In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

中文翻译：

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基于几何代数的带偏置腕6R机器人机械手逆运动学求解。

在本文中，我们提出了一种基于几何代数的有效方法，用于计算具有偏置手腕的 6R 机器人机械手的逆运动学问题 (IKP) 的解决方案。由于这些机器人机械手的运动学方程复杂、高度非线性、耦合多解时求解逆运动学问题存在一定的困难，因此我们将几何代数理论应用到机械臂的运动学建模中。 6R 机器人机械手简单地生成闭合形式的运动学方程，将问题重新表述为具有符号消除技术的广义特征值问题，然后产生 16 个解。最后是符合机器人机械手类型的喷漆机器人，被用作该方法的有效性和实时性的实现示例。实验结果表明，该方法在几何直观性、计算性和实时性上比经典方法有很大的优势，可以直接扩展到所有串行机器人机械手，完全自动化，为分析应用提供了一种新的工具。通用机器人机械手。