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

Abstract

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 jointpositions 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 2 links and 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 3 10 − ) seconds with a position error around (3.116 8 10 − ) 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 9 10 − .

Kinematics Analysis of 5R axis using Evolutionary Algorithms

“…The joint angles for the robotic arm for the position error and absolute error have been calculated and compared using firefly algorithm and ABC algorithm. Firefly uses the principle of absorption and attraction of the fireflies [16], [17], [30].…”

“…The firefly parameters used are γ, α, β 0 , and δ known as light absorption coefficient, mutation coefficient, attraction coefficient base value, and uniform mutation range respectively. α_damp is the mutation coefficient damping ratio [16], [17], [29]. The values of these parameters can be assumed using different combinations of values at different iterations.…”

“…In the 6-DOF robotic arm, location and orientation of the end-effector were determined respectively, with the help of the first three joints and the last three joints, which are convenient to control and teaching [7], [8]. Soft computing techniques have been used by researchers are MATLAB, fuzzy logic, adaptive neuro-fuzzy inference system (ANFIS), genetic algorithm (GA) [6], [9], [11], [17], differential evolution, ant colony, swarm, and evolutionary algorithms (EA) [5], [6], [16], [18], [24], [30] etc. to optimized results.…”

Simulation based calculation of the inverse kinematics solution of 7-DOF robot manipulator using artificial bee colony algorithm

“…In addition, they have used a two-jointed robotic arm for simulation test [19]. Rokbani et al prefer to use the firefly intelligent method which is a new heuristic algorithm based on swarm, in their work and tested the proposed method in a three-jointed robot arm [20]. Koker has proposed a hybrid method which was used with the neural network and genetic algorithm to solve the inverse kinematics solution of a six-joint robotic manipulator to minimize the error of the end effector [21].…”

A Comprehensive Research on The Use Of Swarm Algorithms in The Inverse Kinematics Solution

“…The results of the study were obtained in terms of position error and solution time. [15]. Durmus and his friends have solved this problem using both particle swarm optimization and harmony search algorithm algorithms and have compared their results and they carried out the tests using six jointed puma type robots.…”