This paper proposes a novel method of morphological extended-jump-distance clustering segmentation to improve the steps of noise filtering and clustering segmentation for LiDAR pedestrian detection and trajectory tracking, and applies the novel method to the implementation of the intelligent patrolling security robot. After 2D LiDAR point cloud is input, at the step of noise filtering, this paper adopts morphological opening operator to filter out the noise of 2D LiDAR point cloud. Then, at the step of clustering segmentation, this paper proposes extended-jump-distance clustering segmentation to effectively eliminate redundant cluster and optimize clustering segmentation of 2D LiDAR point cloud for elaborate feature extraction of all human legs. Next, at the step of machine learning and pedestrian detection, this paper adopts leg-feature-based machine learning classifier for pedestrian detection. Finally, at the step of trajectory tracking, this paper switches 3 well-known trajectory tracking methods depending upon various environmental conditions to record the pedestrian trajectory. Experimental results show, under public datasets of Freiburg city center and Freiburg main station, LiDAR pedestrian detection and trajectory tracking based on proposed morphological extended-jump-distance clustering segmentation has better accuracy and immediateness than those based on conventional geometric distance clustering segmentation and conventional geometric agglomerative clustering segmentation.