Due to its flexible and pervasive sensing ability, crowdsensing has been extensively studied recently in research communities. However, the fundamental issue of how to meet the requirement of sensing robustness in crowdsensing remains largely unsolved. Specifically, from the task owner's perspective, how to minimize the total payment in crowdsensing while guaranteeing the sensing data quality is a critical issue to be resolved. We elegantly model the robustness requirement over sensing data quality as chance constraints, and investigate both hard and soft chance constraints for different crowdsensing applications. For the former, we reformulate the problem through Boole's Inequality, and explore the optimal value gap between the original problem and the reformulated problem. For the latter, we study a serial of a general payment minimization problem, and propose a binary search algorithm that achieves both feasibility and low payment. The performance gap between our solution and the optimal solution is also theoretically analyzed. Extensive simulations validate our theoretical analysis.