柔性腿无缘轮黏滞-滑动过程的被动动态行走运动特性分析

Analysis of the Kinematic Characteristics of the Passive Dynamic Walking Stick-Slip Process of the Flexible Leg Rimless Wheel

为了分析存在摩擦力情况下柔性腿无缘轮的运动步态,分析了柔性腿无缘轮黏滞与滑动两种运动状态相互转换的条件,通过拉格朗日第一类方程建立了系统的动力学模型,在建模时解除了单支撑阶段的切向约束条件,增加了摩擦力项以实现当摩擦力不足时的滑动状态建模.分析了不同摩擦因数下柔性腿无缘轮的运动步态情况,发现了最多可能产生4种运动行为.研究了不同步态对于系统能量的影响,并发现滑动的产生增加了系统在单支撑阶段的动能.利用Newton-Raphson迭代法和庞加莱映射发现了4种运动行为均存在不动点并且轨迹稳定,同时发现柔性腿无缘轮具有滑动的步态有着良好的鲁棒性.通过研究不同初始动能对系统滑动步态的影响,发现了系统动能或者角速度在一定的范围内存在一个极小的停滞区间,使得系统单支撑阶段在通过直立平衡面附近时会产生长时间的滑动,导致系统的不稳定.

In order to analyze the motion gait of the flexible leg rimless wheel,the conditions for the transition between the two motion states of viscosity and sliding of the flexible leg rimless wheel were analyzed.The dynamic model of the system was established through the first-order Lagrange equation.During modeling,the tangential constraint condition during the single-support phase was removed,and the friction term was added to achieve the modeling of sliding state when the friction force was insufficient.The motion gait of the flexible leg rimless wheel under different friction coefficients was analyzed,and it is found that up to four possible motion behaviors could occur.The influence of different gaits on the energy of the system was studied,and it is found that the occurrence of sliding increased the kinetic energy of the system during the single-support phase.Using Newton-Raphson iteration method and Poincare mapping,it is found that all four motion behaviors had fixed points and stable trajectories,and it is also found that the gait with sliding of the flexible leg rimless wheel had good robustness.By studying the influence of different initial kinetic energy on the system’s sliding gait,it is found that there is a very small stagnation interval when the kinetic energy or angular velocity of the system is within a certain range,which makes the single support stage of the system slide for a long time near the vertical equilibrium surface,resulting in instability of the system.