四足机器人腿部并联机构末端位置误差分析与验证

Analysis and verification of terminal position error of leg parallel mechanism of quadruped robot

为合理确定应用于四足机器人腿部机构的2自由度平面并联机构零件制造公差范围,该文进行了并联机构末端位置误差灵敏度分析与工作空间内的位置精度预估,建立2自由度平面并联机构位置方程;采用全微分理论建立2自由度平面并联机构的误差模型,得到各误差源相对于末端位置误差的映射关系;建立机构位置误差灵敏度模型与评价指标,借助灵敏度评价指标揭示出统计意义下各几何误差源对末端位置精度的影响程度;依据3?原则与灵敏度评价指标,确定了各误差源的零件制造公差;采用三坐标测量仪对试验样机制造误差值进行测量,依据误差模型对末端位置精度在工作空间内的分布进行预估及实例验证。结果表明:实际位置精度值与理论位置精度预估值最大误差绝对值为0.0038 mm,最小误差绝对值为0.001 5 mm,各误差值均较小,验证了误差传递模型、位置精度预估的正确性及该方法确定构件制造公差的有效性。研究结果可为四足机器人腿部机构的运动学标定、误差补偿及执行精确任务时的轨迹规划提供理论依据。

In order to reasonably determine the manufacturing tolerance range of 2-DOF planar parallel mechanism parts on quadruped robot,the error sensitivity analysis of the leg parallel mechanism and the position precision estimation in the working space were proposed in this paper.The leg mechanism of the quadruped robot analyzed in the paper was composed of a 2-DOF planar parallel mechanism and a RPR mechanism in series.The planar parallel mechanism realized the forward direction of leg lifting and stepping,and the RPR mechanism realized the lateral pendulum movement of leg mechanism,and the coordinate movement of the 2 mechanisms realized the spatial movement of leg mechanism.The advantage of the leg structure was that the planar parallel mechanism could enlarge the stroke of the end position to achieve rapid leg lifting and stride,and the RPR mechanism could achieve lateral swing decoupling motion.In the manufacturing process of the leg mechanism,due to the relatively simple structure of RPR mechanism and the coupling and complexity of parallel mechanism,the manufacturing of 2-DOF planar parallel mechanism was emphatically analyzed.Firstly,the composition of the leg mechanism was introduced,the position equation of 2-DOF planar parallel mechanism was established,an error model of 2-DOF planar parallel mechanism was established by using the full differential theory,the mapping relation of each error source to the end position error was obtained.Secondly,the position error sensitivity model and evaluation index of the mechanism were established.The histogram of each geometric error source on the end position precision under the significance of generalization was drawn according the sensitivity evaluation index,and the influence degree of each error source on the end position precision was revealed.The result showed that the angle error sources had a great influence on the position precision of leg mechanism,the angle error between the rod BC and the X axis was the most sensitive,other angle errors were more sensitive,while the influence of other manufacturing error sources was relatively small.Then,according to the 3 principle and sensitivity evaluation index,the allowable manufacturing tolerances of the parts of each error source were determined.Finally,according to the allowable manufacturing tolerance range,the actual parts were designed and processed.The manufacturing error values of each part were measured by using the three coordinate measuring instrument,and the actual manufacturing errors of each part were obtained.According to the error transfer model and the sensitivity evaluation index,the distribution of the end position precise in the workspace was estimated.At the same time,the representative 6 pose points in the working space of the experimental prototype were measured with the three coordinate measuring instrument,and the end precision estimation was verified by some examples.The result of precision estimation showed that the error value of the lower part of the working space was within the range of 0.18-0.3 mm,and the precision was higher;the error value of the upper part of the working space was within the range of 0.4-1 mm,and the precision was poor;and the precision of the upper part of the working space was worse,and the error of the left upper and top part was up to 1 mm.Therefore,when performing more precise tasks,the trajectory of the foot contacting to ground could be planned in the lower part of the workspace to improve the foot positioning precision.The experiments results showed that the maximum error absolute value between the actual position precision value and the theoretical position precision estimation was 0.003 8 mm,and the minimum error absolute value was 0.001 5 mm,which verifies the correctness of the error transfer model and the position precision estimation,and the validity of the method to determine the manufacturing tolerance of components.The results laid a foundation for the kinematics calibration,error compensation and trajectory planning of the leg mechanism of the quadruped robot.