平面四索机器人运动平台定位误差与优化

Positioning Error and Optimization of Plane Four-cable Robot Motion Platform

忽略平面柔索并联机器人的末端运动平台的姿态会造成定位误差。在考虑平台姿态的前提下,构建了机器人运动学模型并对末端平台进行静力学分析,再以各柔索张力的最小方差为优化目标,提出张力均匀化优化算法并利用罚函数、梯度法计算得到满足最优索力分布条件下的位姿,然后分析了静平台出绳点布置形状、平台形状等因素对定位精度的影响规律。MATLAB的仿真试验表明:张力均匀化优化算法定位误差小于10-6mm,张力大小满足预期要求,考虑运动平台姿态的模型可修正偏转角度6°以上,不同的出绳点布置引起偏转角误差最大可达4.5°,运动平台长度和宽度相差越大,其对姿态影响也越大。样机实验表明:优化算法具有较高的精确度和可行性,对实现柔索并联机器人运动平台高精度定位具有重要意义。

Ignoring the posture of the end motion platform of a plane flexible four-cable parallel robot may cause positioning errors.On the premise that the platform posture is considered,this paper sets up the robot’s kinematics model and carries out the static analysis of the end platform so as to optimize the minimum variance of the tension of each flexible cable.The paper proposes the tension homogenization optimization algorithm and uses the penalty function and the gradient method to calculate the posture under the condition that the optimal cable force distribution is satisfied.It then analyzes the influence of factors such as the layout shape of the rope exit points of the static platform and the platform shape on the positioning accuracy.MATLAB simulation results show that the positioning error of the tension homogenization optimization algorithm is less than 10-6 mm,and that the tension meets the expected requirements.The model that considers the posture of the motion platform can correct the deflection angle of more than 6°.The deflection angle error caused by different rope exit points can reach at most 4.5°.The greater the difference between the length and width of the motion platform,the greater its influence on the posture.Prototype experimental results show that the algorithm has high accuracy and feasibility.The research can help realize the high-precision positioning of the flexible four-cable parallel robot motion platform.