Safe and efficient cooperative planning of multiple robots in pedestrian participation environments is promising for applications. In this paper, a novel multi-robot social-aware efficient cooperative planner on the basis of off-policy multi-agent reinforcement learning (MARL) under partial dimension-varying observation and imperfect perception conditions is proposed. We adopt a temporal-spatial graph (TSG)-based social encoder to better extract the importance of social relations between each robot and the pedestrians in its field of view (FOV). Also, we introduce a K-step lookahead reward setting in the multi-robot RL framework to avoid aggressive, intrusive, short-sighted, and unnatural motion decisions generated by robots. Moreover, we improve the traditional centralized critic network with a multi-head global attention module to better aggregate local observation information among different robots to guide the process of the individual policy update. Finally, multi-group experimental results verify the effectiveness of the proposed cooperative motion planner.