Investigation of the Use of Commercial Robotic Arms for Real-Time Hybrid Substructuring 107 0 1 2 3 4 −4 −2 0 2 4 · 10−3 t / s etrack / m τ =10ms: Trial 1 τ =10ms: Trial 20 τ =25ms: Trial 1 τ =25ms: Trial 20 τ =60ms: Trial 1 τ =60ms: Trial 13 (a) The tracking error etrack over time for the different delay values without ILC (Trial 1) and after its convergence (Trial 20). 0 5 10 15 20 10−4 10−3 10−2 Trial j e RMS,rel track τ =0ms τ =10ms τ =25ms τ =60ms (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 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 ABB IRB120 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 delay values without ILC (Trial 1) and after its convergence (Trial 20). 0 1 2 3 4 −4 −2 0 2 4 · 10−3 t / s etrack / m τ =10ms: Trial 1 τ =10ms: Trial 20 τ =25ms: Trial 1 τ =25ms: Trial 20 τ =60ms: Trial 1 τ =60ms: Trial 13 (a) The tracking error etrack over time for the different delay values without ILC (Trial 1) and after its convergence (Trial ). 0 5 10 15 20 10−4 10−3 10−2 Trial j e RMS,rel track τ =0ms τ =10ms τ =25ms τ =60ms (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 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 ABB IRB120 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 delay values. The light green values represent the result for τ =60ms after adjusting the robustness filter Q, i.e. choosingfQ,cut =2Hz. Fig. 5 Simulative 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. In fig. 5 the robustness of our controller to different amounts of delayτ in the virtual RTHS experiments is investigated. Again we use the KUKA®KR16 as actuator. We show the tracking error etrack over time for the different delay values without ILC(Trial 1) and after its convergence (Trial 20) in fig. 5a, while in fig. 5b we visualize the convergence of the ILC over the trials by calculating the relative root-mean-square (RMS) tracking error e RMS,rel track = RMS(etrack) MAX(|z|) per trial. It becomes apparent that our control scheme can cope with varying amounts of delay without retuning its parameters, since it significantly reduces the total tracking error and thus compensates for the delays. Note, however, that with a robustness filter Qless than 1 for frequencies above fQ,cut, the residual error after convergence is non-zero. Furthermore, this residual error depends on the transfer behavior of the reference system itself as well as the transfer behavior of the Transfer System. See [18] for the convergence analysis of the ILC in RTHS. This explains why the tracking error is not completely zero after convergence, and its final value also depends on the chosen delay value. In [18] we also show that a convergence criterion must be satisfied for ILC in RTHS. Thus, there is a limit to how much the delayτ can be increased without violating the convergence criterion. This can be seen in fig. 5 for the results for τ =60ms as the error diverges over the iterations. However, after retuning the ILC by adjusting the robustness filter Q, e.g. by choosing fQ,cut = 2Hz, stable convergence could be achieved also for τ =60ms as shown by the light green values in fig. 5b. In fig. 6 we show the robustness of our controller to different actuators in the virtual RTHS experiments. The delay is chosen as τ =10ms for the simulations with all three actuators. Again, the applicability and robustness of our approach is demonstrated as the tracking error converges similarly for all three actuator types and a significantly lower residual tracking error is achieved after convergence. Experimental Results The experimental realization of the RTHS test including the proposed control scheme is visualized in fig. 7. A dSpace® MicroLabBox dS1202 [23] is used to run the numerical time-integration of the Numerical Substructure and the control scheme in real-time. Both are developed in MATLAB®/Simulink® (version R2016b, MathWorks®) on a Host PC and compiled and executed in real-time on the MircoLabBox. The software ControlDesk® (version 6.0, dSpace®) is used on the Host PC to monitor and log relevant variables during real-time execution. The output of the numerical simulation z is adjusted to compensate the measured tracking error of the robot etrack. For these first experiments, we do not use a zero-phase low-pass filter as robustness filter Q, but a scalar constant Q=QKuka ∈]0, 1] for simplicity. Parallel to the ILC, an additional outer-loop
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