Resolution of kinematic redundancy using optimization techniques

Path planning techniques for kinematically redundant manipulators are developed which involve the optimization of integral cost criteria. For a variety of such criteria, the necessary condition consists of n+l first-order differential equations, where n is the number of manipulator degrees of freedom and l is the degree of the redundancy. This necessary condition is essentially equivalent to the system of 2n equations announced by Y. Nakamura, H. Hanafusa (Int. J. Robotics Res., vol.6, no.1, pp.32-42, 1987). Refinements to these basic necessary conditions involve various boundary conditions. Numerical examples highlight the advantages of optimally resolving kinematic redundancy according to an integral cost criterion (compared with the more common approach of optimizing an instantaneous criterion). It is seen, however, that care must be taken regarding trajectories which meet the necessary conditions yet fail to be optimal. It is concluded that any sufficiency conditions for such optimization will involve explicit consideration of the topology of liftings of workspace paths.>