柔性机器人系统碰撞动力学建模

MODELING OF IMPACT DYNAMICS OF FLEXIBLE ROBOTS

讨论柔性机器人与其工作环境发生碰撞时的动力学建模问题。以空间链式柔性机器人为研究系统,该机器人由n杆n铰构成,柔性杆的变形用假设模态法表示。引入冲量势,运用拉格朗日方程推导出柔性机器人系统受外冲击的广义冲量-动量方程。结合碰撞恢复系数方程,进一步推导出两个柔性机器人系统发生碰撞的动力学方程。该方程中碰撞冲量和广义速度增量是解耦的,且适合于计算机程式求解。求解方程能得到因碰撞而产生的系统广义速度突变量和在碰撞点处的碰撞冲量。给出柔性机器人与其工作环境发生碰撞的算例,验证了所提出方法的有效性。

The dynamic modeling of flexible robots colliding with its working environments is discussed. The system considered is an n-axis serial flexible-link manipulator connected by n joints. The flexibility of each flexible link is described by using the approach of assumed modes. The concept of impulse potential energy is introduced, and the generalized impulse-momentum equations which describe the dynamic responses of the flexible robots with external impacts are developed by employing Lagrange equations. The dynamic responses of the two flexible robots colliding with each other are obtained by combining the generalized impulse-momentum equations and the equations involving coefficient of restitution. The resuiting equations are not coupled between the increment of generalized velocities and the impulses, and they are ready for computer programming. The jump discontinuities in system generalized velocities and the impulses at the impact points can be explicitly obtained by solving this mathematic model. In order to validate the method presented, the dynamic simulation of a robot involving impact with its environments is given as an example, which demonstrates the availability of the method.