Resolving redundant manipulator joint rates and identifying special arm configurations using Jacobian null-space bases

Joint rate solutions for redundant manipulators are formulated in terms of a particular solution and a homogeneous solution formed using a basis for the Jacobian null space. Solutions for several local optimization objectives are formulated in terms of Jacobian null-space bases. A method based on a decomposition of screw coordinates is presented for finding null-space bases and particular solutions. The screw decomposition is applied in the derivation of the analytical expressions for the null-space bases and in the identification of special configurations for a seven-revolute manipulator. The analysis is then extended to multiple-arm systems with common degrees of freedom, and is applied to an analytical example involving industrial manipulators mounted on a common platform