As robots are spreading in diverse environments, new collision avoidance challenges arise. Real world collision avoidance often includes dynamic, complex, unstructured and uncertain environments. While these constraints are rarely considered all together in perception and navigation research works, we present a broad integration from perception to navigation in a versatile collision avoidance approach that is designed to operate under these constraints. Our solution relies on a new Predictive Collision Detector that we propose as an interface between state-of-art grid-based perception and sampling-based planners. Unlike most other approaches, ours operates only on elementary spatial occupancy and does not use the concept of objects such that it captures the richness and versatility of modern occupancy grid perception. With simulated and experimental results on 2 robots, including a robotic car, we show that our solution generates advanced driving behaviors that compare with the related state-of-art and comply with safety standards even in complex scenarios. With this contribution, we hope to facilitate the use of probabilistic occupancy grids for collision avoidance and to enhance the connectivity of the state-of-art of perception and navigation.