Correct by construction design of autonomous vehicles through a barrier function method

This paper presents a supervisory control structure to ensure safety of low speed autonomous vehicles. The method can provably ensure safety for an autonomous robotic vehicle to navigate in an urban/indoor environment with multiple moving objects. A polar algorithm is developed to construct a polytopic avoidable set, which is then used to construct barrier functions. Then the mixed integer programming (MIP) is used to solve for the control action ensuring safety. The method was tested in simulations with multiple random walking and non-hostile objects. The results show that the proposed method can effectively navigate the autonomous vehicle with guaranteed safety.