In order for a mobile robot to move under unknown or uncertain environment. it is very important to collect environmental information. This paper suggests a traveling algorithm which leads to the map building algorithm and the $A^*$ algorithm under the assumption that environmental information should already be collected. In order to apply the proposed traveling algorithm to a real mobile robot. this paper additionally discusses a path amendment algorithm. For the purpose of verifying the proposed algorithms, several simulations are executed based on a UI host program-based simulation interface and an experiment is executed using a mobile robot under a real unknown environment.