两个单侧接触平面刚体稳定性理论的实验验证
Experimental Verification of Stability Theory for a Planar Rigid Body with Two Unilateral Frictional Contacts
摘要：
具有多个单侧摩擦接触的机械系统中的平衡状态的稳定性是重要的实际要求，与机器人应用高度相关。在我们以前的工作中，我们从理论上分析了两点摩擦接触的平面刚体极小模型的有限时间李雅普诺夫稳定性。在假定非弹性碰撞和库仑摩擦的条件下，导出了平衡位形的稳定性和不稳定性条件。在这项工作中，我们首次提出了这种稳定性理论的实验演示，使用一个可变结构的刚性的“”与摩擦脚垫上的斜面。通过改变粒子的质心位置，我们得到了不同的平衡态，这些平衡态对小扰动的反应是发散或收敛，与稳定性理论的预测非常一致。使用高速录像电影，实验和数值模拟之间获得了良好的定量协议，刚体模型和非弹性碰撞假设的局限性也进行了研究。结果证明了我们的稳定性理论的实用性和实用价值。
英文摘要：
Stability of equilibrium states in mechanical systems with multiple unilateral frictional contacts is an important practical requirement, with high relevance for robotic applications. In our previous work, we theoretically analyzed finite-time Lyapunov stability for a minimal model of planar rigid body with two frictional point contacts. Assuming inelastic impacts and Coulomb friction, conditions for stability and instability of an equilibrium configuration have been derived. In this work, we present for the first time an experimental demonstration of this stability theory, using a variable-structure rigid ''biped'' with frictional footpads on an inclined plane. By changing the biped's center-of-mass location, we attain different equilibrium states, which respond to small perturbations by divergence or convergence, showing remarkable agreement with the predictions of the stability theory. Using high-speed recording of video movies, good quantitative agreement between experiments and numerical simulations is obtained, and limitations of the rigid-body model and inelastic impact assumptions are also studied. The results prove the utility and practical value of our stability theory.
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