FSOC: Flexible Subgrouping and Ordering of Multirobot Coordination for Convoying Multiple Scattered Targets

In this article, we propose the flexible subgrouping and ordering coordination (FSOC) algorithm that enables a team of robots to cooperatively convoy multiple scattered targets (MSTs) of different moving velocities, where each target is convoyed into the interior of distinct convex hulls formed by different subgroups of robots in dynamic environments. Therein, the algorithm/convoying is flexible in the sense that no specific numbers and indexes of robots are preassigned for each subgroup, and no specific spatial ordering sequences of robots are predetermined for each convex hull. To attain such a flexible convoying for scattered targets, we first encode the three subtasks of flexible subgrouping, target convergence, and neighboring collision avoidance into control barrier function constraints and then formulate the FSOC problem as a decentralized constraint-based task-execution optimization one. In particular, by embedding convoying matching conditions into hard integer constraints and soft cost functions, the robots can be divided into subgroups of flexible numbers and indexes. Then, for each subgroup of robots, the flexible-ordering convex hull for each specific target is realized through the balance between the attraction resulting from the target convergence constraints and the repulsion from time-varying collision avoidance constraints. Rigorous analysis is provided to guarantee the asymptotic convergence of the closed-loop systems, which have strong nonlinear couplings due to the flexible subgrouping and ordering. Finally, extensive 2-D and 3-D simulations have been conducted to confirm the effectiveness of the proposed algorithm across different initial positions, the robustness in the face of robot sudden breakdown and target sudden appearances, the adaptability to navigate through obstacle environments, and the scalability when accomplishing high-dimensional MST convoying missions.