108 A. Kist et al. different delay values. The light green values represent the result for τ =60ms after adjusting the robustness filter Q, i.e. choosing fQ,cut =2Hz. Fig. 5Simulative investigation of the robustness of our control scheme to different amounts of delay τ for the KUKA® KR16 used as actuator in virtual RTHS experiments. 0 1 2 3 4 −2 0 2 ·10−4 t / s etrack / m Stewart platform: Trial 1 Stewart platform: Trial 20 ABB IRB 120: Trial 1 ABB IRB 120: Trial 20 KUKA KR16: Trial 1 KUKA KR16: Trial 20 (a) The tracking error etrack over time for the different actuators without ILC (Trial 1) and after convergence (Trial 20). 0 5 10 15 20 10−4 10−3 Trial j e RMS,rel track Stewart platform ABBIRB120 KUKAKR16 (b) The relative RMS tracking error e RMS,rel track over the trials for the different actuators. Fig. 6Simulative investigation of the robustness of our control scheme to different actuators in virtual RTHS experiments with τ =10ms. In this work, we use UDP/IP communication via Ethernet. To send the motion commandzad from the MicroLabBox to the KR C4 controller, we implemented a UPD server in Simulink® based on [25] and utilizing the RTI Ethernet Blockset [26] provided by dSpace®. The UDP server is compiled with the rest of the software and executed on the MicroLabBox. The RSI, which acts as the UDP client in our structure, initiates the communication by sending the current measured position of the robot’s end effector z0meas. As soon as the UPD server on the MicroLabBox receives a data packet, it processes it, calculates the current motion command zad and responds by sending this command back to the UPD client on the KR C4. The RSI processes the received data packet, forwards it to the internal KUKA® controller as the desired end-effector position and waits until the next communication cycle starts before sending the next data packet. Before using it in the RTHS setup, we validated the UDP communication in a simple benchmark test similar to [27]. In this test, a 3D sine trajectory in the robot’s task-space is commanded to the robot from the MicroLabBox via the UDP communication and recorded for 90 seconds. During this time, no packet loss was detected and we estimated the total delay to be 32ms. This delay includes delays for receiving and (a) The tracking error etrack over time for the different actuators without ILC (Trial 1) and after convergence (Trial 20). (a) The tracking error etrack over time for the different delay values without ILC (Trial 1) and after its convergence (Trial 20). (b) The relative RMS tracking error e RMS,rel track over the trials for the different delay values. The light green values represent the result for τ =60ms after adjusting the robustness filter Q, i.e. choosing fQ,cut =2Hz. Fig. 5Simulative investigation of the robustness of our control scheme to different amounts of delay τ for the KUKA® KR16 used as actuator in virtual RTHS experiments. 0 1 2 3 −2 0 2 ·10−4 t / s etrack / m Stewart platform: Trial 1 Stewart platform: Trial 20 ABB IRB 120: Trial 1 ABB IRB 120: Trial 20 KUKA KR16: Trial 1 KUKA KR16: Trial 20 (a) The tracking error etrack over time for the different actuators without ILC (Trial 1) and after convergence (Trial 20). 0 5 10 15 20 10−4 10−3 Trial j e RMS,rel track Stewart platform ABBIRB120 KUKAKR16 (b) The relative RMS tracking error e RMS,rel track over the trials for the different actuators. Fig. 6Simulative investigation of the robustness of our control scheme to different actuators in virtual RTHS experiments with τ =10ms. In this work, we use UDP/IP communication via Ethernet. To send the motion commandzad from the MicroLabBox to the KR C4 controller, we implemented a UPD server in Simulink® based on [25] and utilizing the RTI Ethernet Blockset [26] provided by dSpace®. The UDP server is compiled with the rest of the software and executed on the MicroLabBox. The RSI, which acts as the UDP client in our structure, initiates the communication by sending the current measured position of the robot’s end effector z0meas. As soon as the UPD server on the MicroLabBox receives a data packet, it processes it, calculates the current motion command zad and responds by sending this command back to the UPD client on the KR C4. The RSI processes the received data packet, forwards it to the internal KUKA® controller as the desired end-effector position and waits until the next communication cycle starts before sending the next data packet. Before using it in the RTHS setup, we validated the UDP communication in a simple benchmark test similar to [27]. In this test, a 3D sine trajectory in the robot’s task-space is commanded to the robot from the MicroLabBox via the UDP communication and recorded for 90 seconds. During this time, no packet loss was detected and we estimated the total delay to be 32ms. This delay includes delays for receiving and (b) The relative RMS tracking error eRMS,rel track over the trials for the different actuators. Simulative investigation of the robustness of our control scheme to different actuators in virtual RTHS experiments withτ =10ms. z0 F g z @1kHz @fKUKA Real-Time Loop @250Hz F0 F0ad Fd z zex g UDP Server ILC NPC KUKA RSI KUKA Controller ADC dSpace MicroLabBox Host PC KUKAKRC4 KUKAKR16 SCHUNK Amplifier Analog Signal SCHUNK FTS 330/30 F0ad Experimental Substructure Numerical Substructure Transfer System z0meas UDP/IP via Ethernet zad ∆ILC Code Generation Data Logging Fig. 7Illustration of the experimental realization of the RTHS experiment using a KUKA® KR16 as actuator, including all used hardware components, the signal flow and the used cycle rates. Note that the inputs for the NPC are not drawn for the sake of clarity. preprocessing the motion command, trajectory tracking errors, and delays for measuring, postprocessing, and transmitting the actual motion of the robot5. The actual motion of the KR16 robot z0 is transferred to the Experimental Substructure, which consists of a compression spring and a 3D-printed half-sphere attached to the robot’s end effector. A table is used as a ground to which the half-sphere intermittently makes contact. A SCHUNK® FTS 330/30 [28] is placed between the compression spring and the robot end effector to measure the interface force. The amplified force signal is fed to one of the analog inputs of the MicroLabBox where, after analog-to-digital conversion (ADC) and adaptation by the NPC, it is used as input for the numerical time-integration in Fig. 7 Illustration of the experimental realization of the RTHS experiment using a KUKA® KR16 as actuator, including all used hardware components, the signal flow and the used cycle rates. Note that the inputs for the NPC are not drawn for the sake of clarity.
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