# Multi-Robot Trajectory Planning and Position/Force Coordination Control in Complex Welding Tasks
## 5 Simulations and Experiments
### Experimental Studies  
To demonstrate the performance of the proposed algorithm, experiments were conducted using the test-bed as shown in Figure 13. And the logical scheme of the control software is shown in Figure 14.  
The test platform consisted of asf-developed open controller, servo drivers, two ESTUN ER16 industrial manipulators, one ESTUN ER4 industrial manipulators, two force/torque sensors, a collision sensor, and two pairs of gripper. The self-developed open controller used an industrial PC with a configuration of Intel Celeron @1.2 GHz, 512 MB of RAM, V  
Figure 14: The logical scheme of the control software. Figure 12: The simulation result of the internal force tracking effect. Figure 13: Hardware architecture of the test-bed. drivers used ESTUN ProNet series, the bandwidth of the servo driver is from 125 Hz to 1000 Hz. Hischer CIFX communication card is used to EtherCAT communication between industrial PC and servo drivers. The force/torque sensors use Optoforce HEX-70-XE-1000N, the collision sensor uses ATI SR-61. The self-developed open controller was used for task coordination, position/force control, motion planning, forward/inverse kinematics, 18-axis cycle synchronization interpolation and human-machine interface. The force/torque sensor was mounted at the wrist of each manipulator. An ATI collision sensor was installed between the end-effector and the gripper of the 1-\(st\) robot was added for the protection of the whole system. The force/torque sensor provided the UDP protocol with the fastest frequency of 1 kHz, so the force sensor and the controller communicate through UDP. Consider the controller computing power, the bandwidth of the servo drivers and communication frequency of the force sensor at the same time, the communication cycles of the controller and the servo drivers, the controller and the force sensor are both set to 5 ms. Two force sensors were initialized by gravity compensation. The physics experiment was consistent with the simulation. The transfer robots separately grasp a part of the workpiece to be welded, which was spliced at the initial welding point. The welding robot started arcing at the initial welding point. Then the transfer robots coordinated the workpiece to be displace, and the welding robot completed the welding of the weld seam. The key frames of the whole welding task is shown in Figure 15.  
During the welding process, due to the presence of unknown factors such as mechanical calibration error, base coordinate calibration error, and external disturbance, the transfer robots produced an uncertain wrench to the welding workpiece. The internal wrench exerting on the end-effector without force control is shown in Figure 16.  
From the above results, we can see that the internal wrench without the force control is large. In order to control the internal forces in a proper range, a symmetrical adaptive variable impedance control is proposed in this paper. To certify the performance of the proposed algorithm, the traditional constant impedance control and the proposed algorithm are compared as shown in Figure 17.  
Figure 17 shows that the force control effect has been significantly improved. The desired trajectory of transfer robots' end-effector and the center of workpiece are shown in Figure 18.  
From Figure 17, we can conclude that the variable adaptive impedance control can achieve a better effect than the traditional constant impedance control. By using the proposed algorithm, the trajectory deviations of the transfer robots are shown in Figure 19, the trajectory deviations of the welding robot is shown in Figure 20.  
Through Figures 17-20, it shows that the internal force of the transfer robots exerting on the workpiece to be welded is within the controllable range and does not cause damage to the welding system. The welding result has been shown in Figure 14.0 It indicates that a uniform smooth weld seam without cracks has been got by our method. And the welding quality is much better compared with novice welders.