Navigation with a safe longitudinal distance

A system for navigating a host vehicle, the system comprising:

• at least one processing device programmed to:
• receive, from an image capture device, at least one image representative of an environment of the host vehicle;
• determine, based on at least one driving policy, a planned navigational action for accomplishing a navigational goal of the host vehicle;
• analyze the at least one image to identify a target vehicle in the environment of the host vehicle, wherein a direction of travel of the target vehicle is toward the host vehicle;
• determine a next-state distance between the host vehicle and the target vehicle that would result if the planned navigational action was taken;
• determine a host vehicle braking rate, a host vehicle maximum acceleration capability, and a current speed of the host vehicle;
• determine a stopping distance for the host vehicle based on the host vehicle braking rate, the host vehicle maximum acceleration capability, and the current speed of the host vehicle;
• determine a current speed of the target vehicle, a target vehicle maximum acceleration capability, and a target vehicle braking rate;
• determine a stopping distance for the target vehicle based on the target vehicle braking rate, the target vehicle maximum acceleration capability, and the current speed of the target vehicle;
• and
• implement the planned navigational action if the determined next-state distance is greater than a sum of the stopping distance for the host vehicle and the stopping distance of the target vehicle.