This article presents the sensing and safety algorithms for autonomous excavators operating on construction sites. Safety is a key concern for autonomous construction to reduce collisions and machinery damage. Taking this point into consideration, our study deals with LiDAR data processing that allows for object detection, motion tracking/prediction, and track management, as well as safety evaluation in terms of potential collision risk. In the safety algorithm developed in this study, potential collision risks can be evaluated based on information from excavator working areas, predicted states of detected objects, and calculated safety indices. Experiments were performed using a modified mini hydraulic excavator with Velodyne VLP-16 LiDAR. Experimental validations prove that the developed algorithms are capable of tracking objects, predicting their future states, and assessing the degree of collision risks with respect to distance and time. Hence, the proposed algorithms can be applied to diverse autonomous machines for safety enhancement.