing still on a slope and kinematics and dynamics analysis are achieved. Equations of motion between collisions and under collision conditions are established. The theory of Poincare map is applied to conduct the analysis of motion stability of the rimless wheel rolling on the slope. The result indicates that the fixed point and the limit cycle are characterization parameters of the motion stability, and the existence of the fixed point and the limit cycle is related to the number of spokes, the inertia moment parameter, initial motion conditions and the slope angle. The simulation based on the MATLAB is conducted to validate the existence of the fixed point and the limit cycle, and it is verified that the rimless wheel can roll down the slope stably and continuously under certain slope angles and initial motion conditions. The driven-less passive bipedal walking model rolling on the slope can be built based on the model of the rimless wheel. The rolling down power from the gravity can be taken as the active driven power, which can be applied to the driven-less passive bipedal walking model for walking on the level surface to reduce the driven energy loss and simplify the walking control theory.

关 键 词：无轮辐轮 被动双足行走 庞加莱映射 不动点 极限环 

分 类 号：TH113[机械工程—机械设计及理论]