Solution of the direct and inverse kinematic problems by a common algorithm based on the mean of multiple computations

For the control of the movement of a multijoint manipulator a “mental model” which represents the geometrical properties of the arm may prove helpful. Using this model the direct and the inverse kinematic problem could be solved. Here we propose such a model which is based on a recurrent network. It is realized for the example of a three-joint manipulator working in a two-dimensional plane, i.e., for a manipulator with one extra degree of freedom. The system computes the complete set of variables, in our example the three joint angles and the two work-space coordinates of the endpoint of the manipulator. The system finds a stable state and a geometrically correct solution even if only a part of these state variables is given. Thus, the direct and the inverse kinematic problem as well as any mixed problem, including the underconstrained case, can be solved by the network.