Coordinated swarm behavior in certain types of animals can also occur in groups of autonomous vehicles. Swarm "cohesiveness" is characterized as a stability property. Conditions for one-dimensional asynchronous swarms to achieve collision-free convergence even in the presence of sensing delays and asynchronism during movements are provided. Each finite-size swarm member has proximity sensors and neighbor position sensors that only provide delayed position information. Such stability analysis is of fundamental importance if one wants to understand the coordination mechanisms for "platoons" of autonomous vehicles, where intermember communication channels are less than perfect and collisions must be avoided.