The article presents a friction dynamic modeling method for a flexible parallel robot considering the characteristics of nonlinear friction. An approximate friction model which is proposed by Kostic et al. is applied to establish the dynamic model with Lagrange method. Parameters identification is completed by least square method, and the tracking accuracy and the stability of the robot are systematically analyzed before and after dynamic compensation at different speeds. Its position error of the robot after compensation is only 0.98 mm at low speed. The accuracy is improved 10 times than that before compensation. In addition, the peak velocity errors are 3.97 mm·s−1 and 1.49 mm·s−1 at high and low speed, respectively, which are reduced 2.5 times than that before compensation. The experimental data also indicate that velocity tracking curve has no obvious peak error compared with the common method based on Coulomb and viscous friction model. The curve is much smoother with proposed model, and the motion stability of robot at high speed has been greatly improved. The proposed method just needs the robot to collect some positions before path tracing, and the parameters identification of dynamic model can be completed quickly. The compensation effect is much more better than common method. So the proposed method can be extended to complete the dynamic identification for complex robot with more joints. It is helpful to further improve the stability and the accuracy at high speed.

中文翻译：

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柔性并联机器人非线性摩擦动力学建模与性能分析

提出一种考虑非线性摩擦特性的柔性并联机器人摩擦动力学建模方法。Kostic 等人提出的近似摩擦模型。应用拉格朗日方法建立动力学模型。采用最小二乘法完成参数辨识，系统分析了机器人在不同速度下动态补偿前后的跟踪精度和稳定性。补偿后的机器人在低速时的位置误差仅为0.98mm。精度比补偿前提高10倍。此外，高速和低速时的峰值速度误差分别为3.97 mm·s-1和1.49 mm·s-1，比补偿前降低了2.5倍。实验数据还表明，与基于库仑和粘性摩擦模型的常用方法相比，速度跟踪曲线没有明显的峰值误差。提出的模型曲线更加平滑，机器人高速运动的稳定性有了很大的提高。该方法只需要机器人在路径跟踪前采集一些位置，即可快速完成动态模型的参数辨识。补偿效果比普通方法好得多。因此，该方法可以扩展到完成具有更多关节的复杂机器人的动态识别。有助于进一步提高高速时的稳定性和精度。并且机器人在高速下的运动稳定性有了很大的提高。该方法只需要机器人在路径跟踪前采集一些位置，即可快速完成动态模型的参数辨识。补偿效果比普通方法好得多。因此，该方法可以扩展到完成具有更多关节的复杂机器人的动态识别。有助于进一步提高高速时的稳定性和精度。并且机器人在高速下的运动稳定性有了很大的提高。该方法只需要机器人在路径跟踪前采集一些位置，即可快速完成动态模型的参数辨识。补偿效果比普通方法好得多。因此，该方法可以扩展到完成具有更多关节的复杂机器人的动态识别。有助于进一步提高高速时的稳定性和精度。因此，该方法可以扩展到完成具有更多关节的复杂机器人的动态识别。有助于进一步提高高速时的稳定性和精度。因此，该方法可以扩展到完成具有更多关节的复杂机器人的动态识别。有助于进一步提高高速时的稳定性和精度。