Positioning Error and Optimization of Plane Four-cable Robot Motion Platform
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摘要: 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
${10^{ - 6}}\;{\text{mm}}$ ，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^\circ $ 以上，不同的出绳点布置引起偏转角误差最大可达$4.5^\circ $ ，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。Abstract: 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. -
表 1
${}^O{A_i}$ 坐标实际值表坐标值 ${}^O{{\boldsymbol{A}}_1}$ ${}^O{{\boldsymbol{A}}_2}$ ${}^O{{\boldsymbol{A}}_3}$ ${}^O{{\boldsymbol{A}}_4}$ X/mm 590 670 −590 −940 Y/mm −670 850 430 −580 
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表 2
${}^D{{\boldsymbol{B}}_i}$ 坐标实际值表坐标值 ${}^D{{\boldsymbol{B}}_1}$ ${}^D{{\boldsymbol{B}}_2}$ ${}^D{{\boldsymbol{B}}_3}$ ${}^D{{\boldsymbol{B}}_4}$ X/mm $a/2$ $a/2$ $ - a/2$ $ - a/2$ Y/mm $ - b/2$ $b/2$ $b/2$ $ - b/2$
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表 3 正方形1坐标
${}^O{\dot {\boldsymbol{A}}_i}$ 实际值表坐标值 ${}^O{\dot {\boldsymbol{A} }_1}$ ${}^O{\dot {\boldsymbol{A} }_2}$ ${}^O{\dot {\boldsymbol{A} }_3}$ ${}^O{\dot {\boldsymbol{A} }_4}$ X/mm 504 504 −756 −756 Y/mm −739 521 521 −739
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表 4 矩形2坐标
${}^O{\ddot {\boldsymbol{A}}_i}$ 实际值表坐标值 ${}^O{\ddot {\boldsymbol{A}}_1}$ ${}^O{\ddot {\boldsymbol{A}}_2}$ ${}^O{\ddot {\boldsymbol{A}}_3}$ ${}^O{\ddot {\boldsymbol{A}}_4}$ X/mm 682 682 −933 −933 Y/mm −739 521 521 −739
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表 5 矩形3坐标
${}^O{\dddot {\boldsymbol{A}}_i}$ 实际值表坐标值 ${}^O{\dddot {\boldsymbol{A}}_1}$ ${}^O{\dddot {\boldsymbol{A}}_2}$ ${}^O{\dddot {\boldsymbol{A}}_3}$ ${}^O{\dddot {\boldsymbol{A}}_4}$ X/mm 866 866 −1118 −1118 Y/mm −739 521 521 −739
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表 6 机器人实验参数
组成部分 选用参数 控制器 Arduino MEGA2560开发板 驱动电机 飞特SM60-360M舵机 运动平台 50*50(mm)亚克力板 电源 开关电源 柔索 普通钢丝 绕线轮 特制3D打印组件 静平台 铝型材及铝合金板 其他 黑色马克笔和A3纸
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