Synthesis of optimal trajectory of industrial robots

Industrial robots driven electrically with a feedback control loop (and even then hydrauhcally) create highly nonlinear dynamic systems, the control of which in real time is a difficult problem of the control theory. From the theoretical point of view it is a classical problem of optimal control. A system is to be controlled from the initial state to the terminal state so as to minimize some performance index (e.g. energy consumption, time etc.). But the synthesis of the optimal control as a feedback control has not been till now successful because of high nonlinearity with couplings among the joints and of strict constraint conditions at the terminal state [5], [6]. Otherwise only the computation of the time dependence of optimal control is possible only by numeric iterations the convergence of which has been questionable [7], [3], [13], [2], [11]. So the conventional control of today's industrial robots [5], [6], [8], [1] is universally realized by the programme CNC control, i.e. the controller generates the desired corner points of the path and a conventional positional feedback control (linear servo) for each joint stabilizes the system state according to the varying desired system state. The trajectory of motion is the input to the control system which may be numerically fed into the system (e.g. from a simple programme), or furnished through so-called "teaching by doing", i.e. the corner points are recorded while the hand of the robot is led through these points manually by an operator. The mass use of robots for more difficult application (i.e. the surroundings of the robot is dynamic, the accuracy and complexity of robot's positioning exceeds the