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This paper addresses the problem of provably safe navigation for a mobile robot with a limited field-of-view placed in a unknown dynamic environment. In such a situation, absolute motion safety (in the sense that no collision will ever take place whatever happens in the environment) is impossible to guarantee in general. It is therefore settled for a weaker level of motion safety dubbed passive motion safety: it guarantees that, if a collision is inevitable, the robot will be at rest. The primary contribution of this paper is a relaxation of the Inevitable Collision State (ICS) concept called Braking ICS. A Braking ICS is a state for which, no matter what the future trajectory of the robot is, it is impossible to stop before a collision takes place. Braking ICS are designed with a passive motion safety perspective for robots with a limited field-of-view in unknown dynamic environments. Braking ICS are formally defined and a number of important properties are established. These properties are then used to design a Braking ICS checker, i.e. an algorithm that checks whether a given state is a Braking ICS or not. In a companion paper, it is shown how the Braking ICS checker can be integrated into a reactive navigation scheme whose passive motion safety is provably guaranteed.