On a proof of the deadlock-free property in an on-line path-planning by using world topology

In this paper, we propose a new type of two sensor-based path-planning algorithms running in a 2D uncertain world. In almost all previous sensor-based path-planning algorithms, the automaton comes close to the goal asymptotically when it leaves an obstructed obstacle. Consequently there is no obstacle where the automaton can hit in future at worst and then the automaton arrives at the goal finally. As a result, the proposed algorithms ensure their deadlock-free characteristics in an unknown world. As contrasted with this, the new type of two sensor-based path-planning algorithms ensures its deadlock-free characteristic by using several topological characteristics of an unknown world. Some of them are used for eliminating any local loop and alternatively the others are used for converging all global loops to the goal monotonously in an online manner. In result, even if the automaton encounters many global loops in an uncertain world, it finally catches the goal after leaving their minimum loop