To address the limitations of existing path-planning methods applied to unmanned construction site—particularly their insufficient consideration of equipment geometry and kinematic characteristics, as well as the absence of effective multi-machine coordination—this study proposes a cooperative path-planning approach based on an improved RRT* algorithm. First, mobile construction equipment is modeled as the generalized rectangle in the top-down plan, and collision-detection strategies for both linear motion and rotational motion are developed using the separating axis theorem and vector cross-product operations. Second, a time-window mechanism and a spatiotemporal coordination framework are introduced to design two types of dynamic conflict-detection procedures, namely “straight-line–straight-line motion” and “straight-line–rotation motion”, enabling real-time collision avoidance among multiple machines. Finally, the proposed algorithm is validated through simulations in complex scenarios such as tunnels and beam fabrication yards. The results demonstrate that the planned paths fully account for the actual equipment geometry, dimensions, rotation constraints, and obstacle characteristics (shape, size, and distribution). Compared with conventional algorithms, the proposed method effectively resolves the challenge of obstacle avoidance for large length-width ratio equipment operating in narrow spaces, significantly improving path-search success rates and robustness in complex environments. Furthermore, the constructed spatiotemporal collaborative planning framework ensures that multiple machines can safely, orderly, and efficiently move or operate in complex construction site environments. This research not only verifies the applicability of the algorithm in real engineering contexts—such as tunnels and beam yards—but also provides essential theoretical and technical support for future intelligent and efficient multi-machine collaboration in unmanned construction sites.