This paper presents an actively gaze controlled LiDAR system for the omni-directional wheeled robot, with this system, the LiDAR odometry drift caused by rapid rotation and feature degradation can be greatly mitigated. This is an extension of our previous work [1]. In our previous work, information from the point cloud are extracted and projected to a 2.5-D grid map, this grid map acts as an indicator for the distributions of the feature points, thus can be used to guide the LiDAR to choose an optimal gaze angle. However, errors and randomness inside the map are not accounted and quantified. In this paper, we investigate the mechanisms of error propagation during map building, and derive the formulas for map updates using an 1-D Kalman filter. Several simulations are conducted to verify the usefulness and practicability of the proposed system with an omni-directional robot.