闭环实时反馈控制依据运动学正解，但是运动学正解问题一直没有彻底解决。6-UPS并联机构（6-UPS）的运动学解析正解可通过消除变量，获得一元高次多项式方程，也有通过添加至少2个附加位移传感器方法求解，虽然随着研究的深入有所进展，但是仍然不足以应用于实时的闭环反馈控制。为了高性能的闭环实时反馈控制，提出一种6-UPS运动学正解的解析算法：在平面平台型6-UPS中心添加一个位移传感器，通过测出第7个杆长，基于四元数并采用新符号表示动平台的姿态矩阵，结合代数消元等方法对11个相容方程进行降次、降次、升次处理，最终求出面向闭环实时反馈控制所需要的6-UPS机构解析正解，解决了奇异性局限，且位置和姿态可获得唯一解，解决了多解选择的难题。通过数值算例验证了所提算法的正确性和有效性。
刘艳梨
,
程世利
,
蒋素荣
,
杨小龙
,
李耀
,
吴洪涛
. 带位移传感器的6-UPS并联机构运动学正解[J]. 机械工程学报, 2018
, 54(5)
: 1
-7
.
DOI: 10.3901/JME.2018.05.001
The closed-loop real-time feedback control requires the forward kinematics analysis, which has not been solved completely in the field of parallel robots. A system of high degree univariate polynomial equations of the analytical forward kinematics analysis of 6-UPS parallel manipulators (6-UPS) can be obtained by eliminating variables. Also they can be analyzed by adding at least 2 extra displacement sensors. Although with this progress, it is still not capable to be applied to the real-time closed-loop feedback control. In order to achieve the closed-loop feedback control with high performance, a new analytical algorithm is proposed. In the new algorithm, only one displacement sensor is installed in the center of 6-UPS to obtain the seventh rod length, the elements of rotation matrix based on quaternions are replaced by new symbols, and the 11 compatible equations can be solved by reducing the degree twice and then raising the degree of the equations' variables combining with algebraic elimination methods. The analytical forward kinematics solutions of 6-UPS, which is needed by the closed-loop real-time feedback control system, are obtained in the end. Taking advantages of the proposed method, the singularity problem is solved and the multi-solution problem is also solved because unique position and orientation can be obtained. Finally, one numerical example is presented and the result is verified. Results indicate that the proposed forward kinematics algorithm is both correct and effective.
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