A numerical method of predetermined optimal resolution for a redundant manipulator

A numerical method for 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, the authors 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 using Powell´s method. This results in an approximate optimal solution in a desirable homotopy class without topological liftings of paths. To show the validity of the method, the authors apply it to a three-link planar manipulator and analyze both optimal and extremal solutions using the fast Fourier transform (FFT)