This study presents an intelligent distribution framework based on edge computing and proposes navigation and obstacle avoidance algorithms for connected logistics vehicles (CLVs) on the basis of Trimble BD982 positioning sensor and tentacle algorithm (TA). An edge computing framework for the distribution of CLVs is established, and the functions of three layers (cloud server, edge equipment, and terminal) are described in detail. The basic functions, hardware, and software systems of the CLV are designed and presented. Focusing on autonomous driving, a Global Positioning System (GPS) navigation algorithm and an obstacle avoidance control strategy on the layer of edge equipment are developed on the basis of the TA. Autonomous GPS navigation is realized by combining the entire road network with the local road network to avoid obstacles. The TA is improved to help the CLV for avoiding obstacles. Experiments show that the hardware system and designed algorithms of the CLV are effective. The tracking error on the straight-line track is within 3 cm, the change rate of longitudinal velocity is within 0.3 g/s, the change rate of tire side deflection angle is less than 1°/s, and the calculation time is shortened by 25% when the calculation time is 30 ms. These results indicate that the vehicle has good stability and performance during obstacle avoidance in real time, and the proposed algorithms are superior to traditional algorithms. The CLV can realize autonomous GPS navigation, with high navigation accuracy, reliable obstacle avoidance performance, and stable vehicle handling.