1. Introduction

During the past two decades, researchers in mobile robotics have dealt with different path planning methods. In most cases, the methods goal is to find free collision paths; which will meet the initial and final configurations to complete a mission.
In this research, the data coming from the dead reckoning sensors are used to obtain the initial location of the mobile robot and it is corrected through the position estimation procedure using the information on the moving object/walking human. For the quantitative analysis of this approach, the position uncertainty of the mobile robot is represented by an uncertainty ellipsoid that shows the directional uncertainty quantitatively. The trajectory of the moving object is transformed to the image frame and represented as a geometrical constraint equation that is used for the Kalman filtering process that estimates the position of the mobile robot to reduce the size of the uncertainty ellipsoid. And a mobile robot cooperates with multiple intelligent sensors, which are distributed in the environment. The distributed sensors recognize the mobile robot and the moving objects/walking human, and give control commands to the mobile robot.
Fig. 1 illustrates the effectiveness of the uncertainty ellipsoid as an example. It shows that the uncertainty ellipsoid becomes larger with the movement of a mobile robot, and that the geometrical shape of the ellipsoid directly represents the position estimation uncertainty along a given axis.

2.  Image Projection of Walking human

During navigation, a mobile robot may need to re-locate its position. When there is a walking human that can be captured by the CCD camera of DINDs and the motion information on the walking human is available to the mobile robot, it may stop at its current position to improve the position estimation accuracy of itself by observing the walking human. The given object trajectory can be represented as a linear equation in the image frame, and using the current position estimation of the mobile robot, geometric constraint equations can be derived through coordinate transformation. The derivation procedure of geometric constraint equations is going to be illustrated with an example shown in Fig.2.

3.  Position correction

The calculated position of the walking human in the image frame, based on the estimated robot position, has some discrepancy from the actual value. Utilizing this error, the practical position of the robot can be corrected recursively. To overcome vague input information, i.e., the human position in the image frame includes noise and the position estimation of the robot has uncertain components, the Kalman filtering technique is adopted to form a robust observer. The geometric constraint equations between the human image coordinates and the robot position are approximated to a linear system equation, and the Kalman filtering technique is applied to estimate the robot position.