The difficult problem of orientating robot control in Cartesian space is solved by utilizing the Euler parameters for the first time. The complexity of the utilization of the approach is discussed in detail. A simple explicit algorithm is obtained, and its superiority over other methods is shown. The application the Euler parameters to other control schemes for robots in Cartesian space is considered. It is expected that this approach will, and make the practical implementation of the Cartesian control strategies possible.