One of the main challenges in robot swarming arises from the need to design controllers that guarantee safety and motion planners that guarantee collision avoidance. This translates into sensors that measure proximity to neighbors and algorithms that scale exponentially with the number of robots. In many cases, these problems are solved very differently in nature, especially at smaller scales. The penalty due to collisions is small at these scales and sensors and controllers are not precise enough to guarantee collision-free trajectories. We explore a similar approach with small flying robots. We present a design that is capable of sustaining collisions, controllers that are able to recover from collisions, and simple motion planners that allow the robots to navigate without complete knowledge of the environment. We illustrate the potential of bioinspired swarms using simulations and experimental results.