解决机械臂奇异点处逆运动学求解难题，结合解析与数值方法确保稳定性。
Analytically Informed Inverse Kinematics Solution at Singularities
- 通过解析描述奇异运动方向，构造正则初值
- 在Kuka iiwa机械臂上实现稳定求解，避免数值发散
- 适合需要高精度轨迹规划的工业机器人应用
串联机械臂在接近运动学奇异点时，逆运动学（IK）问题变得病态，导致数值求解困难。现有方法多基于速度空间下的伪逆（PI）解法，如阻尼最小二乘法（DLS），虽具鲁棒性且收敛可控，但在奇异点处，当指定某些末端执行器运动时，任何伪逆解法均可能失效。为此，本文提出一种解析引导的逆运动学（AI-IK）方法。其核心在于显式描述奇异运动的切向特性（解析部分），由此推导出使系统进入非奇异配置的扰动量，作为迭代求解的初始状态（数值部分）。在7自由度Kuka iiwa机械臂上的数值实验表明，该方法能有效克服奇异点带来的求解障碍。
原文摘要 · Abstract (English)
Near kinematic singularities of a serial manipulator, the inverse kinematics (IK) problem becomes ill-conditioned, which poses computational problems for the numerical solution. Computational methods to tackle this issue are based on various forms of a pseudoinverse (PI) solution to the velocity IK problem. The damped least squares (DLS) method provides a robust solution with controllable convergence rate. However, at singularities, it may not even be possible to solve the IK problem using any PI solution when certain end-effector motions are prescribed. To overcome this problem, an analytically informed inverse kinematics (AI-IK) method is proposed. The key step of the method is an explicit description of the tangent aspect of singular motions (the analytic part) to deduce a perturbation that yields a regular configuration. The latter serves as start configuration for the iterative solution (the numeric part). Numerical results are reported for a 7-DOF Kuka iiwa.
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