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This study presents a cooperative underwater box-pushing scenario, in which three autonomous robotic fish that sense, plan and act on its own move an elongated box from some initial location to a goal location. With the onboard monocular camera, the robotic fish can estimate the pose of the object in the swimming tank. Considering the complexity of the underwater environment and the limited capability of a single robotic fish, the authors address the task by decomposing it into three subtasks and assigning them to capable robotic fish. With one robotic fish observing the box at the goal location and two robotic fish pushing the left and right ends of the box, the box can be moved gradually towards the goal location. The subtask consists of a series of behaviours, each designed to fulfil one step of the subtask. The robotic fish coordinate through explicit communications and distribute the subtasks with a market-based dynamic task allocation method. Task reallocation mechanism that permits robotic fish to auction its assigned task to capable ones is used to cope with unexpected changes in the environment and the limited sensing range of the robotic fish. Experiments are conducted to verify the feasibility of the proposed methods.