A successive approximation algorithm for the inverse position analysis of the general serial manipulators

A new fast numerical algorithm for the solution of the inverse position analysis of the serial manipulator is presented. With the algorithm, the inverse solution of the general serial manipulators can be achieved quickly under the desired precision when we know the position of the three non-collinear end-effector points, which is much easier to be measured than the orientation of the end-effector. The difference between the new numerical algorithm and the general iterative method is that it can search out the solution when the manipulator is at the singular configuration; and the initial configuration used in the successive approximation process may also be the singular configuration. So the convergence domain is bigger than that of the general iterative method. The position analysis of the general 6R serial manipulator is illustrated in the literature as an example and the simulation results to verify the efficiency of the proposed algorithm. Since the three non-collinear end-effector points can be selected at random, the algorithm can be applied to any other serial manipulator.