A new algorithm for a minimum infinity-norm solution and its application to trajectory planning of kinematically redundant manipulators

Abstract

We propose a new algorithm for finding a minimum infinity-norm solution of consistent linear equations. The proposed algorithm includes the advantages of previous works such as computational efficiency of Cadzow's algorithm and geometric interpretation of Shim's algorithm, and overcomes the disadvantages of them such as incompleteness of Cadzow's algorithm and computational inefficiency of Shim's algorithm. Also, for redundant robot trajectory planning based on minimum infinity-norm solution, an efficient approach avoiding discontinuity in trajectory is proposed by resolving the non-uniqueness problem of minimum infinity-norm solution. An example of calculating the minimum infinity-norm solution for comparing the computational efficiency as well as the trajectory planning for a redundant robot manipulator is included.