DMAC using the staggered wakeup schedule can achieve both low latency and low energy consumption. However, the data gathering tree built by DMAC is fixed permanently. A fixed data gathering tree can't adapt to the variability in the environment of wireless sensor networks, and it needs to be reconstructed frequently to suit the current environment. For example, the interference is a factor that will change the environment because it changes node connectivity of wireless sensor networks. In this paper, we propose Robust-DMAC (RDMAC) which can dynamically construct the data gathering tree according to the changing environment. Because RDMAC separates the formation of the data gathering tree from the arrangement of the wakeup schedules, it can easily construct a new data gathering tree without adjusting nodes' schedules. From simulation results in variable environments affected by interference, it is shown that RDMAC performs closely with DMAC in effective energy consumption and has remarkable improvement in packet arrival ratio, network throughput, and packet delivery latency over DMAC.