This paper addresses the scheduling of electrical drilling machines in open-pit mines, proposing three constraint programming formulations to account for uncertain drilling durations: two-stage stochastic, a novel probability-free method, and a chance-constrained model. These approaches aim to create robust schedules for drilling operations. The probability-free method introduces a "Resilient" constraint for deterministic representation of uncertainty, while the chance-constrained approach combines elements of two-stage stochastic and resilient programming using scenario approximation. Evaluated using simulated instances from real coal mine data, all models efficiently handle problem sizes comparable to or exceeding typical daily operations. The probability-free model demonstrates particular efficiency and scalability. This study contributes to mining operations research by providing flexible, robust constraint programming models for drill rig scheduling under uncertainty, offering mining practitioners tools to optimize operations in uncertain environments.