Vector summation of end-point impedance in kinematically redundant manipulators

One way to control the mechanical interactions between a manipulator and its environment is by specifying the manipulator's end-point impedance. According to this view, the function of a controller is to determine the force that the controlled system should apply in response to an externally imposed state, i.e., to determine an output force field. The possibility of combining the output force fields generated by a number of separate controllers in order to approximate an arbitrary output field is considered for a kinematically redundant manipulator. The end-point force fields of a simulated kinematically redundant manipulator operated by a set of spring-link actuators is numerically derived. The results indicate that the linear superposition of end-point fields may provide a quite good approximation of the actual passive behavior. This offers a simple way for solving the ill-posed problems associated with the specification of end-point impedance fields in a kinematically redundant system.