Brains and sensory systems evolved to guide motion. Central to this task is controlling the approach to stationary obstacles and detecting moving organisms. Looming has been proposed as the main monocular visual cue for detecting the approach of other animals and avoiding collisions with stationary obstacles. Elegant neural mechanisms for looming detection have been found in the brain of insects and vertebrates. However, looming has not been analyzed in the context of collisions between two moving animals. We propose an alternative strategy, Generalized Regressive Motion (GRM), which is consistent with recently observed behavior in fruit flies. Geometric analysis proves that GRM is a reliable cue to collision among conspecifics, whereas agent-based modeling suggests that GRM is a better cue than looming as a means to detect approach, prevent collisions and maintain mobility.