冗余 SGCMG 系统非奇异逆运动学闭环求解

Nonsingular Closed-Loop Inverse Kinematics Schemesfor Redundant SGCMG Systems

为进一步简化单框架控制力矩陀螺（ＳＧＣＭＧ）系统逆运动学的求解，在借鉴国内外相关研究的基础上，将冗余机械臂逆运动学闭环求解方法引入到ＳＧＣＭＧ系统中来，并在闭环求解过程中，施加非奇异条件，即得到冗余ＳＧＣＭＧ系统非奇异逆运动学闭环解。这种方法不但可以得到逆运动学的非奇异解，且可通过选择适当的增益阵，控制算法的收敛速度。而且由于此种方法不用计算Ｊａｃｏｂｉ矩阵的伪逆，而是代之以Ｊａｃｏｂｉ阵的转置，大大简化了计算量，适于实时实现。对金字塔构形的４－ＳＧＣＭＧ系统的仿真结果表明，上述算法是可行的。

In order to simplify the solution to the inverse kinematics for redundant SGCMG systems, A nonsingular closed-loop solution is derived from the corresponding method used in redundant manipulators with nonsingular constraint. This method not only can achieve the nonsingular solution to the inverse kinematics, but also can control the convergent speed of the algorithm through the proper choice of the gain matrix. Furthermore, this method greatly reduces the calculation burden and can be realized in real-time because it uses the transpose instead of the pseudo-inverse of the Jacobian matrix. Simulation results of the pyramid-type 4-SGCMG system indicate that the algorithm above is feasible.