This paper presents a first part, Part-I of two, of a complete exploration and navigation methodology that enables a robot to safely navigate in an unknown environment. Reactive sensor-based navigation tasks and control laws are derived from the interaction between the robot and its workspace. The perception is performed by a 2-D laser nge finder mounted on the robot. Reactive navigation tasks are defined based on the task function framework in a such a way that the robot can explore an unknown indoor environment without any reference rajectory computation. Obstacle avoidance is ensured as a straight property implicit to the definition of the navigation tasks. The stability and obustness of the derived control laws with respect to the model errors are analyzed. The experimental results validate the proposed methodology.