The construction industry has been suffering from both low labor productivity growth and safety issues, due to the increasing project site complexities and the lack of skilled labors. As a potential technical solution, Augmented Reality (AR) has been studied to reduce the cognitive workloads in construction job sites by visualizing task-related information in the direct context of the workspace and operations. Instead of using helmets/goggles that may decrease users field of views, we advocate mobile projectors for AR (MPAR), and propose a camera-projector system to ensure consistent AR projection even if the projectors may change poses when installed on mobile platforms such as human workers or even construction collaborative robots (co-robot). By obtaining the projectors pose relative to the projection plane (e.g., a wall or panel on construction site) via composing a series of homography transformations in this system, we could determine how to warp virtual information (images or 3D models) for desired projections, no matter whether human observers head poses are needed. We demonstrate the effectiveness of the method using two construction AR applications: displaying occluded as-planned or as-built facility information behind a mock-up wall.