Abstract

In this paper, the phenomenon of impact-contact in a closed-loop robotic chain has been dynamically modeled. The motion of this system, which comprises rigid links and ideal joints, has two phases. In the flight phase, the system is suspended in the air and moves only under the effect of Earth’s gravity. And in the impact phase, the mentioned robotic mechanism collides with a rough surface. We first present the direct form of dynamic equations for an open chain robotic system in the suspension phase. Then by applying the constraints that originate from the closed topology of the examined kinematic chain, the differential equations of the closed-loop system are obtained for the flight phase. In the impact phase, the contact force model is employed for modeling the impact-contact phenomenon. Although this method of impact modeling is more realistic, it leads to the stiffening of motion equations. In order to solve these equations, a special computational algorithm has been developed in this paper. To achieve more realistic results, the force of friction has also been considered in the collision of system joints with the ground. The dynamic formulations of friction have been used to obtain the friction force. In these models, an additional state variable is added to system variables in order to simulate some of the existing friction phenomena. Another objective of this paper is to present a criterion for selecting the most suitable model for simulating the motion of closed-loop robotic systems in the presence of friction. In this regard, the four dynamic friction force models of Dahl, reset integrator, LuGre, and elasto-plastic have been compared with the two static models of Coulomb and Bengisu & Akay. Although the developed algorithm is able to simulate any closed-loop robotic system that comes into contact with an uneven surface, the simulation of a 5-rigid-link closed-loop mechanism in collision with a rough surface of sinusoidal profile has been presented in this paper.

摘要

在本文中，对闭环机器人链中的碰撞接触现象进行了动态建模。该系统由刚性连杆和理想关节组成，其运动有两个阶段。在飞行阶段，系统悬浮在空中，仅在地球重力的作用下移动。在撞击阶段，上述机器人机构会与粗糙的表面发生碰撞。我们首先提出了开链机器人系统在悬浮阶段的动态方程的直接形式。然后，通过应用源自所检查运动链的闭合拓扑的约束，获得飞行阶段的闭环系统的微分方程。在冲击阶段，采用接触力模型对冲击接触现象进行建模。虽然这种影响建模方法更加真实，它导致运动方程的僵化。为了求解这些方程，本文开发了一种特殊的计算算法。为了获得更真实的结果，系统关节与地面的碰撞也考虑了摩擦力。摩擦的动态公式已用于获得摩擦力。在这些模型中，系统变量中添加了一个额外的状态变量，以模拟一些现有的摩擦现象。本文的另一个目标是提出一个标准，用于选择最合适的模型来模拟存在摩擦的闭环机器人系统的运动。对此，Dahl、reset integrator、LuGre、四种动摩擦力模型 和弹塑性模型与 Coulomb 和 Bengisu & Akay 的两个静态模型进行了比较。虽然开发的算法能够模拟任何与不平坦表面接触的闭环机器人系统，但本文中提出了与正弦轮廓的粗糙表面碰撞的 5 刚性连杆闭环机构的模拟纸。