Trajectory planning for kinematically redundant robots using jacobi matrix – an industrial implementation

The widespread use of robots in industry contributes significantly to high productivity. Serial 6-axis robots are used in large quantities, e.g. for assembly or welding. A current emerging trend is the use of robots for classic tasks of a machine tool like finishing of milled workpieces. For such applications, standard robots are usually extended by additional axes like linear axes or rotary tilting tables. Therefore, the overall system becomes kinematically redundant. To be able to calculate the axis quantities via inverse kinematics for a given path, additional degrees of freedom must be bound. In order to automatically and optimally consider the additional axis motion a method, using the pseudoinverse of the Jacobian matrix, is discussed. Due to the dependence of the Jacobi matrix on the robot's current joint position, numerical inaccuracies, which in turn reflect a path error, are inherent to this method. By feedback control of the path error, in the form of a classic control loop, the error can be reduced so that a practical implementation on industrial robot controller is possible. In the article possibilities for parameterisation of the algorithm as well as proof of stability of the closed loop are presented. The results obtained are verified by a concrete application.