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In swarm robotics, any of the robots in a swarm may be affected by different faults, resulting in significant performance declines. To allow fault recovery from randomly injected faults to different robots in a swarm, a model-free approach may be preferable due to the accumulation of faults in models and the difficulty to predict the behaviour of neighbouring robots. One model-free approach to fault recovery involves two phases: during simulation, a quality-diversity algorithm evolves a behaviourally diverse archive of controllers; during the target application, a search for the best controller is initiated after fault injection. In quality-diversity algorithms, the choice of the behavioural descriptor is a key design choice that determines the quality of the evolved archives, and therefore the fault recovery performance. Although the environment is an important determinant of behaviour, the impact of environmental diversity is often ignored in the choice of a suitable behavioural descriptor. This study compares different behavioural descriptors, including two generic descriptors that work on a wide range of tasks, one hand-coded descriptor which fits the domain of interest, and one novel type of descriptor based on environmental diversity, which we call Quality-Environment-Diversity (QED). Results demonstrate that the above-mentioned model-free approach to fault recovery is feasible in the context of swarm robotics, reducing the fault impact by a factor 2-3. Further, the environmental diversity obtained with QED yields a unique behavioural diversity profile that allows it to recover from high-impact faults.