Bézier Curve-Based Optimization Framework for Multirobot Motion Planning in Unknown Environments

In recent years, multirobot systems (MRSs) have witnessed significant growth because of their capability of solving complex problems involving collaborative missions. A two-phase approach is typically employed in such applications, encompassing task planning and assignment among the robots, followed by motion planning to execute the assigned tasks. This work focuses on the motion planning phase, which facilitates the optimal navigation of multiple robots from their initial to desired goal configurations. A novel multirobot Bézier curve-based trajectory planner (MrBTP) is proposed. MrBTP generates optimal trajectories for multiple robots navigating in an unknown environment, including the polygonal characterization of the available open space. The optimization process is based on using a weighted objective function that combines the navigation time of each robot and the length of its trajectory, allowing for various path optimization strategies. The effectiveness of MrBTP has been evaluated in various scenarios, and its performance is compared with that of a selected trajectory planner based on three performance metrics. Over the three robots used in the test, MrBTP reduced the navigation time by 21%–49% and the trajectory length by 10%–18% compared to the selected benchmark trajectory planner. In addition, it ensures$C^{2}$rather than just$C^{1}$continuity.