In an autonomous mobile robot, ultrasonic time-of-flight (TOF) ranging systems are widely used for distance measurements. However, ultrasonic TOF ranging systems tend to neglect infinitesimal reflected waves below a threshold level. Therefore, we have proposed an integration-type ultrasonic wave sensor that utilizes the integration value of the sonar's reflected wave to recognize a traversable area for an autonomous mobile robot. The proposed method simultaneously determines the path and velocity; however, the calculated velocity varies significantly because of sensor noise or error. This paper presents a novel approach to filter the velocity by considering the accelerated velocity. This enables us to consider the limitation of the force exerted by the robot. The validity of the proposed method is investigated in various environments by applying this method to an autonomous mobile robot.