非惯性系下弹性欠驱动机器人动力学建模及应用

摘要

A dynamics model of elastic underacutated robot in a non-inertial frame was established based on screws.Firstly,the acceleration mapping of robot which was in inertia frame was obtained re-ferring to the Lie bracket of two screws.The acceleration mapping in a non-inertia frame was deducted through the transformation of the rigid-body velocity and acceleration in different frames.Then the dynamics model of robot in a non-inertia frame was obtained using the rigid-body Newton-Euler equa-tion.The dynamics model is simple because of the use of the twist and wrench in the process of deriva-tion.Finally,the aerial refueling system,which was a typical application of an elastic underactuated ro-bot in a non-inertia frame,was taken as an example.The dynamics model of the system was presen-ted,and was verified by dynamics simulation software,which demonstrates the correctness and feasi-bility of the theoretical analysis.%以旋量为基本运算单元，建立了非惯性系下弹性欠驱动机器人的动力学模型。首先以两个旋量的李括弧运算为基础，得到了惯性系下机器人的加速度映射关系。利用多刚体系统的速度、加速度旋量在不同坐标系之间的变换，推导出非惯性系下机器人在惯性系中的加速度映射关系。然后利用刚体的牛顿-欧拉公式，建立了非惯性系下机器人的动力学模型。推导的过程中始终以运动旋量、力旋量为基本的运算单元，简化了动力学建模过程。最后，以空中加油系统这种典型的非惯性系下的弹性欠驱动的应用为例，建立了其在非惯性系下的动力学模型，并用动力学仿真软件进行了验证，验证了理论分析的正确性和可行性。