A robot may extrude a tower or column. The robot may include an extrusion nozzle, a positioning system, a climbing apparatus, and a controller. The extrusion nozzle may controllably extrude uncured construction material. The positioning system may controllably cause the extrusion nozzle to traverse a perimeter layer of the tower or column. A climbing apparatus may controllably cause the robot to climb. A controller may autonomously: direct the positioning system to cause the nozzle to traverse the perimeter layer of the tower or column; direct the nozzle to extrude uncured construction material during the traverse; direct the climbing apparatus to cause the robot to climb an incremental amount; and repeat each of the foregoing positioning, extrusion, and climbing steps until the extruded tower or column attains a desired height.