Recursive modeling and control of multi-link manipulators with vacuum grippers

Manipulators equipped with vacuum grippers are a new and flexible element in innovative material-flow solutions. The limited holding forces of vacuum grippers require elaborate strategies of control to prevent the contact between gripper and load from breaking off especially in time optimal motion. Mathematically this can be modeled as a constraint on internal forces of a multi-link manipulator. A Maximum Principle based approach is presented for the accurate solution of the control problem. Not only the equations of motion of the manipulator, but the complete optimal control problem is modeled recursively. By this, the structural properties of the control problem are revealed. Direct access becomes possible to all information necessary to restrict internal forces efficiently.