Forward Displacement Analysis of the 4SPS-2CCS Generalized Stewart Platform Based on Hyper-Chaotic Neural Network Mathematical Programming Method

Abstract

The displacement analysis problem of parallel robot mechanism can be finally transformed into solving nonlinear equations and the finding-process is very difficult. Moreover, the more CCS kinematic pair the more complexly to find. The mathematical programming method is adopted when the iteration diverges with the Newton and quasi-Newton methods. If chaotic sequences are considered as the initial guess value, the mathematical programming method can find all solutions. Based on the existing chaos system or finding new chaotic system to obtain chaotic sequences with good characteristic is the key problem of chaos-based mathematical programming. By eliminating the simulated annealing mechanism of transiently chaotic neuron, this paper presents a kind of chaotic neuron which can permanently sustain chaotic search. Based on the connection topology of chaotic neural network composed of the four chaotic neurons, hyper-chaos exists in the chaotic neural network system. A new method to find all solutions by utilizing hyper-chaotic neural network to obtain locate initial points of mathematical programming method to find all solutions of the nonlinear questions was proposed. The forward displacement mathematic model of a 4SPS-2CCS Stewart platform robot was created based on quaternion. An example was given and the result and the find-process were compared with homotopy continuation method. The analysis results proves that the proposed algorithm is simple, the solution-find is carried through real number range, the efficiency is high and can be used to kinematics of other generalized Stewart platform. The research builds the theory basis for dimensional design, trajectory planning and control of this type of manipulator.