A PARALLEL ALGORITHM AND ARCHITECTURE FOR THE CONTROL OF KINEMATICALLY REDUNDANT MANIPULATORS

Kinematically redundant manipulators are inherently capable of more de xtrous manipulation due to their additional degrees of freedom. To ach ieve this dexterity, however, one must be able to efficiently calculat e the most desirable configuration from the infinite number of possibl e configurations that satisfy the end-effector constraint. It has been previously shown that the singular value decomposition (SVD) plays a crucial role in doing such calculations. In this work, a parallel algo rithm for calculating the SVD is incorporated into a computational sch eme for solving the equations of motion for kinematically redundant sy stems. This algorithm, which generalizes the damped least squares form ulation to include solutions that utilize null-space projections and t ask prioritization as well as augmented or extended Jacobians, is then implemented on a simple linear array of processing elements. By takin g advantage of the error bounds on the perturbation of the SVD, it is shown that an array of only four AT&T DSP chips can result in control cycle times of less than 3 ms for a seven degree-of-freedom manipulato r.