Mobile Crowdsensing (MCS), which assigns outsourced sensing tasks to volunteer workers, has become an appealing paradigm to collaboratively collect data from surrounding environments. However, during actual task implementation, various unpredictable disruptions are usually inevitable, which might cause a task execution failure and thus impair the benefit of MCS systems. Practically, via reactively shifting the pre-determined assignment scheme in real time, it is usually impossible to develop reassignment schemes without a sacrifice of the system performance. Against this background, we turn to an alternative solution, i.e., proactively creating a robust task assignment scheme offline. In this work, we provide the first attempt to investigate an important and realistic RoBust Task Assignment (RBTA) problem in MCS systems, and try to strengthen the assignment scheme's robustness while minimizing the workers' traveling detour cost simultaneously. By leveraging the workers' spatiotemporal mobility, we propose an assignment-graph-based approach. Firstly, an assignment graph is constructed to locally model the assignment relationship between the released MCS tasks and available workers. And then, under the framework of evolutionary multi-tasking, we devise a population-based optimization algorithm, namely EMTRA, to effectively achieve adequate Pareto-optimal schemes. Comprehensive experiments on two real-world datasets clearly validate the effectiveness and applicability of our proposed approach.