IK-FA, a New Heuristic Inverse Kinematics Solver Using Firefly Algorithm

In this paper, a heuristic method based on Firefly Algorithm is proposed for inverse kinematics problems in articulated robotics. The proposal is called, IK-FA. Solving inverse kinematics, IK, consists in finding a set of joint-positions allowing a specific point of the system to achieve a target position. In IK-FA, the Fireflies positions are assumed to be a possible solution for joints elementary motions. For a robotic system with a known forward kinematic model, IK-Fireflies, is used to generate iteratively a set of joint motions, then the forward kinematic model of the system is used to compute the relative Cartesian positions of a specific end-segment, and to compare it to the needed target position. This is a heuristic approach for solving inverse kinematics without computing the inverse model. IK-FA tends to minimize the distance to a target position, the fitness function could be established as the distance between the obtained forward positions and the desired one, it is subject to minimization. In this paper IK-FA is tested over a 3 links articulated planar system, the evaluation is based on statistical analysis of the convergence and the solution quality for 100 tests. The impact of key FA parameters is also investigated with a focus on the impact of the number of fireflies, the impact of the maximum iteration number and also the impact of (α, β, γ, δ) parameters. For a given set of valuable parameters, the heuristic converges to a static fitness value within a fix maximum number of iterations. IK-FA has a fair convergence time, for the tested configuration, the average was about 2.3394 × 10⁻³ seconds with a position error fitness around 3.116 × 10⁻⁸ for 100 tests. The algorithm showed also evidence of robustness over the target position, since for all conducted tests with a random target position IK-FA achieved a solution with a position error lower or equal to 5.4722 × 10⁻⁹.