Forward Kinematics Solution of Stewart Platform based on Improved Non-dominated Sorting Genetic Algorithm

Qiguo Hu; Yanli Luo; Yuqian Wang

doi:10.16578/j.issn.1004.2539.2019.03.009

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Forward Kinematics Solution of Stewart Platform based on Improved Non-dominated Sorting Genetic Algorithm

Design· Calculation | 更新时间：2022-10-03

- Forward Kinematics Solution of Stewart Platform based on Improved Non-dominated Sorting Genetic Algorithm
- Journal of Mechanical Transmission Vol. 43, Issue 3, Pages: 48-53(2019)
- 作者机构：
  
  1.重庆交通大学机电与车辆工程学院，重庆 400074
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2019.03.009
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胡启国,骆艳丽,王宇谦.基于多目标遗传算法的Stewart平台运动学正解解算[J].机械传动,2019,43(03):48-53.

Hu Qiguo,Luo Yanli,Wang Yuqian.Forward Kinematics Solution of Stewart Platform based on Improved Non-dominated Sorting Genetic Algorithm[J].Journal of Mechanical Transmission,2019,43(03):48-53.
胡启国,骆艳丽,王宇谦.基于多目标遗传算法的Stewart平台运动学正解解算[J].机械传动,2019,43(03):48-53. DOI： 10.16578/j.issn.1004.2539.2019.03.009.

Hu Qiguo,Luo Yanli,Wang Yuqian.Forward Kinematics Solution of Stewart Platform based on Improved Non-dominated Sorting Genetic Algorithm[J].Journal of Mechanical Transmission,2019,43(03):48-53. DOI： 10.16578/j.issn.1004.2539.2019.03.009.

摘要

Stewart平台的运动学解算是指对驱动杆杆长与动平台位姿的对应关系的求解。其运动学逆解只需根据空间坐标变换求得，而运动学正解需要对12个非线性方程进行解算。普通的数值解算方法迭代步数多，求解精度低。为解决Stewart平台运动学正解的解算问题，将pareto最优化理论引入遗传算法，提出一种基于多目标遗传算法（NSGA-II）和最小二乘理论结合的算法。利用算法生成上平台姿态，利用反解解算出姿态对应的杆长，与已知杆长进行最小二乘拟合分析，当拟合度极高时认为此时的位姿即为运动学正解结果。此算法将上平台姿态的6个参数求解转化成多目标最优化问题，其只需迭代102次左右便能输出最优解，单次结果输出用时在1 min以内，且求解的均方根值误差不超过0.1。是一种求解速度快、精度高的可行的运动学正解解算方法。

Abstract

The kinematics solution of Stewart platform is to figure out the relationship between actuator length and posture of moving platform. The inverse kinematics can be easily derivated by space coordinate transformation. Due to the highly multivariate nonlinear function， the forward kinematics solution method is hard to be both fast and accurate. To figure out a solving method， the Improved Non-dominated Sorting Genetic Algorithm （NSGA-II） combined with Least Square（LS） method algorithm is implemented. The moving platform posture is randomly generated by algorithm and the corresponding length solution is solved by inverse kinematics. While the corresponding length solution fits the known length solution best， the best forward kinematics solution is appeared. According to the example calculating， this algorithm can export the best forward solution within 102 iterations， the output time of a single result is less than 1 min. The RMSE value is lower than 0.1 during 10 times solve. In conclusion， the NSGA-II with LS algorithm is fast and of high accuracy while using on forward solution of parallel platform.

关键词

Stewart平台运动学正解多目标遗传算法最小二乘理论

Keywords

Stewart platformForward kinematics solutionImproved non-dominated sorting genetic algorithmLeast square theory

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