Quasi-local solution for inverse kinematics of a redundant robot arm

A four-joint machine with possible movements in a horizontal, planar area is considered. A neural network mechanism to solve the problem of inverse kinematics for this system is constructed. The mechanism is based on the idea that the joint which is most suitable for generating a given trajectory element should contribute most to the actual movement. The possible contributions of the joints are linearized and scaled by a gain function due to the geometry of the physical four-joint machine. A hierarchical sequence determines an order and therefore the directions of function as flexor or extensor for the four actuators for each step along the trajectory. The hierarchical sequence specifies that the vectors of the contribution of the first two selected actuators are added up, whereas the remaining two joints are used to compensate the vector components perpendicular to the vector of the currently processed trajectory element. This is realized by deciding about the contribution of the various joints in a geometrical manner. Since this local mechanism provides a satisfactory solution only for some parts of the working area, a small amount of knowledge about the history of the join movement has to be incorporated to generate an overall good solution