A modified firefly algorithm for the inverse kinematics solutions of robotic manipulators

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.