Investigation of the Use of Commercial Robotic Arms for Real-Time Hybrid Substructuring 103 Since the user typically does not have access to the low-level control of individual joints on industrial robots, we adapted our learning-based joint-space control scheme [18] to directly adjust the desired task-space trajectory to mitigate synchronization errors. We demonstrate the performance and robustness of this adapted control scheme through simulation, i.e., in a virtual RTHS experiment, by treating the controlled actuator as a black box and inducing different amounts of artificial delay. RTHS Test Setup For the investigations of this contribution, we analyze the system shown in fig. 2 using RTHS. It consists of a one-dimensional two-mass oscillator including a contact scenario. The upper mass mNUM is connected to a moving point by a spring with stiffness kNUM and a damper with damping ratio dNUM. The lower mass mEXP is attached to the upper mass by a spring with stiffness kEXP. To excite the system, a cosine trajectory zex(t) with frequency fex is prescribed for the moving point so that the lower mass intermittently contacts the ground. For the investigation using RTHS, the moving point, the upper spring-damper and the upper mass are chosen as the Numerical Substructure, while the lower spring, the lower mass and the ground contact are chosen as the Experimental Substructure. The interface displacement is denoted as z(t). A detailed description of this system has been given in our previous work, e.g.[20, 10, 13, 18], and further description is omitted here. The simplicity of the system allows us to compute a reference solution to assess the fidelity of the RTHS experiments, which is generally not possible for RTHS experiments. The fig. 3 illustrates the signal flow of the entire RTHS loop executed in real-time. It includes the control scheme to ensure a robust and high-fidelity experiment, which we adapted from our previous work [18] to serve as a pure outer-loop control scheme. The numerical time-integration of the Numerical Substructure provides as output for each hybrid simulation step the interface displacement z (and its corresponding velocity ˙z). This serves as the desired task-space motion command for the robot to synchronize the interface displacements and satisfy the compatibility condition. The Experimental Substructure is mounted on the interface to the robot’s end-effector. In this work, we investigate the use of a commercial robot as an actuator, so we assume that the low-level control of this robot is not accessible and the controlled actuator is treated as a black box. Possible processing and communication delays are accounted for using delay blocks as shown in fig. 3. The robot executes the motion z′, ˙z′ and moves the Experimental Substructure. This motion is not the same as the commanded motion due to the preprocessing delay block (which accounts for delays in the robot for receiving and processing the motion command) and imperfect trajectory tracking of the low-level actuator controller. For our outer-loop control, a measurement of z′ is required. Since acquiring this measurement may introduce additional delay compared to the actual motion of the robot, we introduce a postprocessing delay block that accounts for delays due to acquiring, processing, and transmitting the actual task-space position of the robot. The measured task-space motion of the robot is denoted as z′meas, and it is generally assumed that z̸ =z′̸ =z′meas. g kNUM kEXP mEXP dNUM mNUM t flight phase contact phase flight phase zex 1 fex z g. 2Overall system whose dynamics are investigated with RTHS in this work. The Numerical Substructure is colored in blue, ile the Experimental Substructure is colored in green. Figure adapted from [21]. been given in our previous work, e.g.[10, 13, 18, 20], and further description is omitted here. The simplicity of the system ows us to compute a reference solution to assess the fidelity of the RTHS experiments, which is generally not possible for HS experiments. Fig. 2 Overall system whose dynamics are investigated with RTHS in this work. The Numerical Substructure is colored in blue, while the Experimental Substructure is colored in green. Figure adapted from [21].
RkJQdWJsaXNoZXIy MTMzNzEzMQ==