Mobile robots are used to operate in urban environments, for surveillance, reconnaissance, and inspection, as well as for military operations and in hazardous environments. Some are intended for exploration of only natural terrains, but others also for artificial environments, including stairways. This paper presents a mobile robot design that achieves autonomous climbing and descending of stairs. The robot uses sensors and embedded intelligence to achieve the task. The robot is a reconfigurable tracked mobile robot that has the ability to traverse obstacles by changing its track configuration. Algorithms have been further developed for conditions under which the mobile robot would halt its motion during the climbing process when at risk of flipping over. Technical problems related to the implementation of some of the robot functional attributes are presented, and proposed solutions are validated and experimentally tested. The experiments illustrate the effectiveness of the proposed approach to autonomous climbing and descending of stairs.