A NUMERICAL-METHOD OF PREDETERMINED OPTIMAL RESOLUTION FOR A REDUNDANT MANIPULATOR

Abstract

A numerical method of predetermined optimal redundancy resolution for a redundant manipulator is proposed. To resolve redundancy, a performance index is optimized globally in time. Instead of deriving the necessary condition for optimality and searching optimal boundary values, we predetermine the trajectories of redundant joints in terms of the Nth partial sum of Fourier series. Then, the optimal coefficients of the Fourier series are determined by using Powell's method. As a result, we can obtain an approximate optimal solution in a desirable homotopy class without topological liftings of paths. To show the validity of the proposed method, we apply the method to a three-link planar manipulator and analyze both optimal and extremal solutions by using Fast Fourier transform (FFT).