## 4 Results Analysis  
In this study, a cooperative robotic system comprising two SCARA robots was developed and simulated for coordination and obstacle avoidance in cooperative tasks. The results obtained from virtual simulations demonstrate that the proposed system can effectively handle object transfer and avoid collisions in various scenarios of varying complexity. Compared to previous studies that used manipulator robots, this approach stands out for the implementation of advanced trajectory planning and coordination algorithms in cooperative tasks, which significantly improves the adaptability and autonomy of robotic system. The results obtained in the three simulated scenarios show that SCARA robots are capable of effectively coordinating and performing pick-and-place tasks without collisions. In the first scenario, where obstacles were in the working area of Robot 1, the robot demonstrated a robust ability to navigate and avoid obstructions, transferring the object to the transfer point without incidents. In the second scenario, the obstacles in the working area of Robot 2 were handled with equal effectiveness, highlighting the system's ability to operate in constrained environments. The third scenario, which is the most complex, revealed the system's capability to avoid collisions between robots and obstacles, underscoring the efficiency of the synchronization and trajectory planning algorithms. The evaluation of the performance indices of the NLMPCs and SMCs applied to Robots 1 and 2 revealed significant differences in their performance. Regarding the steady-state error e\({}_{88}\), the NLMPC demonstrates greater precision for both robots, with values of 0.0017 for Robot 1 and 1.0697 \(\times\) 10\({}^{-6}\) for Robot 2, compared with 0.0131 and 0.0023, respectively, for the SMC. Analyzing the Integral Squared Error (ISE) index, the NLMPC again showed better performance with values of 0.9576 for Robot 1 and 0.0199 for Robot 2; whereas, the SMC presented significantly higher values of 0.3609 and 0.0619, respectively. In the Integral  
Figure 17: Cartesian error generated by Robot 1. Figure 18: Cartesian error generated by Robot 2. Absolute Error (IAE) index, the NLMPC also stands out, with 0.9598 for Robot 1 and 0.1652 for Robot 2, in contrast to the SMC values of 0.9220 and 0.9896, respectively. The Integral Time-weighted Absolute Error (ITAE) index shows a clear superiority of the NLMPC, with values of 1.4984 for Robot 1 and 8.2306 for Robot 2, compared to the high values of 9.1086 and 32.432 for the SMC, as shown in Table 7. These results indicate that the NLMPC is not only more precise, but also more efficient in terms of stability and temporal response, which are especially relevant in applications where error minimization and rapid response are crucial. When evaluating the trajectories generated by each robot with the two controllers using performance indices, it can be verified that the NLMPC generates fewer errors compared to the SMC, as presented in Table 8. For example, the ISE index for Robot 1 is significantly lower with the NLMPC (1.5217 \(\times\) 10\({}^{-5}\)) compared to the SMC (0.0148). Similarly, Robot 2 shows a lower ISE index with the NLMPC (9.0684 \(\times\) 10\({}^{-4}\)) compared to SMC (0.0615). Additionally, it can be analyzed that the trajectory performed by Robot 1 is more complex than that of Robot 2, resulting in higher errors in both controllers. This difference in trajectory complexity is evident in the IAE and ITAE values, where Robot 1 presents significantly higher values under the SMC. In contrast, Robot 2, although it also shows higher errors with the SMC, maintains a less marked difference compared to Robot 1. Finally, the IA performance index also indicates better efficiency of the NLMPC for both robots, being especially notable in the case of Robot 2.