Unlike robotics in the manufacturing industry, on-site construction robotics has to consider and address two unique challenges: 1) the rugged, evolving, and unstructured environment of typical work sites; 2) the reversed spatial relationship between the product and the manipulator, i.e. the manipulator has to travel to and localize itself at the work face, rather than a partially complete product arriving at an anchored manipulator. The presented research designed and implemented algorithms that address these challenges and enable autonomous robotic assembly of freeform modular structures on construction sites. Building on the authors previous work in computer-vision-based pose estimation, the designed algorithms enable a mobile robotic manipulator to: 1) autonomously identify and grasp prismatic building components (e.g., bricks, blocks) that are typically non-unique and arbitrarily stored on-site; and 2) assemble these components into predesigned modular structures. The algorithms use a single camera and a visual marker-based metrology to rapidly establish local reference frames and to detect staged building components. Based on the design of the structure being assembled, the algorithms automatically determine the assembly sequence. Implemented using a 7-axis KUKA KR100 robotic manipulator, the presented robotic system has successfully assembled various structures autonomously as shown in Figure 1, demonstrating the designed algorithms effectiveness in autonomous on-site construction robotics applications.