含不确定性参数的锚杆钻机机械臂运动学误差分析

矿用锚杆钻机广泛用于井下顶板和侧帮的打孔和支护,极大地缓解了掘锚失调的问题。为此以机械臂为研究对象,对含有不确定性区间参数的机械臂运动学进行了误差分析。由于传统微分法对机械臂运动学误差分析存在很大的局限性,故将Chebyshev扩张函数算法应用在求解含不确定性区间参数的机械臂运动学中。具体方法是采用了扫描法(SAS)、张量积(CTP)、与配点法(CCM)3种代理模型对含有不确定性参数的机械臂运动学正解矩阵进行响应区间的包络研究,3种代理模型在CPU时间消耗上均有所减少。其中配点法(CCM)的优势较为突出,与原始计算方法相比时间消耗减少了97.65%。同时也将理论值和3种区间代理模型计算出的上、下边界响应值进行了对比。结果表明配点法(CCM)、扫描法(SAS)计算出的边界值与理论值更加接近,产生较小范围的误差。最后在样机上对所提算法进行验证,紧密的包裹效果验证了本文提出算法的精度和有效性。其中扫描法(SAS)和配点法(CCM)这两种代理模型在上下边界值的求解中拥有较小的保守估计,张量积法(CTP)代理模型则在局部求解中获得较好的估计。对含有不确定性参数的响应区间研究,成为了预测机械臂空间轨迹跟踪和定位的新方法,确保机械臂的预测误差值最小。同时也为实现机械臂的最优结构的设计和高速、高精度的控制,提供一定的理论指导。

Kinematic error analysis of mine bolter manipulator with uncertain parameters

Mine bolter is widely used in drilling and supporting the roof and side wall of underground mine,which greatly alleviates the problem of heading anchoring imbalance.In this study,the manipulator is taken as the re search object,and the error analysis of the kinematics of the manipulator with uncertain interval parameters was carried out.Due to the limitation of differential method in the error analysis of manipulator kinematics,Chebyshev expansion function algorithm was used to solve this problem.In the study,the scanning method (SAS),tensor product (CTP) and collocation method (CCM) were used to analyze the envelope of the response interval of the forward kinematics solution matrix of the manipulator with uncertain parameters,and the time consumption of CPU was reduced.Among these methods,the CCM was found to be an effective method which results in a reduction of 97.65% in time consumption.Furthermore,the theoretical values were compared with the upper and lower boundary response values calculated by the three interval proxy models.It was found that the boundary values calculated by CCM and SAS are closer to the theoretical values and resulting in smaller errors.Finally,the accuracy and effectiveness of the proposed algorithm were experimentally validated by the compact package on the prototype.The testing results show that the SAS and CCM lead to the small conservative estimates in the solution of upper and lower boundary values,while the CTP leads to a better estimate in the local solution.In conclusion,the study of response interval with uncertain parameters was developed as a new method for predicting the spatial trajectory tracking and location of the manipulator to ensure that the prediction error of the manipulator is minimized.This work provides a theoretical guidance for the optimal structure design and high speed and high precision control of the manipulator.