Determining states of inevitable collision using reachability analysis

In this paper the states of inevitable collision for mobile robots are determined using reachable set theory. With this theory the safety for robotic platforms can be guaranteed, still allowing maximum flexibility for navigation. Making use of reachability analysis, limitations due to input sampling as in previous approaches are avoided. Using reachability analysis the obstacles are grown in the state space. The mathematical background is shown in this paper and an exemplary algorithm is given for static environments. This implementation can handle arbitrary environments with multiple obstacles and different high-dimensional linear and non-linear system dynamics including the car-like kinematic model. By means of experimental results in simulated environments, the validity of the proposed concept is shown.