In this paper, we propose a cooperative long-term task execution (LTTE) algorithm for protecting a moving target into the interior of an ordering-flexible convex hull by a team of robots resiliently in the changing environments. Particularly, by designing target-approaching and sensing-neighbor collision-free subtasks, and incorporating these subtasks into the constraints rather than the traditional cost function in an online constraint-based optimization framework, the proposed LTTE can systematically guarantee long-term target convoying under changing environments in the n-dimensional Euclidean space. Then, the introduction of slack variables allow for the constraint violation of different subtasks; i.e., the attraction from target-approaching constraints and the repulsion from time-varying collision-avoidance constraints, which results in the desired formation with arbitrary spatial ordering sequences. Rigorous analysis is provided to guarantee asymptotical convergence with challenging nonlinear couplings induced by time-varying collision-free constraints. Finally, 2D experiments using three autonomous mobile robots (AMRs) are conducted to validate the effectiveness of the proposed algorithm, and 3D simulations tackling changing environmental elements, such as different initial positions, some robots suddenly breakdown and static obstacles are presented to demonstrate the multi-dimensional adaptability, robustness and the ability of obstacle avoidance of the proposed method.

翻译：本文提出一种面向移动目标保护的协同长期任务执行（LTTE）算法，通过机器人团队在动态环境中弹性地将目标围入可灵活排序的凸包内部。具体而言，通过设计目标接近与感知邻居避碰子任务，并在在线约束优化框架中将子任务以约束条件（而非传统代价函数）形式嵌入，所提LTTE算法可在n维欧氏空间中系统性保障长期目标护送任务在动态环境中的执行。引入松弛变量后，不同子任务的约束可被松弛——即目标接近约束的吸引力与时变避碰约束的排斥力相互作用，从而形成具有任意空间排序序列的期望编队。严格的理论分析证明了系统在含时变避碰约束引发的非线性耦合条件下具有渐近收敛性。最终，通过三台自主移动机器人的二维实验验证了算法有效性，并开展三维仿真模拟动态环境要素（包含不同初始位置、部分机器人突发故障及静态障碍物），充分证明了所提方法的多维适应性、鲁棒性及障碍规避能力。