This work deals with the real-time robot control implementation. In this paper, an algorithm for solving Inverse Dynamic Problem based on the Gibbs-Appell equations is proposed and verified. It is developed using mainly vectorial variables, and the equations are expressed in a recursive form, it has a computational complexity of O(n). This algorithm will be compared with one based on Newton-Euler equations of motion, formulated in a similar way, and using mainly vectors in their recursive formulation. This algorithm was implemented in an industrial PUMA robot. For the robot control a new and open architecture based on PC had been implemented. The architecture used has two main advantages. First it provides a total open control architecture, and second it is not expensive. Because the controller is based on PC, any control technique can be programmed and implemented, and in this way the PUMA can work on high level tasks, such as automatic trajectory generation, task planning, control by artificial vision, etc.