The inverse kinematics of robotic manipulators consists of finding a joint configuration to reach a desired end-effector pose. Since inverse kinematics is a complex non-linear problem with redundant solutions, sophisticated optimization techniques are often required to solve this problem; a possible solution can be found in metaheuristic algorithms. In this work, a modified version of the firefly algorithm for multimodal optimization is proposed to solve the inverse kinematics. This modified version can provide multiple joint configurations leading to the same end-effector pose, improving the classic firefly algorithm performance. Moreover, the proposed approach avoids singularities because it does not require any Jacobian matrix inversion, which is the main problem of conventional approaches. The proposed approach can be implemented in robotic manipulators composed of revolute or prismatic joints of n degrees of freedom considering joint limits constrains. Simulations with different robotic manipulators show the accuracy and robustness of the proposed approach. Additionally, non-parametric statistical tests are included to show that the proposed method has a statistically significant improvement over other multimodal optimization algorithms. Finally, real-time experiments on five degrees of freedom robotic manipulator illustrate the applicability of this approach.

中文翻译：

---

机械臂逆运动学求解的改进萤火虫算法

机器人操纵器的逆向运动学包括寻找关节配置以达到所需的末端执行器姿势。由于逆运动学是一个具有冗余解的复杂非线性问题，因此通常需要复杂的优化技术来解决这个问题；可以在元启发式算法中找到可能的解决方案。在这项工作中，提出了一种用于多模态优化的萤火虫算法的修改版本来解决逆运动学问题。这个修改后的版本可以提供多个关节配置，导致相同的末端执行器姿势，提高了经典萤火虫算法的性能。此外，所提出的方法避免了奇异性，因为它不需要任何雅可比矩阵求逆，这是传统方法的主要问题。考虑到关节限制约束，所提出的方法可以在由 n 个自由度的旋转关节或棱柱关节组成的机器人操纵器中实现。使用不同机器人操纵器的模拟显示了所提出方法的准确性和鲁棒性。此外，还包括非参数统计测试，以表明所提出的方法与其他多模态优化算法相比具有统计学上的显着改进。最后，五自由度机器人机械手的实时实验说明了这种方法的适用性。包括非参数统计测试以表明所提出的方法比其他多模态优化算法具有统计上的显着改进。最后，五自由度机器人机械手的实时实验说明了这种方法的适用性。包括非参数统计测试以表明所提出的方法比其他多模态优化算法具有统计上的显着改进。最后，五自由度机器人机械手的实时实验说明了这种方法的适用性。