When autonomous robots begin to share the human living and working spaces, safety becomes paramount.
It is legally required that the safety of such systems is ensured, e.g. by certification according to relevant standards
such as IEC61508. However, such safety considerations are
usually not addressed in academic robotics. In this paper
we report on one such successful endeavour, which is ... [Show full abstract] concerned with designing, implementing, and certifying a collision avoidance safety function for autonomous vehicles and
static obstacles. The safety function calculates a safety zone
for the vehicle, depending on its current motion, which is
as large as required but as small as feasible, thus ensuring safety against collision with static obstacles. We outline
the algorithm which was specifically designed with safety
in mind, and present our verification methodology which
is based on formal proof and verification using the theorem prover Isabelle. The implementation and our methodology have been certified for use in applications up to SIL3
of IEC61508 by a certification authority (TÜV Süd Rail
GmbH, Germany). Throughout, issues we recognised as being important for a successful application of formal methods
in robotics are highlighted. Moreover, we argue that formal analysis deepens the understanding of the algorithm, and
hence is valuable even outside the safety context.