## 1 Introduction
Although these methods can guarantee completeness and optimality, their resolution is computationally expensive, and they adapt well to real-time configurations. In contrast, decoupled methods plan trajectories individually, adjust speeds to avoid collisions, and reduce computational overhead while compromising optimality. Decentralized Model Predictive Control (DMPC) and multi-criteria optimization algorithms have also been successfully applied to the coordination of dual and multiple robots, as indicated in [14]. These approaches plan over a time horizon to mitigate deadlock scenarios and improve the cooperation between robots. For example, optimization algorithms have proven effective in the coordination and collision avoidance of manipulator robots, improving efficiency and reducing execution time in shared environments. The evolution of obstacle avoidance strategies in manipulator robots has been an area of intense research driven by the need to improve efficiency, safety, and flexibility in industrial and collaborative environments. The most notable feature is the use of enhanced artificial potential field algorithms. According to [15], a methodology that used a velocity field to guide the robot arms, optimize the trajectory, and improve the dynamic response capability was presented. This approach shows a significant improvement in the real-time obstacle avoidance capability, which is crucial for applications in complex industrial environments. Similarly, an adaptive approach that focuses on operator safety and robot flexibility was proposed [16]. This strategy dynamically adjusts the radius of the safety regions of the manipulator links based on the speed of obstacles. Detailedsimulations demonstrate the effectiveness of adaptive control in different scenarios with dynamic and fixed obstacles, highlighting its versatility for manipulators with six degrees of freedom (DoF). Another innovative approach is the sampling-based non-fixed orientation search method for cooperative manufacturing with dual manipulators. This method allows for greater flexibility in motion planning and improves the cooperation between manipulator arms during manufacturing tasks. Cooperative dynamic motion planning for dual manipulator arms, based on the Rapidly exploring Random Tree Smart Adaptive Dynamic (RRTSmart-AD) algorithm, enhances the efficiency and precision in trajectory planning in dynamic environments, enabling faster adaptation to changes in the environment and optimizing collaboration between the robot arms [17]. Trajectory planning for obstacle avoidance uses an improved Rapidly exploring Random Tree (RRT) algorithm for dual-arm robots. This approach focuses on optimizing trajectories and enhancing the responsiveness of robots in complex and dynamic environments. A hybrid control scheme for the navigation of multiple disc-shaped robots with independent goals within obstacle-filled environments utilizes a hierarchical cell decomposition methodology and harmonic transformations to ensure safe transitions between adjacent cells and near-global convergence to the desired configuration [18]. In the field of collaborative control, the use of deep reinforcement learning for dual-arm robots has shown promising results [19], allowing robots to autonomously learn and adapt to new tasks and environments, thereby improving their efficiency and collaboration capabilities. Additionally, collision avoidance for multiple robotic manipulators using a non-cooperative multi-agent game enables each robot to make decisions independently, quickly adapt to changes in the environment, and improve trajectory coordination efficiency in dynamic environments [20]. A method of impedance control for coordinated robots using state and output feedback was also presented, which improved the precision and stability of the manipulators when interacting with their environment [21].