To cooperatively carry large food items to the nest, individual ants conform their efforts and coordinate their motion. Throughout this expedition, collective motion is driven both by internal interactions between the carrying ants and a response to newly arrived informed ants that orient the cargo towards the nest. During the transport process, the carrying group must overcome obstacles that block their path to the nest. Here, we investigate the dynamics of cooperative transport, when the motion of the ants is frustrated by a linear obstacle that obstructs the motion of the cargo. The obstacle contains a narrow opening that serves as the only available passage to the nest, and through which single ants can pass but not with the cargo. We provide an analytical model for the ant-cargo system in the constrained environment that predicts a bi-stable dynamic behavior between an oscillatory mode of motion along the obstacle and a convergent mode of motion near the opening. Using both experiments and simulations, we show how for small cargo sizes, the system exhibits spontaneous transitions between these two modes of motion due to fluctuations in the applied force on the cargo. The bi-stability provides two possible problem solving strategies for overcoming the obstacle, either by attempting to pass through the opening, or take large excursions to circumvent the obstacle.