Abstract: The function of the scale factor of the gradient projection method is firstly studied on the basis of analysis of the methods, and the performance index PH is proposed to measure the feasible scale factor. Based on the PH index, a new gradient projection method with balanced scale factors, which is suited for all kinds of performance indices, is established, and some numerical experiments is given to verify the method to be a general effective method. The method of structuring multi-performance indices function is established, and is verify versatile by a numerical experiments.

Key words: Gradient projection, Kinematically redundancy, Robot manipulators, Scale factors