This paper presents a set of generalized iterative algorithms to find the inverse position kinematics of n-degree-of-freedom kinematic chains with revolute joints. As a first approach, an iterative algorithm is developed using the gradient descent method in Quaternion Algebra to find both the inverse position and velocity kinematics solution in redundant systems closest to their initial configuration. Additionally, a generalized extension of this approach is developed employing screw rotors and Conformal Geometric Algebra, where efficient update rules are obtained to solve the problem of inverse position kinematics. Simulation experiments using different degree-of-freedom models as well as real-time experiments using a Geomagic Touch Haptic device are carried out to demonstrate the effectiveness of the proposed methods.

本文提出了一套广义迭代算法来求解具有旋转接头的n自由度运动链的逆位置运动学。作为第一种方法，使用四元数代数中的梯度下降法开发了一种迭代算法，以在最接近其初始配置的冗余系统中找到逆位置和速度运动学解。此外，使用螺杆转子和保形几何代数开发了这种方法的广义扩展，其中获得了有效的更新规则来解决逆位置运动学问题。进行了使用不同自由度模型的仿真实验以及使用 Geomagic Touch Haptic 设备的实时实验，以证明所提出方法的有效性。