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

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