Multi-UAV affine formation control enables flexible formation maneuvering according to formation needs. This paper proposes a robust affine formation control strategy for a group of UAVs which is subjected to unknown external disturbances. Collision avoidance is also achieved with the proposed control strategy. A robust control algorithm based on the robust integral of the signum of error(RISE) is developed to deal with issues associated with the formation and transformation problem of affine formation under external disturbances. This control algorithm can effectively compensate for the effects of unknown external disturbances and enhance the robustness of the multi-UAV affine formation. The stability of the formation control system is proved via Lyapunov based stability analysis. To address the issue of collision avoidance among multiple UAVs, the space occupied by each UAV is partitioned using a buffered voronoi cell(BVC) method. Then the collision avoidance during both the affine formation and transformation can be achieved. To deal with the possible deadlock problem that may arise during the collision avoidance process, a heuristic algorithm is designed to facilitate the smooth recovery of UAVs from deadlock. Finally, the proposed algorithm's effectiveness is validated through the experimental platform.