  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.
