基于增广乘子法的限位全姿态四轴转台框架角解算和实验研究

Frame angle solution and experimental research of full-pose four-axis turntable with pose constraints based on augmented multiplier method

关键词:  四轴转台  框架位姿限制  增广乘子法  迭代算法

Key words:  Four-axis turntable  Frame pose constraints  Augmented multiplier method  Iterative algorithm

摘要:

三轴转台在仿真过程中会产生运动学奇异，因此很难模拟大角度全姿态的飞行运动。四轴转台通过在其基础上增加一个冗余轴，利用冗余自由度的特点，可以有效规避三轴转台的奇异性。一般的四轴转台解算算法都是基于连续旋转推导的，但由于成本和结构尺寸要求，越来越多的转台进行了位姿限制。为了针对性使用带限位的四轴转台模拟大角度飞行运动，采取增广乘子法，将框架的限位作为新的不等式约束，参与优化解算以保证转台合理运行，并进行了仿真实验。实验比较了新算法和连续旋转下的计算误差，结果验证了增广乘子法的可行性，并表明其小角度解算精度优于约束优化方法，同时大角度解算精度仅比小角度的情况低1个数量级。本研究探讨了增广乘子法在限位四轴转台仿真上的可行性，在满足转台实时性要求的同时获得了很高的仿真精度，也便于后续的精度优化。

Abstract:

Due to the kinematic singularity of the three-axis turntable in the simulation process, it is difficult to simulate large angle flight motions with full attitude. The four-axis turntable effectively avoids the singularity by adding a redundant axis to the three-axis turntable, exploiting the characteristics of redundant degrees of freedom. Normally, the solution for the full-pose four-axis turntable is based on its continuous rotation. However, it is more common to use turntables with pose constraints due to cost and structural size requirements. In order to simulate the large angle flight motion using four-axis turntables with pose constraints, the augmented multiplier method is adopted, where the pose constraints of the frame are used as new inequality constraints and included in the optimization solution to ensure reasonable operation. Simulation experiments are conducted. The experimental calculation error comparison of the new algorithm and the continuous rotation-based algorithm validates the feasibility of the augmented multiplier method and shows that its small angle solution accuracy is superior to the constrained optimization method. Meanwhile, the accuracy of the large angle solution is only one order of magnitude behind that of the small angle solution. This study explores the feasibility of the augmented multiplier method in the simulation of four-axis turntables with pose constraints, achieving high simulation accuracy while meeting the real-time requirements of the turntable, and laying the foundation for subsequent accuracy optimization.