LMF Algorithm Based on Hyper-Chaos for the Solving of Forward Displacement in a Parallel Robot Mechanism

The forward displacement problem of the parallel robot mechanism can be converted to nonlinear equations in order to find solutions, but it is very difficult to find all solutions because of the strong coupling of the nonlinear equations. Given the problems of having only one solution and sometimes no convergence when solving the nonlinear equations with the Newton method and quasi-Newton method, a LMF algorithm based on hyper-chaos is proposed to solve the general 6-6 platform parallel mechanism, based on the combination of the hyper-chaos system and the Levenberg-Marquardt-Fletcher (abbreviated as LMF) algorithm. This method uses the hyper-chaotic system to produce the initial point of the LMF algorithm, and takes advantage of the characteristics of the chaotic sequence and the LMF algorithm to find all the real solutions. The numerical example shows that the new method has some characteristics such as that it runs in the initial value range, it has fast convergence, it finds all the real solutions that can be found, and it proves the correctness and validity. It provides a new approach to mechanism design.