Accuracy improvement of 6-UPS Stewart forward kinematics solution based on self-aggregating MFO algorithm

Abstract

In this paper, a Stewart’s positive solution optimization model is proposed, for obtaining the complex solution to a Stewart’s forward kinematics problem, considering the existence of multiple solutions. The model converts the positive kinematics problem into an optimization problem, in which the value of the objective function is used to represent the precision of Stewart’s positive solution. A self-aggregating moth–flame optimization algorithm (SMFO) is used to improve the accuracy of Stewart’s forward kinematics solution. Two features were added to the conventional MFO algorithm to obtain a more stable balance between global and local explorations. First, Gaussian distribution was used for the flame population to select suitable individuals for Levy Flight operation, increase the diversity of the population, and enhance the algorithm’s ability to jump out of a local optimum. Second, in the middle and late iterations, the positions of the flames were periodically adjusted using the light intensity-attraction characteristic (LIAC) to strengthen the connection between individual flames and enhance the local exploration ability of the algorithm. The proposed SMFO algorithm is compared with three classic meta-heuristic algorithms for eight benchmark functions. Experimental results indicate that the SMFO algorithm is significantly better than the other three algorithms in terms of solution quality and convergence rate. To verify the effectiveness of the SMFO algorithm in solving the Stewart positive kinematics optimization model, values of eight sets of conventional position and posture parameters as well as limiting position and posture parameters were randomly obtained, and values of 16 sets of position and posture parameters were obtained using four algorithms. The results indicate that the SMFO algorithm can improve the accuracy of the forward kinematics solution to 4.05E-09 mm.

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“…In the MFO algorithm, the moth is represented by m. Assuming that m is a candidate solution to the problem to be solved. In the feasible domain, the vector position of m is used to represent the variable to be solved; then, m can fly in a one-dimensional or even multi-dimensional manner in the feasible domain [13]. e flight path is the range of the solution, and its position coordinates are the possible solutions.…”