Model-Based On-Line Compensation of Path Deviations for Milling Robots
Authors: Roesch Oliver 
Published: September 2013

Handling, welding or painting are currently the main fields of application for industrial robots. Due to their high flexibility and low investment costs industrial robots are increasingly used for machining processes in production environments. Robotic milling is one example of these processes, which nowadays can only be applied for tasks with low accuracy requirements and minor cutting forces. The main reason for this is the low stiffness of the robot structure and hence the huge deflection of the tool caused by the cutting forces. Robotic milling tests of aluminum show deviations of the programmed track in the millimeter range even with moderate depth of cut. To harness high possible savings of milling robots, a new method to increase the machining accuracy was developed at the Institute of Machine Tools and Industrial Management (iwb). The core of the method is a model-based controller for the compensation of deviations that are caused by the cutting forces. The input variables of the controller are the axis angles of the robot (provided by the robot controller) and the cutting forces (measured by a three-component force plate). Based on the cutting forces and the axis angles, the deflection of the Tool Center Point (TCP) is calculated by means of a simulation model. The calculated offset is transmitted to the robot controller so that the tool path is corrected. To implement the compensation strategy, a real-time model of the robot which includes all major compliances of the structure needs to be developed. Besides the real-time requirement, the model needs to be valid for the main working area of the robot. A major challenge in this regard is the determination of the relevant compliance parameters of the robot. In addition to the stiffness values of the gears and bearings the elasticities of the robot links need to be identified. The paper presents a novel method to determine the relevant stiffness parameters of a robot by measurements with a 3D-Scanning-Laser-Doppler-Vibrometer (LDV). In these measurements the robot is loaded with a defined force induced by an actuator at its TCP. During this process, the deflection of the robot is detected by the LDV at a multitude of measuring points. From the relative movements of the measuring points, the tilting-angles of the gears, bearings, and the structural components are calculated. Using the known torques caused by the defined load the stiffness parameters are calculated. In order to minimize the experimental effort it is aspired to identify all necessary parameters by one single measurement. To achieve this goal, the best measurement setup consisting of the position and the orientation of the TCP as well as the direction of the actuator force, is identified by a multibody system (MBS) to ensure sufficient torques in every axis of the robot and all directions (transmission direction and perpendicular to it). The simulation shows that such a measuring setup exists, so that the required parameters, which were validated in additional experiments, could be determined with a single measurement. The determined parameters are used in a controller model to calculate the displacement of the TCP due to the cutting forces during the machining process. Since this model needs to be very efficient regarding the computation time, a MBS cannot be used so that an analytical model must be developed. The analytical model is based on conventional forward kinematics, which is used for determining the position and orientation of the TCP of the robot. In conventional forward kinematics, the rotation of an axis is described by a transformation matrix, which also takes the (constant) dimensions of the robot arms into account. This description only includes a single degree of freedom to the joint angle of the axis and is extended to provide additional degrees of freedom to represent the elasticity of the gear and the bearing. To be able to consider the elasticity of the robot arms, additional transformation matrices are introduced in the center of the arm and the link arm. The computing time of this analytical model is in the range of 1 to 2 ms, so that the model is suitable for the control. In initial machining experiments with a robot of type KR 240 R2500 prime the proposed approach was validated. Milling tests with aluminium showed a significant reduction of the process-related path deviations using the presented control strategy.