To cooperatively carry food, orders of magnitude larger than their own size and weight, individual ants conform their efforts and coordinate their motion to reach their collective goal, the nest. In this study we investigate cooperative transport when the motion of the ants is frustrated by a linear obstacle with a small opening, which allows single ants to pass through, but not with the carried cargo. We provide an analytical model for the ant-cargo system in the constraint environment, that predicts bi-stability between an oscillatory mode of motion along the obstacle, and a convergent mode of motion near the opening. Using both experiments and stochastic simulations, we show how for small cargo sizes the system exhibits spontaneous transitions between the two modes of motion due to fluctuations in the applied forces on the cargo. Our results provide two possible problem solving strategies for overcoming the obstacle: either by dwelling near the opening and attempt to pass the cargo through, or by taking large excursions that can lead to obstacle circumvention.