基于阻尼最小范数法的四轴转台逆运动学算法分析  

Inverse Kinematics Algorithm Analysis of Four-axis Turntable Based on Damping Least-norm Method

作　　者：林笑亦 刘军[1] 苏浩 钟正虎[1] LIN Xiao-yi;LIU Jun;SU Hao;ZHONG Zheng-hu(Beijing Instituteof Aerospace Control Devices,Beijing 100039)

机构地区：[1]北京航天控制仪器研究所,北京100039

出　　处：《导航与控制》2022年第2期56-66,共11页Navigation and Control

摘　　要：由于三轴转台在仿真过程中会产生运动学奇异,因此无法模拟大角度全姿态的飞行运动。四轴转台通过在三轴转台的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。针对四轴转台中冗余自由度的逆运动学求解,采用加权最小范数法构建了等式的约束优化条件,并通过引入阻尼因子增强了求解的鲁棒性。最后,为了降低由消除闭环迭代引起的误差,在算法中进一步引入了二次计算,从而最大程度地提高了框架角解算的准确性。通过仿真分析,所提出的方法可以进行四轴转台的框架角解算且角度变化平稳,满足仿真周期为1ms的测试需求,理论解算精度可以达到10量级。Due to the kinematic singularity of the three-axis turntable in the simulation process, it is impossible to simulate the large angle full attitude flight motion. By adding a redundant axis to the three-axis turntable, the singularity of the three-axis turntable can be effectively avoided by using the characteristics of redundant degrees of freedom(DOF). In order to solve the inverse kinematics of redundant DOF in four-axis turntable, equality constrained optimization condition is constructed by using the weighted least-norm method, and the damping factor is introduced to enhance the robustness of the solution. Finally, in order to reduce the error caused by eliminating the closed-loop iteration, the quadratic calculation is further introduced in the algorithm, so as to maximize the accuracy of the frame angle solution. Simulation analysis shows that the method proposed in this paper can solve the frame angle of the four-axis turntable, and the angle changes smoothly, which meets the test requirements of the simulation period of 1 ms, and the theoretical solution accuracy can reach 10magnitude.

关 键 词：四轴转台 四元数 加权最小范数 阻尼因子 冗余自由度 

分 类 号：TP273.2[自动化与计算机技术—检测技术与自动化装置]