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In the current unmanned aircraft systems (UASs) for sensing services, unmanned aerial vehicles (UAVs) transmit their sensory data to terrestrial mobile devices over the unlicensed spectrum. However, the interference from surrounding terminals is uncontrollable due to the opportunistic channel access. In this paper, we consider a cellular Internet of UAVs to guarantee the Quality-of-Service (QoS), where the sensory data can be transmitted to the mobile devices either by UAV-to-Device (U2D) communications over cellular networks, or directly through the base station (BS). Since UAVs’ sensing and transmission may influence their trajectories, we study the trajectory design problem for UAVs in consideration of their sensing and transmission. This is a Markov decision problem (MDP) with a large state-action space, and thus, we utilize multi-agent deep reinforcement learning (DRL) to approximate the state-action space, and then propose a multi-UAV trajectory design algorithm to solve this problem. Simulation results show that our proposed algorithm can achieve a higher total utility than policy gradient algorithm and single-agent algorithm. [ABSTRACT FROM AUTHOR]