Abstract:

In order to solve the singularity problem of Jacobian matrix in the inverse kinematics numerical solutions, an algorithm for singular handling was proposed. Based on the damped least-square method, by Jacobi singular value decomposition, the second condition number k2 was made up as a new singular index, which compensated the deficiency of condition number k representing the singularity. Experiments verified the practicability and accuracy of k2. A new self-adaptive adjustment of the damped coefficient was proposed related to k2 and strengthened the singularity robustness of inverse kinematics algorithm. Experimental and simulation results were presented to verify the validity of the proposed algorithm. The contrast results show that the algorithm is stable near singular points, and that the continuity and stableness of the joints motion are guaranteed.

Key words: inverse kinematics, damped least-square, condition number, singularity

摘要：

为了解决机器人逆运动学数值解法中的雅可比矩阵奇异性问题,提出了一种新的奇异处理算法。在阻尼最小二乘法的基础上,利用雅可比矩阵奇异值分解,构建了一个新的奇异性指标——第二条件数k2,弥补了条件数k对奇异性表示的不全面性,并通过实验验证了k2的实用性和准确性,继而基于k2提出了一种新的阻尼系数自适应调整方法,增强了逆解算法的奇异鲁棒性。实验及仿真结果验证了算法的有效性,即在奇异点附近求逆稳定,各关节运动连续平稳。

关键词: 逆运动学, 阻尼最小二乘, 条件数, 奇异性